
Citation: Romilda Z. Boerleider, Nel Roeleveld, Paul T.J. Scheepers. Human biological monitoring of mercury for exposure assessment[J]. AIMS Environmental Science, 2017, 4(2): 251-276. doi: 10.3934/environsci.2017.2.251
[1] | Meili Tang, Qian Pan, Yurong Qian, Yuan Tian, Najla Al-Nabhan, Xin Wang . Parallel label propagation algorithm based on weight and random walk. Mathematical Biosciences and Engineering, 2021, 18(2): 1609-1628. doi: 10.3934/mbe.2021083 |
[2] | Kun Zhai, Qiang Ren, Junli Wang, Chungang Yan . Byzantine-robust federated learning via credibility assessment on non-IID data. Mathematical Biosciences and Engineering, 2022, 19(2): 1659-1676. doi: 10.3934/mbe.2022078 |
[3] | Izzat Alsmadi, Michael J. O'Brien . Rating news claims: Feature selection and evaluation. Mathematical Biosciences and Engineering, 2020, 17(3): 1922-1939. doi: 10.3934/mbe.2020101 |
[4] | Yanghan Ou, Siqin Sun, Haitao Gan, Ran Zhou, Zhi Yang . An improved self-supervised learning for EEG classification. Mathematical Biosciences and Engineering, 2022, 19(7): 6907-6922. doi: 10.3934/mbe.2022325 |
[5] | Ruoqi Zhang, Xiaoming Huang, Qiang Zhu . Weakly supervised salient object detection via image category annotation. Mathematical Biosciences and Engineering, 2023, 20(12): 21359-21381. doi: 10.3934/mbe.2023945 |
[6] | Wen Cao, Jiaqi Xu, Feilin Peng, Xiaochong Tong, Xinyi Wang, Siqi Zhao, Wenhao Liu . A point-feature label placement algorithm based on spatial data mining. Mathematical Biosciences and Engineering, 2023, 20(7): 12169-12193. doi: 10.3934/mbe.2023542 |
[7] | Tinghua Wang, Huiying Zhou, Hanming Liu . Multi-label feature selection based on HSIC and sparrow search algorithm. Mathematical Biosciences and Engineering, 2023, 20(8): 14201-14221. doi: 10.3934/mbe.2023635 |
[8] | Shiyou Chen, Baohui Li, Lanlan Rui, Jiaxing Wang, Xingyu Chen . A blockchain-based creditable and distributed incentive mechanism for participant mobile crowdsensing in edge computing. Mathematical Biosciences and Engineering, 2022, 19(4): 3285-3312. doi: 10.3934/mbe.2022152 |
[9] | Xiangtao Chen, Yuting Bai, Peng Wang, Jiawei Luo . Data augmentation based semi-supervised method to improve COVID-19 CT classification. Mathematical Biosciences and Engineering, 2023, 20(4): 6838-6852. doi: 10.3934/mbe.2023294 |
[10] | Lu Lu, Jiyou Fei, Ling Yu, Yu Yuan . A rolling bearing fault detection method based on compressed sensing and a neural network. Mathematical Biosciences and Engineering, 2020, 17(5): 5864-5882. doi: 10.3934/mbe.2020313 |
Traditional machine learning algorithms can be generally divided into three categories: (1) Supervised learning, which aims to learn from a large number of labeled samples and predicts the label of new unknown samples from the learned knowledge. In the practice, usually we can collect a large number of unlabeled samples, but the process of assigning labels to the samples is time consuming [1]. (2) Unsupervised learning, there is no corresponding category known in advance, so the classifier can only be learned from the sample set without labels. The unsupervised learning models are usually built based on the similarity between samples. (3) Semi-supervised learning, it relies on a small number of labeled samples to guide the label prediction of unlabeled samples [2,3]. New labeled samples are continuously added to the training set to compensate for the small number of labeled samples, which leads to performance defects in supervised learning.
Recently, the application of semi-supervised learning algorithm is more and more extensive, and scholars have done a lot of researches in this area. In addition to the traditional semi-supervised learning algorithm, such as S3VM [4], many new methods have been proposed. J. Levatic, et al. [5] proposed an extension of predictive clustering trees for multi-target regression (MTR) and ensembles thereof towards semi-supervised learning. This approach preserves the attractive properties of the decision tree while allowing the use of unlabeled samples. In particular, it is interpretable, easy to understand, quick to learn, and can handle numerical and nominal description characteristics. B. Jiang, et al. [6] proposed a novel graph-based semi-supervised learning framework which includes the sparse Bayesian semi-supervised learning method and the incremental sparse Bayesian semi-supervised learning method. The proposed algorithms can generate sparse solutions and make probabilistic prediction by transformation and induction. Label propagation algorithm (LPA) is a semi-supervised learning method based on graph. The labels are propagated from some known samples (vertices) to the unknown ones based on the similarities between the vertices in the graph [7]. LPA has the advantages of low complexity and high efficiency, and it has been widely applied in the fields of network community mining [8,9], information classification [10,11] and multimedia recognition and processing [12]. However, the traditional LPA simply takes the similarities between samples as the basis of label propagation, which lacks the evaluation criteria of new labeled samples. In addition, since the algorithm incorporates the new labeled samples into the training set, the propagation error may gradually increase, leading to the degeneration of the performance [13]. Due to the randomness during the process of propagation and the weak ability of LPA to deal with uncertain points, many new improved methods are proposed. C. Gong et al. [14] proposed a novel iterative LPA, in which each propagation alternates between two paradigms, teaching to learn and learning to teach (TLLT). In the "teaching to learn" process, learners disseminate the simplest unmarked examples assigned by the teacher. In the "learning-to-teach" step, the teacher adjusts the selection of the simplest subsequent example based on the learner's feedback. J. Hao, et al. [15] adopted the fuzzy method when dealing with the categories of unlabeled samples. The categories of unlabeled samples are represented by the fuzzy membership degree in the interval of [0, 1]. The final step of the algorithm is to remove the ambiguity. X. K. Zhang, et al. [16] dealt with the problem of random label selection by the value of node similarity. B. Wang et al. [17] proposed dynamic label propagation (DLP) to simultaneously deal with the multiclass and multi-label problem, the method in DLP is to update similarity measures dynamically by fusing multi-label and multi-class information.
In this paper, we put forward a Label Propagation based on Roll-back and Credibility (LPRC) algorithm to solve these problems. First, the credibility (label confidence) of each unlabeled sample is evaluated. According to the evaluation results, the label propagation order of the samples is determined, and the samples with high credibility are labeled in advance. Then, in order to avoid the impact of false label propagation, a roll-back mechanism based on feedback performance evaluation is proposed. In the process of label propagation in every fixed number of iterations, the new labeled samples will be default with the correct labels and added to the training set. At the same time, the samples in the original training set with the same size of new labeled samples will be chosen to moved out as a new dataset waiting to be labeled. The new labeled samples cannot be added to the training set until the propagation accuracy reached a predefined threshold, so we can reuse these new labeled samples in LPA with certain confidence.
The traditional LPA is described in section 2, and the details of LPRC algorithm is present in section 3. In section 4, we give the comparison results both on artificial synthetic dataset and UCI dataset, respectively. Finally, the conclusions and future research plan are given in section 5.
In label propagation algorithm, first, all categories in the sample set are required to be known. Assuming the number of categories in the samples set is t, C={c1,c2,...,ct} represents the collection of all the categories in the dataset. Then, the dataset is defined as follows: using XL={x1,x2,...,xl} to represent the dataset of labeled samples, and XU={x1,x2,...,xu} to represent the dataset of unlabeled samples. X=XL∪XU, and xi∈Rd, 1≤l<<u. In addition, YL={y1,y2,...,yl} represents the labels set of labeled samples, YU={y1,y2,...,yu} represents the labels set of unlabeled samples. At the beginning, all labels of unlabeled samples can be set as 0 for the initial value of YU is not so important.
The label propagation algorithm aims to spread labels of labeled samples to the samples with the greatest similarity. Take X as the initial training matrix, classify the samples in XU through the labeled samples in XL, add each round of newly labeled samples in XU to XL, and then use the updated XL to conduct a new round of training on the unlabeled samples in XU. The label propagation algorithm will repeat the above process until it reaches a certain end condition.
For a labeled sample xa∈XL, the similarity between it and the unlabeled sample xb∈XU determines whether xa will spread its label to xb. X. Zhu et al.[18] defines the similarity between any samples xi and xj as:
wij=exp(−d2ijσ2)=exp(−∑Dd=1(xdi−xdj)2σ2) | (2.1) |
The label of samples will be spread according to the similarity between samples themselves. Clearly, the greater the similarity between sample xa and xb, the easier it is for xa to propagate its own label to xb. In [18], a (l+u)×(l+u) probabilistic transition matrix T is defined as (2.2), and Tij represents the possibility that node i propagates its own label to node j.
Tij=P(i→j)=wij∑l+uk=1wkj | (2.2) |
Meanwhile, a (l+u)×t label matrix Y records the relationship between each sample and each category. Yij represents the probability that the i−th sample xi belongs to the j−th class. The initial value of the unlabeled sample in the label matrix Y is not very necessary to the classification result, and all the initial values in Y can be set as 0. Using the probability propagation matrix T to continuously update the label matrix Y, and then the maximum s values in Y are chosen. In other words, finding the s unlabeled samples with the greatest similarity to the labeled samples, and assigning them to corresponding labels, then, moving them from XU to XL. Repeat the process until the stop condition is satisfied.
The traditional LPA only need a small number of labeled samples in the training process. In each subsequent training, the number of labeled sample dataset is continuously expanded by using the newly labeled samples to improve the accuracy of classification. But in this process, there are also some problems that we cannot ignore. In reality, the differences between samples belong to different categories are often not so clear, and the samples at the edge of the category are sparser than those at the center of the category.
As shown in Figure 1(a), the samples on the boundary of two categories are identified as key nodes. If the key nodes are wrongly labeled during the label propagation procedure, it would bring serious impacts on the latter label propagation of unknown samples. Just as Figure 1(b) shows.
Therefore, we propose LPRC algorithm. First, we will evaluate the credibility of these unlabeled samples, instead of classifying them directly, and the sequence of classification operation of unlabeled samples is determined according to the credibility value of themselves. For those samples with high credibility values, will be classified first. This part will be described in detail in section 3.2.
In addition, considering the distribution differences of samples in each category in the dataset, we also put forward new ideas on how to select samples for labeling in each round. And this part will be described in section 3.1.
Finally, as the label propagation algorithm constantly updates the training matrix and increases the number of labeled samples, the classification error may be continuously expanded, resulting in a drastically reduced accuracy. Therefore, we propose a roll-back mechanism based on feedback effect detection. In the process of label propagation, the algorithm performs feedback accuracy detection on the currently labeled samples every k rounds of iteration. Only when the set conditions are satisfied, the algorithm will continue the next round of iteration. Otherwise, the samples labeled in this round will be discarded and the label propagation of this round will be carried out again. This part will be described in detail in section 3.2.
In a dataset, we can find that the distribution of samples in different categories is often different, which will also have a certain impact on the label propagation algorithm. Figure 2(a) shows a distribution of the samples in a dataset. We can see that the samples of class A are more densely distributed than those of the other two categories. The distribution of class B samples gradually becomes sparse from the center. The distribution of class C samples is relatively uniform. There is an obvious distance between each pair of adjacent samples in Class C, which means C is sparser than the other two categories.
According to the label propagation algorithm, each round will spread corresponding labels to s unlabeled samples that are most similar to the labeled samples. At this time, since the samples of class C are more sparsely distributed than those of the other two classes, the similarity wc between any two samples xc1 and xc2 of class C is generally lower than wa (wb) between wa1 and wa2 of any two samples of class A (class B). This may lead to that class C has not received any labels spread from the labeled samples of the class during the first n iterations.
However, the labeled sample dataset of the other two classes may misclassify the samples on the edge of the category in the subsequent propagation due to the continuous expansion. As a result, with the constant updating of XL, the classification errors in the later stage will become larger and larger, and even the phenomenon of class A (class B) merging the samples of C may occur. Figure 2(b)–2(d) have shown this situation. Although the samples of class B in the dashed box are at the edge, their distribution is sparser than that of the samples in the center of the category. Compared with the samples of class C, whose samples are evenly and sparsely distributed in the original category, they are easier to be spread corresponding labels by the similar samples. So, as shown in figure 2(d), the samples in the solid box that originally belong to class C may be wrongly classified as class B. With iteration after iteration of the algorithm, this error will be gradually amplified, and resulting in a large number of these samples being swallowed by class B.
In order to avoid the situation mentioned above, we no longer select the s most similar samples from the entire unlabeled sample dataset, but from the perspective of each category to consider them separately when we select unlabeled samples to label in each round. That is, β=s/t unlabeled samples most similar to the labeled samples of the class are selected from the t classes for labeling respectively. In each round of iteration, new labeled samples are guaranteed to be added to each category, so that the labeled sample dataset of each class can be uniformly expanded, avoiding the phenomenon of rapid expansion of a certain class and large disparity in volume between categories, thus reducing or even avoiding category annexation.
At the later stage of the algorithm iteration, the value of s may need to be recalculated. 1. All unlabeled samples of t1 certain classes are classified over: set t=t−t1, s=β×t. 2. The number of unlabeled samples α remaining in each class exists α<β: set β=α, s=β×t.
As previously mentioned in section 2, the traditional label propagation algorithm obtains the largest s values directly from the label matrix Y, and continuously updates Y by using the probability propagation matrix T. Namely to find the s unlabeled samples with the highest similarity to the labeled samples, assign them to the corresponding labels, and move them from XU to XL.
However, such a selection mechanism actually only considers one aspect of "similarity". At this point, we need to conduct a classification credibility assessment of these unlabeled samples.
When we get a labeled sample data set, we often hope that these samples can well represent the classes to which they belong, and there are obvious differences between them. It means that these samples are distributed in the center of their respective categories. In practice, however, we cannot guarantee the quality of the labeled samples we get. For example, most of these samples are on the boundary of two adjacent classes, so it is likely that the distance between these samples is not as significant as we expected. If a label propagation algorithm is used at this time, there may be cases where the similarity of some unlabeled samples to two (or more) labeled samples of different classes is close to and higher than all other similarities, which means the probability that the unlabeled sample may be assigned to its own label by two (or more) different categories is similar. The reason is that the label propagation generated by traditional methods is completely controlled by the adjacency relationship between samples, including those labeled and unlabeled samples. The labels of labeled samples are blindly spread to unlabeled adjacent samples without considering the difficulty and risk of transmission [14].
As the labeled sample dataset continues to expand with the iteration of the algorithm, we hope that the quality of this dataset can be guaranteed. In this way, the classification accuracy will not be significantly reduced, and the probability of label propagation between samples of different categories can be controlled. Therefore, we need to make an assessment of the label propagation order of unlabeled samples.
As shown in Figure 3, we assume that there is such a sample distribution: the dividing line of A and B is indicated by the dotted line in the figure, and the existing labeled samples are shown as the red and blue solid circles in the figure. In this round of update of the algorithm, there are samples a-c waiting to be labeled. The distance dAc from sample c to class A is less than the distance dAa from sample a to class A, the distance dBc from sample c to class B is less than the distance dBb from sample b to class B, and here we have: dAc−dBc=λ,λ→0.
So, the probability PAc that sample c belongs to class A, and the probability PBc that sample c belongs to class B are both large and they are very close. In the traditional label propagation algorithm, the label will be assigned to sample c according to max(PAc,PBc), but this may cause the wrong classification of sample c.
In our newly proposed LPRC algorithm, we will further process the label matrix Y after each iteration under the conditions in section 3.1: sorting the label sequence of samples, so as to improve the classification accuracy of the label propagation algorithm.
As we mentioned in Section 2, in the label matrix Y, Yij represents the probability that the i−th sample belongs to the j−th class. Then, when the situation we discussed in this section occurs, it means the set of categories for the dataset C={c1,c2,...,ct}, ∃xi∈XU,Yxic1−Yxic2≤λ,λ→0. At this point, for any sample xi∈XU, there is a set of label vectors YxiC={Yxic1,Yxic2,...,Yxict}, represents the probability that the sample xi belongs to each category. We find out the maximum value Yxicn and the second largest value Yxicm from the set of label vectors, and set Dvalue=Yxicn−Yxicm.
Here we can get: Y=[Yx1c1Yx1c2...Yx1ctYx2c1Yx2c2...Yx2ct............Yxuc1Yxuc2...Yxuct]
It exists in YxiC={Yxic1,Yxic2,...,Yxict}: Yxicn=Dmaxi=max(Yxic1,Yxic2,...,Yxict), and DMmaxi=max(Yxic1,Yxic2,...,Yxic(n−1),Yxic(n+1),...,Yxict). Moreover, here we need to use Class={class1,class2,...,classu}∈C to record the category Cn indicated by Yxicn. Setting Dvpi=(Dvaluei,classi), then we can get a two-dimensional matrix Dvp to store the value of Dvalue, and classn represents the class Cn with the highest probability that the sample belongs to: Dvp=[Dmax1−DMmax1class1Dmax2−DMmax2class2......Dmaxu−DMmaxuclassu]
In each round of update of label matrix Y, the sample set is first divided according to the category set C and the value of the sample in set Class. Samples have the same value in set Class will be divided into a subset. Select β samples with the largest values in Dvalue from each subset to label. That is, β unlabeled samples are selected from t categories each time should be sure that, the probability that these unlabeled samples belong not only to the certain class is as large as possible, but also to other classes is as small as possible. This operation could ensure the credibility of samples added to the labeled sample dataset in each round. We refer to such samples as easy-to-label samples.
If the samples a-c in Figure 4 is evaluated here based on Dvalue and Class, the sequence of them to be labeled can be changed.
The label matrix Y composed of the label vector set of samples a–c is: Y=[YaAYaBYbAYbBYcAYcB]
After calculating its Dvalue and Class, respectively, we can get: Dvp=[Dmaxa−DMmaxaclass1Dmaxb−DMmaxbclass2Dmaxc−DMmaxcclass3]
According to Figure 5, for sample c: YcA−YcB=λ,λ→0, therefore, it will be labeled at the end.
Compared with sample c, sample a and b are not only close to their own classes, but also keep a relatively obvious distance from the different classes to some extent. Such samples like a and b are more reliable in classification.
After samples a and b are given corresponding labels (A and B) respectively, sample c will be affected by both the original labeled samples and the newly labeled samples a and b. We will get the result that sample c is divided into class B by superimposing these effects before, which is exactly in line with the actual distribution of the sample dataset.
The advantage of the label propagation algorithm is that it is simple, fast and efficient, but it also has the drawback that the results of each iteration are unstable and the accuracy is not high. In order to control this instability, we added a detection mechanism in the process of algorithm iteration, which called "roll-back".
As we know, the traditional label propagation algorithm will label s new samples in each round of iteration and add this part of the samples to the labeled sample dataset. If there is a classification error in the newly added sample in this part, then the classification errors in the later stage will increase with the iteration of the algorithm. So here we try to use the "roll-back" detection mechanism to control this error.
After each round of iteration, we will get s samples of new labels. At this time, we add a condition: each iteration of k rounds, a roll-back detection is carried out for the newly labeled s samples of the round. Only when the condition is satisfied, the algorithm continues to execute. Otherwise, the newly labeled s samples of the round will be discarded and the label propagation of the round will be carried out again. Under the conditions in section 3.1, the flow path of the roll-back detection mechanism set for the new labeled samples of the round is as follows:
1. Use Nks to represent the dataset composed of s unlabeled samples with new labels in the k−th round, and add Nks={xn1,xn2,...,xns}∈XU to XL. By default, all labels owned by samples in Nks are correct.
2. Find the center sample of Nks and then calculate the distance Dis={D1,D2,...,DS} between each sample and the center sample. Draw a circle with max(Dis) as the radius r, search for samples in XkL within this range, and remove them out as Us. If the sample number within this range is s1, and s1<s, we will randomly select s−s1 samples from XkL−Us1 to Us.
3. Use XkL to represent the labeled sample dataset used for training in the k−th round, select s samples to be removed out from XkL as a new independent unlabeled sample dataset Us.
4. Let a conduct label propagation on samples in Us, and detect the accuracy of newly transmitted labels on samples in Us.
5. Set the accuracy rate as Rp and the threshold as η. If Rp<η, then the samples in Nks will be discarded and the round of label propagation will be carried out again. If Rp<η, the algorithm continues.
In order to evaluate the effectiveness of the method proposed in this paper, we conducted experiments in the artificial synthetic dataset and UCI dataset, respectively. The hardware environment of the experiment is: Intel(R) Core(TM) i7-9700, CPU 3.00GHz, and the software environment is: Windows10+Matlab2017a+Python3.6.
In Python, we used the method (sklearn.datasets()) provided by the sklearn library to generate the 5 synthetic datasets [19] we needed, as shown in figure 4 and table 1. Dataset circles is a double ring shape, and it contains 1500 samples and 2 classes, 750 samples in each class. Dataset moons is made by 1500 samples and it also contains 2 classes, 750 samples in each class. Dataset varied, aniso, blobs each has 1500 samples and 3 classes, 500 samples in each class.
Datasets | Sum | Classes | Sum of each class |
Circles | 1500 | 2 | 750 |
Moons | 1500 | 2 | 750 |
Varied | 1500 | 3 | 500 |
Aniso | 1500 | 3 | 500 |
Blobs | 1500 | 3 | 500 |
We used 9 algorithms and LPRC algorithm for experimental comparison. These algorithms have been proved to have high classification performance, and have been applied in many fields. And they can adapt well to the situation of only a small number of labeled samples is known. The classification effects of the 10 algorithms on the five artificially synthesized datasets and the original datasets are shown in Figure 5, and the specific classification accuracy is shown in table 2. Labeled rate represents the percentage of labeled samples in each dataset.
![]() |
Circles | Moons | Varied | Aniso | Blobs |
MiniBatchKmeans | 33 % | 17 % | 38 % | 7 % | 0 % |
Meanshift | 50 % | 87 % | 2 % | 32 % | 33 % |
SpectralClustering | 1% | 74 % | 34 % | 99 % | 33 % |
DBSCAN | 50 % | 0 % | 33 % | 33 % | 100 % |
GaussianMixture | 33 % | 9 % | 1 % | 0 % | 33 % |
GaussianNB | 58.48 % | 86.34 % | 93.93 % | 79.26 % | 99.86 % |
DecisionTree | 75.77 % | 89.16 % | 95.42 % | 90.37 % | 100 % |
KNN | 62.25 % | 82.78 % | 89.02 % | 87.88 % | 100 % |
LPA | 99.86 % | 99.93 % | 66.53 % | 67.80 % | 100 % |
LPRC | 100 % | 100 % | 97.80 % | 99.80 % | 100 % |
LPRC (labeled rate = 0.01, s = 15), KNN (labeled rate = 0.01, k = 1) [20], DecisionTreeClassifier (labeled rate = 0.01) [21], GaussianNB (labeled rate = 0.01) [22], LPA(label rate = 0.01, s = 15) and keep the number of labeled samples for each category has the same proportion as the number of samples for that category.
By comparing the classification effects of the above 10 algorithms on 5 synthetic datasets, we can see that the classification ability of LPRC algorithm is better than other algorithms on the whole, and it can also better match the distribution of samples.
The datasets iris, wine, australian, breast, downloaded through UCI [23], also used the above 10 algorithms for experimental comparison. The information for the data set is shown in table 3. Dataset iris has 150 samples and 3 classes, and the number of features is 4. Dataset wine contains 178 samples for 3 classes, and 13 features. Dataset australian contains 690 samples and 14 features, and dataset breast contains 699 samples and 10 features. Both of dataset australian and breast has 2 classes.
Datasets | Sum of samples | Number of features | Number of classes |
Iris | 150 | 4 | 3 |
Wine | 178 | 13 | 3 |
Australian | 690 | 14 | 2 |
Breast | 699 | 14 | 2 |
The classification results of 5 algorithms, LPRC, KNN, GaussianNB (GNB), DecisionTreeClassifier (DTC) and LPA with different labeled rate are shown in figure 6(a)-(d) and table 5 (average value of 50 experiments is taken for each result), and the classification results of the other 5 algorithms are shown in table 4.
![]() |
Iris | Wine | Australian | Breast |
MiniBatchKmeans | 2% | 10% | 47% | 6% |
Meanshift | 33% | 7% | 49% | 4% |
SpectralClustering | 17% | 16% | 32% | 40% |
DBSCAN | 17% | 4% | 52% | 3% |
GaussianMixture | 0% | 18% | 44% | 9% |
Dataset | ![]() |
GaussianNB | DecisionTree | KNN | LPA | LPRC |
iris | 2% | 69.96% | 74.54% | 75.54% | 74.00% | 94.33% |
4% | 78.22% | 84.68% | 84.82% | 81.99% | 95.41% | |
6% | 84.59% | 86.41% | 86.24% | 87.53% | 95.94% | |
8% | 87.82% | 89.01% | 87.67% | 89.71% | 96.16% | |
10% | 89.80% | 90.10% | 89.62% | 90.16% | 96.19% | |
12% | 92.47% | 90.77% | 90.91% | 91.41% | 96.28% | |
14% | 93.00% | 91.46% | 91.40% | 92.05% | 96.48% | |
16% | 93.31% | 91.86% | 92.46% | 91.33% | 96.45% | |
18% | 93.21% | 91.68% | 92.42% | 92.60% | 96.73% | |
20% | 94.11% | 92.72% | 93.63% | 92.60% | 96.68% | |
wine | 2% | 66.02% | 67.19% | 68.17% | 67.58% | 90.44% |
4% | 71.49% | 74.81% | 72.00% | 82.21% | 93.99% | |
6% | 74.06% | 77.65% | 73.34% | 85.71% | 93.43% | |
8% | 76.78% | 80.63% | 75.61% | 86.45% | 94.58% | |
10% | 78.62% | 82.37% | 75.60% | 89.44% | 94.47% | |
12% | 79.68% | 83.30% | 76.30% | 90.07% | 94.84% | |
14% | 79.33% | 84.16% | 76.17% | 90.91% | 95.21% | |
16% | 81.52% | 84.35% | 77.94% | 91.71% | 95.24% | |
18% | 82.34% | 85.00% | 77.99% | 91.97% | 95.41% | |
20% | 83.01% | 87.45% | 78.17% | 91.71% | 95.49% | |
australian | 2% | 73.16% | 75.08% | 76.12% | 75.79% | 79.29% |
4% | 75.21% | 76.71% | 78.05% | 78.09% | 79.29% | |
6% | 77.13% | 77.45% | 78.78% | 79.31% | 80.56% | |
8% | 80.31% | 78.87% | 79.58% | 80.21% | 81.15% | |
10% | 80.45% | 79.70% | 81.15% | 80.49% | 81.37% | |
12% | 80.73% | 80.51% | 81.62% | 81.63% | 82.36% | |
14% | 80.85% | 80.93% | 82.69% | 82.32% | 82.83% | |
16% | 80.81% | 80.52% | 83.69% | 82.91% | 83.61% | |
18% | 81.32% | 80.43% | 83.47% | 83.35% | 84.13% | |
20% | 81.01% | 81.40% | 84.15% | 83.38% | 84.37% | |
breast | 2% | 87.98% | 88.26% | 90.54% | 92.89% | 96.67% |
4% | 88.04% | 89.68% | 92.15% | 94.71% | 96.78% | |
6% | 88.99% | 89.81% | 93.25% | 94.54% | 96.82% | |
8% | 89.50% | 90.78% | 95.10% | 95.30% | 96.90% | |
10% | 89.73% | 91.70% | 95.47% | 95.85% | 96.94% | |
12% | 90.18% | 91.93% | 95.59% | 95.67% | 96.94% | |
14% | 91.82% | 92.61% | 95.66% | 96.18% | 97.02% | |
16% | 91.41% | 92.91% | 96.24% | 96.12% | 97.21% | |
18% | 91.73% | 92.43% | 96.67% | 96.19% | 97.16% | |
20% | 92.47% | 93.21% | 96.32% | 96.33% | 97.24% |
Otherwise, an additional experiment is made to compare the performance of LPRC with TSVM [24] and negative selection algorithm (NSA), these algorithms just need a small number of labeled samples. The results on UCI datasets of these 3 algorithms are shown in figure 7(a)–(b) and table 6, and the results on synthetic datasets are shown in figure 8.
Dataset | ![]() |
TSVM | NSA | LPRC |
australian | 2% | 72.17% | 59.91% | 79.29% |
4% | 76.58% | 65.75% | 79.29% | |
6% | 77.20% | 68.01% | 80.56% | |
8% | 78.56% | 69.48% | 81.15% | |
10% | 81.85% | 69.71% | 81.37% | |
12% | 81.90% | 71.34% | 82.36% | |
14% | 83.23% | 72.38% | 82.83% | |
16% | 83.89% | 71.35% | 83.61% | |
18% | 83.86% | 72.19% | 84.13% | |
20% | 84.67% | 72.74% | 84.37% | |
breast | 2% | 93.22% | 82.13% | 96.67% |
4% | 93.91% | 88.27% | 96.78% | |
6% | 94.77% | 91.23% | 96.82% | |
8% | 94.72% | 92.57% | 96.90% | |
10% | 94.87% | 93.66% | 96.94% | |
12% | 94.99% | 92.94% | 96.94% | |
14% | 95.11% | 93.16% | 97.02% | |
16% | 95.23% | 93.93% | 97.21% | |
18% | 95.35% | 94.31% | 97.16% | |
20% | 95.14% | 93.53% | 97.24% |
After experimental comparison, we found that the LPRC algorithm has good performance in classification, and it especially has high accuracy when only has a small number of labeled samples. As the number of labeled samples increases, the accuracy rate also shows an increasing trend. In the process of propagation, the error caused by the addition of new labeled samples is reduced, and the case of one class of samples being swallowed by another is prevented. The classification effect has been significantly improved.
Another experiment is made to further test the method LPRC we proposed. The result is analyzed by a significance test to assess the effectiveness of LPRC. Table 7 shows the average results for 50 runs of LPA and LPRC on 5 UCI datasets, and we can find that the accuracies of LPRC are higher than LPA. The statistical test of the results is based on two hypotheses of the average accuracy acc values of LPRC, where u0 is the average accuracy of LPA:
{H0:acc is similar with u0H1:acc is significantly bigger than u0; |
Dataset | ![]() |
LPA | LPRC | Statistical test | ||
acc1 | var1 | acc2 | var2 | |||
iris | 2% | 74.00% | 1.03E-02 | 94.33% | 1.74E-03 | 138.17 |
4% | 81.99% | 7.25E-03 | 95.41% | 7.26E-04 | 129.57 | |
6% | 87.53% | 6.59E-03 | 95.94% | 4.59E-05 | 89.33 | |
8% | 89.71% | 1.96E-03 | 96.16% | 4.01E-05 | 230.36 | |
10% | 90.16% | 1.67E-03 | 96.19% | 4.27E-05 | 252.75 | |
12% | 91.41% | 1.22E-03 | 96.28% | 4.99E-05 | 279.43 | |
14% | 92.05% | 9.17E-04 | 96.48% | 4.27E-05 | 338.17 | |
16% | 91.33% | 8.02E-04 | 96.45% | 5.41E-05 | 446.88 | |
18% | 92.60% | 5.07E-04 | 96.73% | 4.13E-05 | 570.21 | |
20% | 92.60% | 4.72E-04 | 96.68% | 5.60E-05 | 605.09 | |
wine | 2% | 67.58% | 1.67E-02 | 90.44% | 7.64E-03 | 95.82 |
4% | 82.21% | 1.17E-02 | 93.99% | 4.30E-04 | 70.47 | |
6% | 85.71% | 6.44E-03 | 93.43% | 1.65E-03 | 83.91 | |
8% | 86.45% | 5.85E-03 | 94.58% | 3.50E-05 | 97.28 | |
10% | 89.44% | 1.63E-03 | 94.47% | 2.10E-04 | 216.01 | |
12% | 90.07% | 1.28E-03 | 94.84% | 6.53E-05 | 260.86 | |
14% | 90.91% | 1.33E-03 | 95.21% | 7.35E-05 | 226.32 | |
16% | 91.71% | 7.66E-04 | 95.24% | 4.83E-05 | 319.84 | |
18% | 91.97% | 7.70E-04 | 95.41% | 5.98E-05 | 312.72 | |
20% | 91.71% | 5.85E-04 | 95.49% | 6.25E-05 | 452.31 | |
australian | 2% | 75.79% | 5.46E-03 | 79.29% | 3.12E-03 | 44.87 |
4% | 78.09% | 4.64E-03 | 79.29% | 3.79E-03 | 18.10 | |
6% | 79.31% | 3.51E-03 | 80.56% | 1.38E-03 | 24.93 | |
8% | 80.21% | 2.72E-03 | 81.15% | 1.17E-03 | 24.18 | |
10% | 80.49% | 1.26E-03 | 81.37% | 1.16E-03 | 48.89 | |
12% | 81.63% | 1.36E-03 | 82.36% | 9.49E-04 | 37.57 | |
14% | 82.32% | 6.70E-04 | 82.83% | 6.64E-04 | 53.28 | |
16% | 82.91% | 5.16E-04 | 83.61% | 5.95E-04 | 94.96 | |
18% | 83.35% | 6.27E-04 | 84.13% | 4.27E-04 | 87.08 | |
20% | 83.38% | 6.11E-04 | 84.37% | 5.08E-04 | 113.42 | |
breast | 2% | 92.89% | 2.12E-03 | 96.67% | 8.78E-06 | 124.80 |
4% | 94.71% | 4.79E-04 | 96.78% | 1.31E-05 | 302.50 | |
6% | 94.54% | 7.34E-04 | 96.82% | 1.23E-05 | 217.44 | |
8% | 95.30% | 1.68E-04 | 96.90% | 1.05E-05 | 666.66 | |
10% | 95.85% | 8.29E-05 | 96.94% | 1.11E-05 | 920.39 | |
12% | 95.67% | 1.14E-04 | 96.94% | 1.70E-05 | 779.82 | |
14% | 96.18% | 9.49E-05 | 97.02% | 2.14E-05 | 619.60 | |
16% | 96.12% | 8.01E-05 | 97.21% | 1.79E-05 | 952.55 | |
18% | 96.19% | 1.17E-04 | 97.16% | 2.04E-05 | 580.35 | |
20% | 96.33% | 5.68E-05 | 97.24% | 1.87E-05 | 1121.48 |
Based on the central limit theorem, the average accuracy obtained by repeating the algorithm can be assumed to follow a normal distribution. According to [25], (acc−u0)(s/√n) coincides with T(n−1), and if H0 established, the average accuracy acc would be close to the value of u0 for H0. Otherwise, H0 would be rejected with a confidence level of 1−α when (acc−u0)(s/√n)≥Tα(n−1) is satisfied. We use s to represent the sample variation and n is the number of repetitions.
The results of the statistical test are shown in table 7, acc1 and acc2 represent the average accuracies of LPA and LPRC, respectively.
As can be observed in table 7, for the given confidence level, all the test results are higher than the rejection threshold Tα=0.05(49)=1.6777. It means that H0 does not established and H1 is true. This experiment proved that the proposed method LPRC is effective.
In this paper, a new algorithm LPRC is proposed to improve the stability of the traditional LPA. To achieve better propagation results, a credibility assessment and a roll-back detection schemes are designed. The credibility assessment of each sample is calculated first to determinate the label propagation order, which ensures that the new labeled samples are more reliable to be added to the labeled set for future propagation. Then, a roll-back mechanism based on feedback detection is used to the control the propagation error caused by wrong labels. Only when the exit conditions are satisfied, the new labeled samples could maintain their labels and be moved to labeled sample dataset, or the new labeled samples in this round will be discarded.
LPRC not only maintains the original simple and efficient features of label propagation, but also increases its accuracy in classification. The comparisons based on the artificial synthetic datasets and the UCI datasets demonstrated that classification performance of LPRC are obviously better than traditional algorithms. In particular, it is suitable to the situation with only a small number of labeled samples.
In the feature, we will continue to make deep research in label propagation algorithm in order to let it exert the best performance. The research we made is just based on the static samples, but in the practice, the samples are always dynamical. Considering with this situation, we will focus on the dynamic samples in the next step to fit the practical applications better.
This work was supported by the Natural Science Foundation of China (Grantnos.61872255, U1736212 and U19A2068).
The authors declare there is no conflict of interest.
[1] |
Counter SA, Buchanan LH (2004) Mercury exposure in children: a review. Toxicol Appl Pharmacol 198: 209-230. doi: 10.1016/j.taap.2003.11.032
![]() |
[2] |
Bose-O'Reilly S, McCarty KM, Steckling N, et al. (2010) Mercury exposure and children's health. Curr Probl Pediatr Adolesc Health Care 40: 186-215. doi: 10.1016/j.cppeds.2010.07.002
![]() |
[3] | UNEP (United Nations Environment Programme), Mercury, Negotiations: The Mercury, Negotiations: The Negotiating Process, 2013. Available from: http://www.unep.org/hazardoussubstances/Mercury/Negotiations/tabid/3320/Default.aspx |
[4] | WHO (World Health Organisation), Mercury and health, 2008. Available from: http://www.who.int/mediacentre/factsheets/fs361/en/. |
[5] | U.S. EPA (Environmental Protection Agency) (1990) An assessment of exposure to mercury in the United States. Washington: EPA. |
[6] | United Nations Environment Programme-Chemicals, Global mercury assessment. UNEP Chemicals, 2002. Available from: http://www.unep.org/gc/gc22/Document/UNEP-GC22-INF3.pdf. |
[7] |
Sandborgh-Englund G, Elinder CG, Johanson G, et al. (1998) The absorption, blood levels, and excretion of mercury after a single dose of mercury vapor in humans. Toxicol Appl Pharmacol 150: 146-153. doi: 10.1006/taap.1998.8400
![]() |
[8] | Kudsk FN (1965) Absorption of mercury vapour from the respiratory tract in man. Acta Pharmacol Toxicol (Copenh) 23: 250-262. |
[9] |
AlSaleh I, AlDoush I (1997) Mercury content in skin-lightening creams and potential hazards to the health of Saudi women. J Toxicol Environ Health 51: 123-130. doi: 10.1080/00984109708984016
![]() |
[10] | WHO, Guidance for identifying populations at risk from mercury exposure. UNEP DTIE Chemicals Branch, 2008. Avaliable from: http://www.who.int/foodsafety/publications/risk-mercury-exposure/en/. |
[11] |
Hursh JB, Clarkson TW, Miles EF, et al. (1989) Percutaneous absorption of mercury vapor by man. Arch Environ Health 44: 120-127. doi: 10.1080/00039896.1989.9934385
![]() |
[12] |
Bose-O'Reilly S, Lettmeier B, Gothe RM, et al. (2008) Mercury as a serious health hazard for children in gold mining areas. Environ Res 107: 89-97. doi: 10.1016/j.envres.2008.01.009
![]() |
[13] | Agency for Toxic Substances and Disease Registry (ATSDR), Toxicological Profile for Mercury. US Department of Health and Human Services, Public Health Service, ATSDR, 1999. Available from: http://www.atsdr.cdc.gov/toxprofiles/tp46.html. |
[14] | Gibb H, O'Leary KG (2014) Mercury Exposure and Health Impacts among Individuals in the Artisanal and Small-Scale Gold Mining Community: A Comprehensive Review. Environ Health Perspect 122: 667-672. |
[15] |
Marsh DO, Myers GJ, Clarkson TW, et al. (1980) Fetal methylmercury poisoning: clinical and toxicological data on 29 cases. Ann Neurol 7: 348-353. doi: 10.1002/ana.410070412
![]() |
[16] | Solan TD, Lindow SW (2014) Mercury exposure in pregnancy: a review. J Perinat Med 42: 725-729. |
[17] |
Axelrad DA, Bellinger DC, Ryan LM, et al. (2007) Dose-response relationship of prenatal mercury exposure and IQ: an integrative analysis of epidemiologic data. Environ Health Perspect 115: 609-615. doi: 10.1289/ehp.9303
![]() |
[18] | Jacobson JL, Muckle G, Ayotte P, et al. (2015) Relation of prenatal methylmercury exposure from environmental sources to childhood IQ. Environ Health Perspect 123: 827-833. |
[19] |
Bellinger DC, O'Leary K, Rainis H, et al. (2016) Country-specific estimates of the incidence of intellectual disability associated with prenatal exposure to methylmercury. Environ Res 147: 159-163. doi: 10.1016/j.envres.2015.10.006
![]() |
[20] |
Snoj Tratnik J, Falnoga I, Trdin A, et al. (2017) Prenatal mercury exposure, neurodevelopment and apolipoprotein E genetic polymorphism. Environ Res 152: 375-385. doi: 10.1016/j.envres.2016.08.035
![]() |
[21] |
Angerer J, Ewers U, Wilhelm M (2007) Human biomonitoring: state of the art. Int J Hyg Environ Health 210: 201-228. doi: 10.1016/j.ijheh.2007.01.024
![]() |
[22] |
Schulz C, Angerer J, Ewers U, et al. (2007) The German human biomonitoring commission. Int J Hyg Environ Health 210: 373-382. doi: 10.1016/j.ijheh.2007.01.035
![]() |
[23] |
Scheepers PTJ, Bos PMJ, Konings J, et al. (2011) Application of biological monitoring for exposure assessment following chemical incidents: A procedure for decision making. J Expo Sci Environ Epidemiol 21: 247-261. doi: 10.1038/jes.2010.4
![]() |
[24] |
Scheepers PT, van Ballegooij-Gevers M, Jans H (2014) Biological monitoring involving children exposed to mercury from a barometer in a private residence. Toxicol Lett 231: 365-373. doi: 10.1016/j.toxlet.2014.03.017
![]() |
[25] |
Krystek P, Favaro P, Bode P, et al. (2012) Methyl mercury in nail clippings in relation to fish consumption analysis with gas chromatography coupled to inductively coupled plasma mass spectrometry: a first orientation. Talanta 97: 83-86. doi: 10.1016/j.talanta.2012.03.065
![]() |
[26] |
Sakamoto M, Murata K, Domingo JL, et al. (2016) Implications of mercury concentrations in umbilical cord tissue in relation to maternal hair segments as biomarkers for prenatal exposure to methylmercury. Environ Res 149: 282-287. doi: 10.1016/j.envres.2016.04.023
![]() |
[27] |
Sandborgh-Englund G, Einarsson C, Sandstrom M, et al. (2004) Gastrointestinal absorption of metallic mercury. Arch Environ Health 59: 449-454. doi: 10.1080/00039890409603424
![]() |
[28] | ACGIH (2013) Biological exposure index (BEI) documentation. American Conference of Governmental Industrial Hygienists, Cincinnati, OH. |
[29] |
Hursh JB, Cherian MG, Clarkson TW, et al. (1976) Clearance of mercury (HG-197, HG-203) vapor inhaled by human subjects. Arch Environ Health 31: 302-309. doi: 10.1080/00039896.1976.10667240
![]() |
[30] |
Magos L, Halbach S, Clarkson TW (1978) Role of catalase in the oxidation of mercury vapor. Biochem Pharmacol 27: 1373-1377. doi: 10.1016/0006-2952(78)90122-3
![]() |
[31] |
Piotrowski JK, Trojanowska B, Wisniewska-Knypl JM, et al. (1974) Mercury binding in the kidney and liver of rats repeatedly exposed to mercuric chloride: induction of metallothionein by mercury and cadmium. Toxicol Appl Pharmacol 27: 11-19. doi: 10.1016/0041-008X(74)90169-0
![]() |
[32] |
Cherian MG, Hursh JB, Clarkson TW, et al. (1978) Radioactive mercury distribution in biological fluids and excretion in human subjects after inhalation of mercury vapor. Arch Environ Health 33: 109-114. doi: 10.1080/00039896.1978.10667318
![]() |
[33] |
Jonsson F, Sandborgh-Englund G, Johanson G (1999) A compartmental model for the kinetics of mercury vapor in humans. Toxicol Appl Pharmacol 155: 161-168. doi: 10.1006/taap.1998.8585
![]() |
[34] | International Agency for Research on Cancer (IARC), 2012. Agents reviewed by the IARC monographs, volumes 1-116. |
[35] |
Clarkson TW, Magos L (2006) The toxicology of mercury and its chemical compounds. Crit Rev Toxicol 36: 609-662. doi: 10.1080/10408440600845619
![]() |
[36] |
Pogarev SE, Ryzhov V, Mashyanov N, et al. (2002) Direct measurement of the mercury content of exhaled air: a new approach for determination of the mercury dose received. Anal Bioanal Chem 374: 1039-1044. doi: 10.1007/s00216-002-1601-7
![]() |
[37] | Nakaaki K, Fukabori S, Tjada O (1978) On the evaluation of mercury exposure-A proposal of the standard value for health care of workers. J Sci Labour 54: 1-8. |
[38] | National Research Council (2000) Toxicological Effects of Mercury. Washington, D.C.: National Academy Press. |
[39] | Schaller KH, (1988) Mercury, In: Angerer, J, Schaller, K.H. Author, Analyses of hazardous Substances in Biological Materials, Vol 2, Weinheim: VCH, 195-211. |
[40] | Anthemidis AN, Zachariadis GA, Michos CE, et al. (2004) Time-based on-line preconcentration cold vapour generation procedure for ultra-trace mercury determination with inductively coupled plasma atomic emission spectrometry. Anal Bioanal Chem 379: 764-769. |
[41] |
Bergdahl IA, Schutz A, Hansson GA (1995) Automated determination of inorganic mercury in blood after sulfuric acid treatment using cold vapour atomic absorption spectrometry and an inductively heated gold trap. Analyst 120: 1205-1209. doi: 10.1039/AN9952001205
![]() |
[42] |
Anthemidis AN, Zachariadis GA, Stratis JA (2004) Development of a sequential injection system for trace mercury determination by cold vapour atomic absorption spectrometry utilizing an integrated gas-liquid separator/reactor. Talanta 64: 1053-1057. doi: 10.1016/j.talanta.2004.05.003
![]() |
[43] |
Pellizzari ED, Fernando R, Cramer GM, et al. (1999) Analysis of mercury in hair of EPA region V population. J Expo Anal Environ Epidemiol 9: 393-401. doi: 10.1038/sj.jea.7500056
![]() |
[44] |
McDowell MA, Dillion CF, Osterloh J, et al. (2004) Hair mercury levels in US children and women of childbearing age: reference range data from NHANES 1999-2000. Environ Health Perspect 112: 1165-1171. doi: 10.1289/ehp.7046
![]() |
[45] | Deutsche Forschungsgemeinschaft (DFG), (2005) Addendum to Mercury and its Inorganic Compounds, In: BAT Value Documentations, Vol 5, Weinheim: Wiley-VCH, 71-115. |
[46] |
Schulz C, Wilhelm M, Heudorf U, et al. (2011) Update of the reference and HBM values derived by the German Human Biomonitoring Commission. Int J Hyg Environ Health 215: 26-35. doi: 10.1016/j.ijheh.2011.06.007
![]() |
[47] | Carpi A, Lindberg SE, Prestbo EM, et al. (1997) Methyl mercury contamination and emission to the atmosphere from soil amended with municipal sewage sludge. J Environ Qual 26: 1650-1655. |
[48] |
Halbach S (1985) The octanol/water distribution of mercury compounds. Arch Toxicol 57: 139-141. doi: 10.1007/BF00343125
![]() |
[49] | National Research Council (US) Committee on the Toxicological Effects of Methylmercury, (2000) Toxicological Effects of Methylmercury. Washington DC: National Academies Press (US). |
[50] |
Skerfving S (1988) Mercury in women exposed to methylmercury through fish consumption, and in their newborn babies and breast milk. Bull Environ Contam Toxicol 41: 475-482. doi: 10.1007/BF02020989
![]() |
[51] | Bernhoft RA (2012) Mercury toxicity and treatment: a review of the literature. J Environ Public Health 2012: 1-10. |
[52] |
Aberg B, Ekman L, Falk R, et al. (1969) Metabolism of methyl mercury (203Hg) compounds in man. Arch Environ Health 19: 478-484. doi: 10.1080/00039896.1969.10666872
![]() |
[53] | Bernard SR, Purdue P (1984) Metabolic models for methyl and inorganic mercury. Health Phys 46: 695-699. |
[54] | Miettinen JK, Rahola T, Hattula T, et al. (1971) Elimination of 203Hg-methylmercury in man. Ann Clin Res 3: 116-122. |
[55] | Poulin J, Gibb H (2008) Mercury: assessing the burden of disease at national and local levels, In: Prüss-Üstün, A. Editor, Environmental Burden of Disease Series, No. 16, Geneva: WHO (World Health Organization), Available from: |
[56] |
Clarkson TW (1993) Mercury: major issues in environmental health. Environ Health Perspect 100: 31-38. doi: 10.1289/ehp.9310031
![]() |
[57] |
Kershaw TG, Clarkson TW, Dhahir PH (1980) The relationship between blood levels and dose of methylmercury in man. Arch Environ Health 35: 28-36. doi: 10.1080/00039896.1980.10667458
![]() |
[58] |
Sherlock J, Hislop J, Newton D, et al. (1984) Elevation of mercury in human blood from controlled chronic ingestion of methylmercury in fish. Hum Exp Toxicol 3: 117-131. doi: 10.1177/096032718400300205
![]() |
[59] |
Cox C, Clarkson TW, Marsh DO, et al. (1989) Dose-response analysis of infants prenatally exposed to methyl mercury: an application of a single compartment model to single-strand hair analysis. Environ Res 49: 318-332. doi: 10.1016/S0013-9351(89)80075-1
![]() |
[60] |
Cooper GA, Kronstrand R, Kintz P, et al. (2012) Society of hair testing guidelines for drug testing in hair. Forensic Sci Int 218: 20-24. doi: 10.1016/j.forsciint.2011.10.024
![]() |
[61] |
Stern AH, Smith AE (2003) An assessment of the cord blood: maternal blood methylmercury ratio: implications for risk assessment. Environ Health Perspect 111: 1465-1470. doi: 10.1289/ehp.6187
![]() |
[62] |
Bose-O'Reilly S, Drasch G, Beinhoff C, et al. (2010) Health assessment of artisanal gold miners in Indonesia. Sci Total Environ 408: 713-725. doi: 10.1016/j.scitotenv.2009.10.070
![]() |
[63] |
Kim BG, Jo EM, Kim GY, et al. (2012) Analysis of methylmercury concentration in the blood of koreans by using cold vapor atomic fluorescence spectrophotometry. Ann Lab Med 32: 31-37. doi: 10.3343/alm.2012.32.1.31
![]() |
[64] |
Akagi H, Malm O, Kinjo Y, et al. (1995) Methylmercury pollution in the Amazon, Brazil. Sci Total Environ 175: 85-95. doi: 10.1016/0048-9697(95)04905-3
![]() |
[65] |
Malm O, Branches FJ, Akagi H, et al. (1995) Mercury and methylmercury in fish and human hair from the Tapajos river basin, Brazil. Sci Total Environ 175: 141-150. doi: 10.1016/0048-9697(95)04910-X
![]() |
[66] |
Yamamoto R, Suzuki T (1978) Effects of artificial hair-waving on hair mercury values. Int Arch Occup Environ Health 42: 1-9. doi: 10.1007/BF00385706
![]() |
[67] |
Yamaguchi S, Matsumoto H, Kaku S, et al. (1975) Factors affecting the amount of mercury in human scalp hair. Am J Public Health 65: 484-488. doi: 10.2105/AJPH.65.5.484
![]() |
[68] | Nuttall KL (2006) Interpreting hair mercury levels in individual patients. Ann Clin Lab Sci 36: 248-261. |
[69] | Sherman LS, Blum JD, Franzblau A, et al. (2013) New insight into biomarkers of human mercury exposure using naturally occurring mercury stable isotopes. Environ Sci Technol 47: 3403-3409. |
[70] | IPCS (International Programme on Chemical Safety) (2000) Environmental health criteria 214, Human exposure assessment. World Health Organization, Geneva. Available from: http://www.inchem.org/documents/ehc/ehc/ehc214.htm. |
[71] |
Johnsson C, Schutz A, Sallsten G (2005) Impact of consumption of freshwater fish on mercury levels in hair, blood, urine, and alveolar air. J Toxicol Environ Health Part A 68: 129-140. doi: 10.1080/15287390590885992
![]() |
[72] | Obi E, Okafor C, Igwebe A, et al. (2015) Elevated prenatal methylmercury exposure in Nigeria: Evidence from maternal and cord blood. Chemosphere 119: 485-489. |
[73] | Mahaffey KR, Clickner RP, Bodurow CC (2004) Blood organic mercury and dietary mercury intake: national health and nutrition examination survey, 1999 and 2000. Environ Health Perspect 112: 562-570. |
[74] |
Grandjean P, Budtz-Jorgensen E, White RF, et al. (1999) Methylmercury exposure biomarkers as indicators of neurotoxicity in children aged 7 years. Am J Epidemiol 150: 301-305. doi: 10.1093/oxfordjournals.aje.a010002
![]() |
[75] |
Grandjean P, Budtz-Jorgensen E, Jorgensen PJ, et al. (2005) Umbilical cord mercury concentration as biomarker of prenatal exposure to methylmercury. Environ Health Perspect 113: 905-908. doi: 10.1289/ehp.7842
![]() |
[76] |
Kristensen AK, Thomsen JF, Mikkelsen S (2014) A review of mercury exposure among artisanal small-scale gold miners in developing countries. Int Arch Occup Environ Health 87: 579-590. doi: 10.1007/s00420-013-0902-9
![]() |
[77] | Clarkson TW (2002) The three modern faces of mercury. Environ Health Perspect 110(Suppl 1): 11-23. |
[78] | Tsuji JS, Williams PRD, Edwards MR, et al. (2003) Evaluation of mercury in urine as an indicator of exposure to low levels of mercury vapor. Environ Health Perspect 111: 623-630. |
[79] | Nuttall KL (2004) Interpreting mercury in blood and urine of individual patients. Ann Clin Lab Sci 34: 235-250. |
[80] | Jung RC, Aaronson J (1980) Death following inhalation of mercury vapor at home. West J Med 132: 539-543. |
[81] |
Wilhelm M, Schulz C, Schwenk M (2006) Revised and new reference values for arsenic, cadmium, lead, and mercury in blood or urine of children: basis for validation of human biomonitoring data in environmental medicine. Int J Hyg Environ Health 209: 301-305. doi: 10.1016/j.ijheh.2006.01.004
![]() |
[82] |
Davidson PW, Myers GJ, Cox C, et al. (1998) Effects of prenatal and postnatal methylmercury exposure from fish consumption on neurodevelopment: outcomes at 66 months of age in the Seychelles child development study. JAMA 280: 701-707. doi: 10.1001/jama.280.8.701
![]() |
[83] | IPCS (International Programme on Chemical Safety) (1990) Environmental Health Criteria 101, Methylmercury. World Health Organization, Geneva. Available from: http://www.inchem.org/documents/ehc/ehc/ehc101.htm |
[84] |
Díez S, Montuori P, Pagano A, et al. (2008) Hair mercury levels in an urban population from southern Italy: Fish consumption as a determinant of exposure. Environ Int 34: 162-167. doi: 10.1016/j.envint.2007.07.015
![]() |
[85] | Cernichiari E, Brewer R, Myers GJ, et al. (1995) Monitoring methylmercury during pregnancy: maternal hair predicts fetal brain exposure. Neurotoxicology 16: 705-710. |
[86] | Crump KS, Van Landingham C, Shamlaye C, et al. (2000) Benchmark concentrations for methylmercury obtained from the Seychelles Child Development Study. Environ Health Perspect 108: 257-263. |
[87] |
Liberda EN, Tsuji LJ, Martin ID, et al. (2014) The complexity of hair/blood mercury concentration ratios and its implications. Environ Res 134: 286-294. doi: 10.1016/j.envres.2014.08.007
![]() |
[88] |
Ha E, Basu N, Bose-O'Reilly S, et al. (2017) Current progress on understanding the impact of mercury on human health. Environ Res 152: 419-433. doi: 10.1016/j.envres.2016.06.042
![]() |
[89] |
Yaginuma-Sakurai K, Murata K, Iwai-Shimada M, et al. (2012) Hair-to-blood ratio and biological half-life of mercury: experimental study of methylmercury exposure through fish consumption in humans. J Toxicol Sci 37: 123-130. doi: 10.2131/jts.37.123
![]() |
[90] | Queipo AS, Rodríguez-González P, García Alonso JI.(2016) Evidence of the direct adsorption of mercury in human hair during occupational exposure to mercury vapour. J Trace Elem Med Biol 36: 16-21. |
[91] | Veiga MM, Baker RF (2004) Protocols for Environmental and Health Assessment of Mercury Released by Artisanal and Small-scale Gold Miners. Vienna: GEF/UNDP/UNIDO Global Mercury Project. |
[92] |
Myers GJ, Davidson PW, Cox C, et al. (2003) Prenatal methylmercury exposure from ocean fish consumption in the Seychelles child development study. Lancet 361: 1686-1692. doi: 10.1016/S0140-6736(03)13371-5
![]() |
1. | Chen Xie, Intelligent evaluation method of bank digital transformation credibility based on big data analysis, 2022, 22, 14727978, 1349, 10.3233/JCM-226060 | |
2. | Shuyu Li, Wen Chen, Kaiyan Xing, Hongchao Wang, Yilin Zhang, Ming Kang, MGAN-LD: A sparse label propagation-based anomaly detection approach using multi-generative adversarial networks, 2025, 312, 09507051, 113124, 10.1016/j.knosys.2025.113124 |
Datasets | Sum | Classes | Sum of each class |
Circles | 1500 | 2 | 750 |
Moons | 1500 | 2 | 750 |
Varied | 1500 | 3 | 500 |
Aniso | 1500 | 3 | 500 |
Blobs | 1500 | 3 | 500 |
![]() |
Circles | Moons | Varied | Aniso | Blobs |
MiniBatchKmeans | 33 % | 17 % | 38 % | 7 % | 0 % |
Meanshift | 50 % | 87 % | 2 % | 32 % | 33 % |
SpectralClustering | 1% | 74 % | 34 % | 99 % | 33 % |
DBSCAN | 50 % | 0 % | 33 % | 33 % | 100 % |
GaussianMixture | 33 % | 9 % | 1 % | 0 % | 33 % |
GaussianNB | 58.48 % | 86.34 % | 93.93 % | 79.26 % | 99.86 % |
DecisionTree | 75.77 % | 89.16 % | 95.42 % | 90.37 % | 100 % |
KNN | 62.25 % | 82.78 % | 89.02 % | 87.88 % | 100 % |
LPA | 99.86 % | 99.93 % | 66.53 % | 67.80 % | 100 % |
LPRC | 100 % | 100 % | 97.80 % | 99.80 % | 100 % |
Datasets | Sum of samples | Number of features | Number of classes |
Iris | 150 | 4 | 3 |
Wine | 178 | 13 | 3 |
Australian | 690 | 14 | 2 |
Breast | 699 | 14 | 2 |
![]() |
Iris | Wine | Australian | Breast |
MiniBatchKmeans | 2% | 10% | 47% | 6% |
Meanshift | 33% | 7% | 49% | 4% |
SpectralClustering | 17% | 16% | 32% | 40% |
DBSCAN | 17% | 4% | 52% | 3% |
GaussianMixture | 0% | 18% | 44% | 9% |
Dataset | ![]() |
GaussianNB | DecisionTree | KNN | LPA | LPRC |
iris | 2% | 69.96% | 74.54% | 75.54% | 74.00% | 94.33% |
4% | 78.22% | 84.68% | 84.82% | 81.99% | 95.41% | |
6% | 84.59% | 86.41% | 86.24% | 87.53% | 95.94% | |
8% | 87.82% | 89.01% | 87.67% | 89.71% | 96.16% | |
10% | 89.80% | 90.10% | 89.62% | 90.16% | 96.19% | |
12% | 92.47% | 90.77% | 90.91% | 91.41% | 96.28% | |
14% | 93.00% | 91.46% | 91.40% | 92.05% | 96.48% | |
16% | 93.31% | 91.86% | 92.46% | 91.33% | 96.45% | |
18% | 93.21% | 91.68% | 92.42% | 92.60% | 96.73% | |
20% | 94.11% | 92.72% | 93.63% | 92.60% | 96.68% | |
wine | 2% | 66.02% | 67.19% | 68.17% | 67.58% | 90.44% |
4% | 71.49% | 74.81% | 72.00% | 82.21% | 93.99% | |
6% | 74.06% | 77.65% | 73.34% | 85.71% | 93.43% | |
8% | 76.78% | 80.63% | 75.61% | 86.45% | 94.58% | |
10% | 78.62% | 82.37% | 75.60% | 89.44% | 94.47% | |
12% | 79.68% | 83.30% | 76.30% | 90.07% | 94.84% | |
14% | 79.33% | 84.16% | 76.17% | 90.91% | 95.21% | |
16% | 81.52% | 84.35% | 77.94% | 91.71% | 95.24% | |
18% | 82.34% | 85.00% | 77.99% | 91.97% | 95.41% | |
20% | 83.01% | 87.45% | 78.17% | 91.71% | 95.49% | |
australian | 2% | 73.16% | 75.08% | 76.12% | 75.79% | 79.29% |
4% | 75.21% | 76.71% | 78.05% | 78.09% | 79.29% | |
6% | 77.13% | 77.45% | 78.78% | 79.31% | 80.56% | |
8% | 80.31% | 78.87% | 79.58% | 80.21% | 81.15% | |
10% | 80.45% | 79.70% | 81.15% | 80.49% | 81.37% | |
12% | 80.73% | 80.51% | 81.62% | 81.63% | 82.36% | |
14% | 80.85% | 80.93% | 82.69% | 82.32% | 82.83% | |
16% | 80.81% | 80.52% | 83.69% | 82.91% | 83.61% | |
18% | 81.32% | 80.43% | 83.47% | 83.35% | 84.13% | |
20% | 81.01% | 81.40% | 84.15% | 83.38% | 84.37% | |
breast | 2% | 87.98% | 88.26% | 90.54% | 92.89% | 96.67% |
4% | 88.04% | 89.68% | 92.15% | 94.71% | 96.78% | |
6% | 88.99% | 89.81% | 93.25% | 94.54% | 96.82% | |
8% | 89.50% | 90.78% | 95.10% | 95.30% | 96.90% | |
10% | 89.73% | 91.70% | 95.47% | 95.85% | 96.94% | |
12% | 90.18% | 91.93% | 95.59% | 95.67% | 96.94% | |
14% | 91.82% | 92.61% | 95.66% | 96.18% | 97.02% | |
16% | 91.41% | 92.91% | 96.24% | 96.12% | 97.21% | |
18% | 91.73% | 92.43% | 96.67% | 96.19% | 97.16% | |
20% | 92.47% | 93.21% | 96.32% | 96.33% | 97.24% |
Dataset | ![]() |
TSVM | NSA | LPRC |
australian | 2% | 72.17% | 59.91% | 79.29% |
4% | 76.58% | 65.75% | 79.29% | |
6% | 77.20% | 68.01% | 80.56% | |
8% | 78.56% | 69.48% | 81.15% | |
10% | 81.85% | 69.71% | 81.37% | |
12% | 81.90% | 71.34% | 82.36% | |
14% | 83.23% | 72.38% | 82.83% | |
16% | 83.89% | 71.35% | 83.61% | |
18% | 83.86% | 72.19% | 84.13% | |
20% | 84.67% | 72.74% | 84.37% | |
breast | 2% | 93.22% | 82.13% | 96.67% |
4% | 93.91% | 88.27% | 96.78% | |
6% | 94.77% | 91.23% | 96.82% | |
8% | 94.72% | 92.57% | 96.90% | |
10% | 94.87% | 93.66% | 96.94% | |
12% | 94.99% | 92.94% | 96.94% | |
14% | 95.11% | 93.16% | 97.02% | |
16% | 95.23% | 93.93% | 97.21% | |
18% | 95.35% | 94.31% | 97.16% | |
20% | 95.14% | 93.53% | 97.24% |
Dataset | ![]() |
LPA | LPRC | Statistical test | ||
acc1 | var1 | acc2 | var2 | |||
iris | 2% | 74.00% | 1.03E-02 | 94.33% | 1.74E-03 | 138.17 |
4% | 81.99% | 7.25E-03 | 95.41% | 7.26E-04 | 129.57 | |
6% | 87.53% | 6.59E-03 | 95.94% | 4.59E-05 | 89.33 | |
8% | 89.71% | 1.96E-03 | 96.16% | 4.01E-05 | 230.36 | |
10% | 90.16% | 1.67E-03 | 96.19% | 4.27E-05 | 252.75 | |
12% | 91.41% | 1.22E-03 | 96.28% | 4.99E-05 | 279.43 | |
14% | 92.05% | 9.17E-04 | 96.48% | 4.27E-05 | 338.17 | |
16% | 91.33% | 8.02E-04 | 96.45% | 5.41E-05 | 446.88 | |
18% | 92.60% | 5.07E-04 | 96.73% | 4.13E-05 | 570.21 | |
20% | 92.60% | 4.72E-04 | 96.68% | 5.60E-05 | 605.09 | |
wine | 2% | 67.58% | 1.67E-02 | 90.44% | 7.64E-03 | 95.82 |
4% | 82.21% | 1.17E-02 | 93.99% | 4.30E-04 | 70.47 | |
6% | 85.71% | 6.44E-03 | 93.43% | 1.65E-03 | 83.91 | |
8% | 86.45% | 5.85E-03 | 94.58% | 3.50E-05 | 97.28 | |
10% | 89.44% | 1.63E-03 | 94.47% | 2.10E-04 | 216.01 | |
12% | 90.07% | 1.28E-03 | 94.84% | 6.53E-05 | 260.86 | |
14% | 90.91% | 1.33E-03 | 95.21% | 7.35E-05 | 226.32 | |
16% | 91.71% | 7.66E-04 | 95.24% | 4.83E-05 | 319.84 | |
18% | 91.97% | 7.70E-04 | 95.41% | 5.98E-05 | 312.72 | |
20% | 91.71% | 5.85E-04 | 95.49% | 6.25E-05 | 452.31 | |
australian | 2% | 75.79% | 5.46E-03 | 79.29% | 3.12E-03 | 44.87 |
4% | 78.09% | 4.64E-03 | 79.29% | 3.79E-03 | 18.10 | |
6% | 79.31% | 3.51E-03 | 80.56% | 1.38E-03 | 24.93 | |
8% | 80.21% | 2.72E-03 | 81.15% | 1.17E-03 | 24.18 | |
10% | 80.49% | 1.26E-03 | 81.37% | 1.16E-03 | 48.89 | |
12% | 81.63% | 1.36E-03 | 82.36% | 9.49E-04 | 37.57 | |
14% | 82.32% | 6.70E-04 | 82.83% | 6.64E-04 | 53.28 | |
16% | 82.91% | 5.16E-04 | 83.61% | 5.95E-04 | 94.96 | |
18% | 83.35% | 6.27E-04 | 84.13% | 4.27E-04 | 87.08 | |
20% | 83.38% | 6.11E-04 | 84.37% | 5.08E-04 | 113.42 | |
breast | 2% | 92.89% | 2.12E-03 | 96.67% | 8.78E-06 | 124.80 |
4% | 94.71% | 4.79E-04 | 96.78% | 1.31E-05 | 302.50 | |
6% | 94.54% | 7.34E-04 | 96.82% | 1.23E-05 | 217.44 | |
8% | 95.30% | 1.68E-04 | 96.90% | 1.05E-05 | 666.66 | |
10% | 95.85% | 8.29E-05 | 96.94% | 1.11E-05 | 920.39 | |
12% | 95.67% | 1.14E-04 | 96.94% | 1.70E-05 | 779.82 | |
14% | 96.18% | 9.49E-05 | 97.02% | 2.14E-05 | 619.60 | |
16% | 96.12% | 8.01E-05 | 97.21% | 1.79E-05 | 952.55 | |
18% | 96.19% | 1.17E-04 | 97.16% | 2.04E-05 | 580.35 | |
20% | 96.33% | 5.68E-05 | 97.24% | 1.87E-05 | 1121.48 |
Datasets | Sum | Classes | Sum of each class |
Circles | 1500 | 2 | 750 |
Moons | 1500 | 2 | 750 |
Varied | 1500 | 3 | 500 |
Aniso | 1500 | 3 | 500 |
Blobs | 1500 | 3 | 500 |
![]() |
Circles | Moons | Varied | Aniso | Blobs |
MiniBatchKmeans | 33 % | 17 % | 38 % | 7 % | 0 % |
Meanshift | 50 % | 87 % | 2 % | 32 % | 33 % |
SpectralClustering | 1% | 74 % | 34 % | 99 % | 33 % |
DBSCAN | 50 % | 0 % | 33 % | 33 % | 100 % |
GaussianMixture | 33 % | 9 % | 1 % | 0 % | 33 % |
GaussianNB | 58.48 % | 86.34 % | 93.93 % | 79.26 % | 99.86 % |
DecisionTree | 75.77 % | 89.16 % | 95.42 % | 90.37 % | 100 % |
KNN | 62.25 % | 82.78 % | 89.02 % | 87.88 % | 100 % |
LPA | 99.86 % | 99.93 % | 66.53 % | 67.80 % | 100 % |
LPRC | 100 % | 100 % | 97.80 % | 99.80 % | 100 % |
Datasets | Sum of samples | Number of features | Number of classes |
Iris | 150 | 4 | 3 |
Wine | 178 | 13 | 3 |
Australian | 690 | 14 | 2 |
Breast | 699 | 14 | 2 |
![]() |
Iris | Wine | Australian | Breast |
MiniBatchKmeans | 2% | 10% | 47% | 6% |
Meanshift | 33% | 7% | 49% | 4% |
SpectralClustering | 17% | 16% | 32% | 40% |
DBSCAN | 17% | 4% | 52% | 3% |
GaussianMixture | 0% | 18% | 44% | 9% |
Dataset | ![]() |
GaussianNB | DecisionTree | KNN | LPA | LPRC |
iris | 2% | 69.96% | 74.54% | 75.54% | 74.00% | 94.33% |
4% | 78.22% | 84.68% | 84.82% | 81.99% | 95.41% | |
6% | 84.59% | 86.41% | 86.24% | 87.53% | 95.94% | |
8% | 87.82% | 89.01% | 87.67% | 89.71% | 96.16% | |
10% | 89.80% | 90.10% | 89.62% | 90.16% | 96.19% | |
12% | 92.47% | 90.77% | 90.91% | 91.41% | 96.28% | |
14% | 93.00% | 91.46% | 91.40% | 92.05% | 96.48% | |
16% | 93.31% | 91.86% | 92.46% | 91.33% | 96.45% | |
18% | 93.21% | 91.68% | 92.42% | 92.60% | 96.73% | |
20% | 94.11% | 92.72% | 93.63% | 92.60% | 96.68% | |
wine | 2% | 66.02% | 67.19% | 68.17% | 67.58% | 90.44% |
4% | 71.49% | 74.81% | 72.00% | 82.21% | 93.99% | |
6% | 74.06% | 77.65% | 73.34% | 85.71% | 93.43% | |
8% | 76.78% | 80.63% | 75.61% | 86.45% | 94.58% | |
10% | 78.62% | 82.37% | 75.60% | 89.44% | 94.47% | |
12% | 79.68% | 83.30% | 76.30% | 90.07% | 94.84% | |
14% | 79.33% | 84.16% | 76.17% | 90.91% | 95.21% | |
16% | 81.52% | 84.35% | 77.94% | 91.71% | 95.24% | |
18% | 82.34% | 85.00% | 77.99% | 91.97% | 95.41% | |
20% | 83.01% | 87.45% | 78.17% | 91.71% | 95.49% | |
australian | 2% | 73.16% | 75.08% | 76.12% | 75.79% | 79.29% |
4% | 75.21% | 76.71% | 78.05% | 78.09% | 79.29% | |
6% | 77.13% | 77.45% | 78.78% | 79.31% | 80.56% | |
8% | 80.31% | 78.87% | 79.58% | 80.21% | 81.15% | |
10% | 80.45% | 79.70% | 81.15% | 80.49% | 81.37% | |
12% | 80.73% | 80.51% | 81.62% | 81.63% | 82.36% | |
14% | 80.85% | 80.93% | 82.69% | 82.32% | 82.83% | |
16% | 80.81% | 80.52% | 83.69% | 82.91% | 83.61% | |
18% | 81.32% | 80.43% | 83.47% | 83.35% | 84.13% | |
20% | 81.01% | 81.40% | 84.15% | 83.38% | 84.37% | |
breast | 2% | 87.98% | 88.26% | 90.54% | 92.89% | 96.67% |
4% | 88.04% | 89.68% | 92.15% | 94.71% | 96.78% | |
6% | 88.99% | 89.81% | 93.25% | 94.54% | 96.82% | |
8% | 89.50% | 90.78% | 95.10% | 95.30% | 96.90% | |
10% | 89.73% | 91.70% | 95.47% | 95.85% | 96.94% | |
12% | 90.18% | 91.93% | 95.59% | 95.67% | 96.94% | |
14% | 91.82% | 92.61% | 95.66% | 96.18% | 97.02% | |
16% | 91.41% | 92.91% | 96.24% | 96.12% | 97.21% | |
18% | 91.73% | 92.43% | 96.67% | 96.19% | 97.16% | |
20% | 92.47% | 93.21% | 96.32% | 96.33% | 97.24% |
Dataset | ![]() |
TSVM | NSA | LPRC |
australian | 2% | 72.17% | 59.91% | 79.29% |
4% | 76.58% | 65.75% | 79.29% | |
6% | 77.20% | 68.01% | 80.56% | |
8% | 78.56% | 69.48% | 81.15% | |
10% | 81.85% | 69.71% | 81.37% | |
12% | 81.90% | 71.34% | 82.36% | |
14% | 83.23% | 72.38% | 82.83% | |
16% | 83.89% | 71.35% | 83.61% | |
18% | 83.86% | 72.19% | 84.13% | |
20% | 84.67% | 72.74% | 84.37% | |
breast | 2% | 93.22% | 82.13% | 96.67% |
4% | 93.91% | 88.27% | 96.78% | |
6% | 94.77% | 91.23% | 96.82% | |
8% | 94.72% | 92.57% | 96.90% | |
10% | 94.87% | 93.66% | 96.94% | |
12% | 94.99% | 92.94% | 96.94% | |
14% | 95.11% | 93.16% | 97.02% | |
16% | 95.23% | 93.93% | 97.21% | |
18% | 95.35% | 94.31% | 97.16% | |
20% | 95.14% | 93.53% | 97.24% |
Dataset | ![]() |
LPA | LPRC | Statistical test | ||
acc1 | var1 | acc2 | var2 | |||
iris | 2% | 74.00% | 1.03E-02 | 94.33% | 1.74E-03 | 138.17 |
4% | 81.99% | 7.25E-03 | 95.41% | 7.26E-04 | 129.57 | |
6% | 87.53% | 6.59E-03 | 95.94% | 4.59E-05 | 89.33 | |
8% | 89.71% | 1.96E-03 | 96.16% | 4.01E-05 | 230.36 | |
10% | 90.16% | 1.67E-03 | 96.19% | 4.27E-05 | 252.75 | |
12% | 91.41% | 1.22E-03 | 96.28% | 4.99E-05 | 279.43 | |
14% | 92.05% | 9.17E-04 | 96.48% | 4.27E-05 | 338.17 | |
16% | 91.33% | 8.02E-04 | 96.45% | 5.41E-05 | 446.88 | |
18% | 92.60% | 5.07E-04 | 96.73% | 4.13E-05 | 570.21 | |
20% | 92.60% | 4.72E-04 | 96.68% | 5.60E-05 | 605.09 | |
wine | 2% | 67.58% | 1.67E-02 | 90.44% | 7.64E-03 | 95.82 |
4% | 82.21% | 1.17E-02 | 93.99% | 4.30E-04 | 70.47 | |
6% | 85.71% | 6.44E-03 | 93.43% | 1.65E-03 | 83.91 | |
8% | 86.45% | 5.85E-03 | 94.58% | 3.50E-05 | 97.28 | |
10% | 89.44% | 1.63E-03 | 94.47% | 2.10E-04 | 216.01 | |
12% | 90.07% | 1.28E-03 | 94.84% | 6.53E-05 | 260.86 | |
14% | 90.91% | 1.33E-03 | 95.21% | 7.35E-05 | 226.32 | |
16% | 91.71% | 7.66E-04 | 95.24% | 4.83E-05 | 319.84 | |
18% | 91.97% | 7.70E-04 | 95.41% | 5.98E-05 | 312.72 | |
20% | 91.71% | 5.85E-04 | 95.49% | 6.25E-05 | 452.31 | |
australian | 2% | 75.79% | 5.46E-03 | 79.29% | 3.12E-03 | 44.87 |
4% | 78.09% | 4.64E-03 | 79.29% | 3.79E-03 | 18.10 | |
6% | 79.31% | 3.51E-03 | 80.56% | 1.38E-03 | 24.93 | |
8% | 80.21% | 2.72E-03 | 81.15% | 1.17E-03 | 24.18 | |
10% | 80.49% | 1.26E-03 | 81.37% | 1.16E-03 | 48.89 | |
12% | 81.63% | 1.36E-03 | 82.36% | 9.49E-04 | 37.57 | |
14% | 82.32% | 6.70E-04 | 82.83% | 6.64E-04 | 53.28 | |
16% | 82.91% | 5.16E-04 | 83.61% | 5.95E-04 | 94.96 | |
18% | 83.35% | 6.27E-04 | 84.13% | 4.27E-04 | 87.08 | |
20% | 83.38% | 6.11E-04 | 84.37% | 5.08E-04 | 113.42 | |
breast | 2% | 92.89% | 2.12E-03 | 96.67% | 8.78E-06 | 124.80 |
4% | 94.71% | 4.79E-04 | 96.78% | 1.31E-05 | 302.50 | |
6% | 94.54% | 7.34E-04 | 96.82% | 1.23E-05 | 217.44 | |
8% | 95.30% | 1.68E-04 | 96.90% | 1.05E-05 | 666.66 | |
10% | 95.85% | 8.29E-05 | 96.94% | 1.11E-05 | 920.39 | |
12% | 95.67% | 1.14E-04 | 96.94% | 1.70E-05 | 779.82 | |
14% | 96.18% | 9.49E-05 | 97.02% | 2.14E-05 | 619.60 | |
16% | 96.12% | 8.01E-05 | 97.21% | 1.79E-05 | 952.55 | |
18% | 96.19% | 1.17E-04 | 97.16% | 2.04E-05 | 580.35 | |
20% | 96.33% | 5.68E-05 | 97.24% | 1.87E-05 | 1121.48 |