Multi-indicator stock clustering based on LSPIA-B-spline control-coefficient representation

Siyu Shen; Lijuan Hu; Chengzhi Liu; Siyu Shen; Lijuan Hu; Chengzhi Liu

doi:10.3934/math.20261393

AIMS Mathematics

2026, Volume 11, Issue 11: 35929-35956. doi: 10.3934/math.20261393

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Research article

Multi-indicator stock clustering based on LSPIA-B-spline control-coefficient representation

School of Mathematics and Data Science, Hunan College of Humanities, Science and Technology, Loudi 417000, China

Received: 03 August 2026 Revised: 30 September 2026 Accepted: 14 October 2026 Published: 02 November 2026
MSC : 62H30, 65D07, 65D10

To address the high dimensionality of long stock time series and the limited descriptive capability of a single indicator, this paper proposes a multi-indicator stock-behavior clustering method based on a least-squares progressive iterative approximation (LSPIA)-B-spline control-coefficient representation. First, four financial indicators are constructed from the perspectives of periodic returns, risk exposure, and trading activity, and are standardized in a unified manner. Second, a common cubic B-spline basis is fitted to each stock's standardized multi-indicator series by LSPIA, yielding comparable, low-dimensional control-coefficient matrices without directly solving the least-squares normal equations. Rather than treating the coefficients as ordinary compressed features, we define a distance between the fitted series. On this basis, K-means is used to identify groups of stocks with similar market behavior. The clustering results are comprehensively evaluated using internal clustering indices, clustering stability, and economic-characteristic analysis. The proposed method provides an analytical framework for identifying stock-behavior structures that jointly considers temporal patterns, computational efficiency, and interpretability.
- stock-behavior clustering,
- LSPIA,
- B-spline,
- functional distance,
- K-means
Citation: Siyu Shen, Lijuan Hu, Chengzhi Liu. Multi-indicator stock clustering based on LSPIA-B-spline control-coefficient representation[J]. AIMS Mathematics, 2026, 11(11): 35929-35956. doi: 10.3934/math.20261393

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Abstract

To address the high dimensionality of long stock time series and the limited descriptive capability of a single indicator, this paper proposes a multi-indicator stock-behavior clustering method based on a least-squares progressive iterative approximation (LSPIA)-B-spline control-coefficient representation. First, four financial indicators are constructed from the perspectives of periodic returns, risk exposure, and trading activity, and are standardized in a unified manner. Second, a common cubic B-spline basis is fitted to each stock's standardized multi-indicator series by LSPIA, yielding comparable, low-dimensional control-coefficient matrices without directly solving the least-squares normal equations. Rather than treating the coefficients as ordinary compressed features, we define a distance between the fitted series. On this basis, K-means is used to identify groups of stocks with similar market behavior. The clustering results are comprehensively evaluated using internal clustering indices, clustering stability, and economic-characteristic analysis. The proposed method provides an analytical framework for identifying stock-behavior structures that jointly considers temporal patterns, computational efficiency, and interpretability.

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