Self-Expressive Kernel Subspace Clustering Algorithm for Categorical Data with Embedded Feature Selection

Abstract

Kernel clustering of categorical data is a useful tool to process the separable datasets and has been employed in many disciplines. Despite recent efforts, existing methods for kernel clustering remain a significant challenge due to the assumption of feature independence and equal weights. In this study, we propose a self-expressive kernel subspace clustering algorithm for categorical data (SKSCC) using the self-expressive kernel density estimation (SKDE) scheme, as well as a new feature-weighted non-linear similarity measurement. In the SKSCC algorithm, we propose an effective non-linear optimization method to solve the clustering algorithm’s objective function, which not only considers the relationship between attributes in a non-linear space but also assigns a weight to each attribute in the algorithm to measure the degree of correlation. A series of experiments on some widely used synthetic and real-world datasets demonstrated the better effectiveness and efficiency of the proposed algorithm compared with other state-of-the-art methods, in terms of non-linear relationship exploration among attributes.

Categorical Data Clustering: A Bibliometric Analysis and Taxonomy

“…Furthermore, Y. M. Cheung, as the second author, has proposed numerous methods related to distance metrics with Y. Q. Zhang [73][74][75] and H. Jia [58]. Moreover, F. L. Chen proposed variant methods for optimizing the objective function in subspace clustering algorithms [61,76,77].…”

“…Cao [125], Khan, k-MODET [37], K-modes, K-representatives [126], M-K-Centers (Mod-2) [127] and New (Mod-3) [128] and CD-Clustering [129] Chen et al ( 2021) SKSCC [76] subspace clustering algorithm based on kernel density estimation (KDE), self-expressiveness-based methods, and probability-based similarity measurement K-modes, WKM [130], MWKM [131] Bai & Liang (2022) CDC_DR, CDC_DR + SE [66] graph-based representation method graph-embedding methods: Non-Embedding (NE), Spectral Embedding (SE) [132], Non-negative Matrix Factorization (NMF) [133], and Autoencoder (AE) [134] using joint and mean operation; categorical data encodings: K-modes, K-means with ordinal encoding, one-hot encoding [135], link-graph encoding [136], and coupled data embedding (CDE) [137] Dorman & Maitra (2022) OTQT [82] based on hartigan algorithm for K-means algorithm K-modes One study focused on a matrix-object with a one-many relationship, where one object has multiple feature vectors. Another study addressed set-valued features, where features can possess multiple values for an object-such as a person with multiple job titles and hobbies.…”

“…Chen et al [76] also addressed the sensitivity of the K-modes algorithm in initializing clusters and modes by employing kernel clustering. They utilized the self-expressive kernel density estimation (SKDE) to develop a self-expressive kernel subspace clustering algorithm for categorical data (SKCC).…”

“…Similar to MFk-M, the algorithm proposed by Bai and Liang [76], categorical data clustering based on data representation with spectral embedding (CDC_DR+SE), also employs a conversion method to represent categorical data as a graph representation instead of using direct ordinal or one-hot encoding methods. The algorithm learns the representation of categorical values from their graph structure, easing the capturing of potential similarities between categorical values and their conversion into numerical data.…”

State Monitoring Method for Tool Wear in Aerospace Manufacturing Processes Based on a Convolutional Neural Network (CNN)

“…. , x n ) has the probability density function as f. The density estimation formula can be calculated as follows [36,37]:…”