Latent class analysis by regularized spectral clustering

TL;DR

This paper introduces two novel algorithms for latent class analysis of categorical data using regularized spectral clustering, with proven consistency and practical procedures for determining the number of classes.

Contribution

The authors develop new algorithms based on a regularized Laplacian matrix, providing theoretical convergence rates and practical methods for class number inference.

Findings

Algorithms are consistent under mild conditions

Effective in simulated experiments

Promising results on real-world data

Abstract

The latent class model is a powerful tool for identifying latent classes within populations that share common characteristics for categorical data in social, psychological, and behavioral sciences. In this article, we propose two new algorithms to estimate a latent class model for categorical data. Our algorithms are developed by using a newly defined regularized Laplacian matrix calculated from the response matrix. We provide theoretical convergence rates of our algorithms by considering a sparsity parameter and show that our algorithms stably yield consistent latent class analysis under mild conditions. Additionally, we propose a metric to capture the strength of latent class analysis and several procedures designed based on this metric to infer how many latent classes one should use for real-world categorical data. The efficiency and accuracy of our algorithms are verified by extensive simulated experiments, and we further apply our algorithms to real-world categorical data with promising results.