# Latent class analysis by regularized spectral clustering

arXiv: https://arxiv.org/abs/2310.18727 · HTML: https://mlsanity.com/paper/2310.18727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 28 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Spectral Algorithms for Community Detection in Directed Networks](https://mlsanity.com/paper/2008.03820/) (2020)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)
- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Identifiability of restricted latent class models with binary responses](https://mlsanity.com/paper/1603.04140/) (2016)
- [Beyond the EM Algorithm: Constrained Optimization Methods for Latent Class Model](https://mlsanity.com/paper/1901.02928/) (2019)
- [A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses](https://mlsanity.com/paper/2103.16036/) (2021)
- [A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses](https://mlsanity.com/paper/2305.03149/) (2023)
- [A spectral based goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/2303.14508/) (2023)
- [Mixed membership estimation for categorical data with weighted responses](https://mlsanity.com/paper/2310.10989/) (2023)

## Built on by (most cited first, 1 of 1)

- [Latent class analysis for multi-layer categorical data](https://mlsanity.com/paper/2408.05535/) (2024)

## Abstract (arXiv)

The latent class model is a highly effective tool in the analysis of categorical data from social, psychological, and behavioral sciences, where populations often share hidden common characteristics. In this article, we introduce two new algorithms for estimating the parameters of a latent class model for ordered categorical data with polytomous responses. These algorithms are based on a newly defined regularized Laplacian matrix derived from the response matrix. We provide theoretical convergence rates for our algorithms by considering a sparsity parameter and demonstrate that under a mild condition on data's sparsity, our algorithms yield consistent latent class analysis. Furthermore, we introduce a metric to assess the strength of latent class analysis and develop procedures based on this metric to determine the optimal number of latent classes for real-world ordered categorical data. Extensive simulation experiments demonstrate the efficiency and accuracy of our algorithms, and we demonstrate their practical application to real-world ordered categorical data with promising results.