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.

本文提出了两种基于新定义的正则化拉普拉斯矩阵的算法，用于估计分类数据的潜在类模型。我们在考虑稀疏性参数的基础上，通过理论收敛速度证明了我们的算法在温和条件下能稳定产生一致的潜在类分析结果，并提出了根据这一度量指标设计的若干程序来推断实际分类数据中应使用的潜在类的数量。通过广泛的模拟实验证实了我们算法的效率和准确性，并进一步将它应用于实际分类数据，取得了令人满意的结果。

基于正则化谱聚类的潜在类别分析