Clustering High-Dimensional Noisy Categorical Data

Zhiyi Tian, Jiaming Xu and Jen Tang

Journal of the American Statistical Association, 2024, vol. 119, issue 548, 3008-3019

Abstract: Clustering is a widely used unsupervised learning technique that groups data into homogeneous clusters. However, when dealing with real-world data that contain categorical values, existing algorithms can be computationally costly in high dimensions and can struggle with noisy data that has missing values. Furthermore, except for one algorithm, no others provide theoretical guarantees of clustering accuracy. In this article, we propose a general categorical data encoding method and a computationally efficient spectral-based algorithm to cluster high-dimensional noisy categorical data (nominal or ordinal). Under a statistical model for data on m attributes from n subjects in r clusters with missing probability ϵ, we show that our algorithm exactly recovers the true clusters with high probability when mn(1−ϵ)≥CMr2 log 3M, with M=max(n,m) and a fixed constant C. In addition, we show that mn(1−ϵ)2≥rδ/2 with 0

Date: 2024
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DOI: 10.1080/01621459.2023.2298028

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