Xianshi Yu

Joshua Cape, Xianshi Yu, Jonquil Z. Liao

This paper analyzes the statistical performance of a robust spectral clustering method for latent structure recovery in noisy data matrices. We consider eigenvector-based clustering applied to a matrix of nonparametric rank statistics that is derived entrywise from the raw, original data matrix. This approach is robust in the sense that, unlike traditional spectral clustering procedures, it can provably recover population-level latent block structure even when the observed data matrix includes heavy-tailed entries and has a heterogeneous variance profile. Our main theoretical contributions are threefold and hold under flexible data generating conditions. First, we establish that robust spectral clustering with rank statistics can consistently recover latent block structure, viewed as communities of nodes in a graph, in the sense that unobserved community memberships for all but a vanishing fraction of nodes are correctly recovered with high probability when the data matrix is large. Second, we refine the former result and further establish that, under certain conditions, the community membership of any individual, specified node of interest can be asymptotically exactly recovered with probability tending to one in the large-data limit. Third, we establish asymptotic normality results associated with the truncated eigenstructure of matrices whose entries are rank statistics, made possible by synthesizing contemporary entrywise matrix perturbation analysis with the classical nonparametric theory of so-called simple linear rank statistics. Collectively, these results demonstrate the statistical utility of rank-based data transformations when paired with spectral techniques for dimensionality reduction. Additionally, for a dataset of human connectomes, our approach yields parsimonious dimensionality reduction and improved recovery of ground-truth neuroanatomical cluster structure.

Linqi Lu, Xianshi Yu, Akhil Perumal Reddy

This study investigates the interplay of visual and textual features in online discussions about cannabis edibles and their impact on user engagement. Leveraging the CLIP model, we analyzed 42,743 images from Facebook (March 1 to August 31, 2021), with a focus on detecting food-related visuals and examining the influence of image attributes such as colorfulness and brightness on user interaction. For textual analysis, we utilized the BART model as a denoising autoencoder to classify ten topics derived from structural topic modeling, exploring their relationship with user engagement. Linear regression analysis identified significant positive correlations between food-related visuals (e.g., fruit, candy, and bakery) and user engagement scores, as well as between engagement and text topics such as cannabis legalization. In contrast, negative associations were observed with image colorfulness and certain textual themes. These findings offer actionable insights for policymakers and regulatory bodies in designing warning labels and marketing regulations to address potential risks associated with recreational cannabis edibles.

Ting Li, Ningchen Ying, Xianshi Yu et al.

Community detection was a hot topic on network analysis, where the main aim is to perform unsupervised learning or clustering in networks. Recently, semi-supervised learning has received increasing attention among researchers. In this paper, we propose a new algorithm, called weighted inverse Laplacian (WIL), for predicting labels in partially labeled networks. The idea comes from the first hitting time in random walk, and it also has nice explanations both in information propagation and the regularization framework. We propose a partially labeled degree-corrected block model (pDCBM) to describe the generation of partially labeled networks. We show that WIL ensures the misclassification rate is of order $O(\frac{1}{d})$ for the pDCBM with average degree $d=Ω(\log n),$ and that it can handle situations with greater unbalanced than traditional Laplacian methods. WIL outperforms other state-of-the-art methods in most of our simulations and real datasets, especially in unbalanced networks and heterogeneous networks.

Ting Li, Bingyi Jing, Ningchen Ying et al.

Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different statistical learning models. We will propose a new two-stage scaling method. First, we use some training data to fit linear regression model and then scale the whole data based on the coefficients of regression. Simulations are conducted to illustrate the advantages of our new scaling method. Some real data analysis will also be given.