Related papers: ALPCAHUS: Subspace Clustering for Heteroscedastic …

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

The rise of AI-powered classification techniques has ushered in a new era for data-driven Fault Detection and Diagnosis in smart building systems. While extensive research has championed supervised FDD approaches, the real-world application…

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component…

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatio-temporal datasets. To reduce oversimplifications, new models have been developed to be able to…

Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are…

Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

Problem statement: Clustering has a number of techniques that have been developed in statistics, pattern recognition, data mining, and other fields. Subspace clustering enumerates clusters of objects in all subspaces of a dataset. It tends…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

A particularly challenging context for dimensionality reduction is multivariate circular data, i.e., data supported on a torus. Such kind of data appears, e.g., in the analysis of various phenomena in ecology and astronomy, as well as in…

Clustering performs an essential role in many real world applications, such as market research, pattern recognition, data analysis, and image processing. However, due to the high dimensionality of the input feature values, the data being…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered…

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…