Related papers: Orthogonal Subspace Clustering: Enhancing High-Dim…
This paper studies a factor modeling-based approach for clustering high-dimensional data generated from a mixture of strongly correlated variables. Statistical modeling with correlated structures pervades modern applications in economics,…
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of $n$ points into dimension $O(\log n)$ with low distortion of their distances. This dimension bound is tight…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable…
Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…
Subspace clustering methods face inherent scalability limits due to the $O(n^3)$ cost (with $n$ denoting the number of data samples) of constructing full $n\times n$ affinities and performing spectral decomposition. While deep…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
In an increasingly digitalized commerce landscape, the proliferation of credit card fraud and the evolution of sophisticated fraudulent techniques have led to substantial financial losses. Automating credit card fraud detection is a viable…
We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic…
In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can…
We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…
OPTICS is a density-based clustering algorithm that performs well in a wide variety of applications. For a set of input objects, the algorithm creates a so-called reachability plot that can be either used to produce cluster membership…
Out-of-distribution (OOD) detection is essential for deploying deep learning models in open-world environments. Existing approaches, such as energy-based scoring and gradient-projection methods, typically rely on high-dimensional…
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…
In this paper, we develop a method for unsupervised clustering of two-way (matrix) data by combining two recent innovations from different fields: the Sparse Subspace Clustering (SSC) algorithm [10], which groups points coming from a union…
Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering…
In this paper, we consider clustering data that is assumed to come from one of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS)…