Related papers: Smoothed Separable Nonnegative Matrix Factorizatio…
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…
An unsupervised point cloud registration method, called salient points analysis (SPA), is proposed in this work. The proposed SPA method can register two point clouds effectively using only a small subset of salient points. It first applies…
Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…
This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Spectral unmixing (SU) is a technique to characterize mixed pixels in hyperspectral images measured by remote sensors. Most of the spectral unmixing algorithms are developed using the linear mixing models. To estimate endmembers and…
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…
Signal separation and extraction are important tasks for devices recording audio signals in real environments which, aside from the desired sources, often contain several interfering sources such as background noise or concurrent speakers.…
Anomaly detection is a fundamental yet challenging problem in machine learning due to the lack of label information. In this work, we propose a novel and powerful framework, dubbed as SLA$^2$P, for unsupervised anomaly detection. After…
A semi-coprime array (SCA) interleaves two undersampled uniform linear arrays (ULAs) and a $Q$ element standard ULA. The undersampling factors of the first two arrays are $QM$ and $QN$ respectively where $M$ and $N$ are coprime. The…
Semi-supervised learning (SSL) has emerged as an effective paradigm for medical image segmentation, reducing the reliance on extensive expert annotations. Meanwhile, vision-language models (VLMs) have demonstrated strong generalization and…
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…
Although point-based networks are demonstrated to be accurate for 3D point cloud modeling, they are still falling behind their voxel-based competitors in 3D detection. We observe that the prevailing set abstraction design for down-sampling…
We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…
Vision-Language-Action (VLA) models have emerged as a promising approach for general-purpose robot manipulation. However, their generalization is inconsistent: while these models can perform impressively in some settings, fine-tuned…
In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…