相关论文: Scalable Sparse Subspace Clustering via Ordered We…

We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…

The $\ell_1$ norm is the tight convex relaxation for the $\ell_0$ "norm" and has been successfully applied for recovering sparse signals. For problems with fewer samplings, one needs to enhance the sparsity by nonconvex penalties such as…

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

Large Language Models (LLMs), renowned for their remarkable performance across diverse domains, present a challenge when it comes to practical deployment due to their colossal model size. In response to this challenge, efforts have been…

$\ell_1$ regularization has been used for logistic regression to circumvent the overfitting and use the estimated sparse coefficient for feature selection. However, the challenge of such a regularization is that the $\ell_1$ norm is not…

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…

In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

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…

Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…

In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…

Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity…

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…

Large language models (LLMs) have spurred development in multiple industries. However, the growing number of their parameters brings substantial storage and computing burdens, making it essential to explore model compression techniques for…

Sparse Subspace Clustering (SSC) has been used extensively for subspace identification tasks due to its theoretical guarantees and relative ease of implementation. However SSC has quadratic computation and memory requirements with respect…

Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is $\ell_p$ regularization. However, it may encounter optimization instability due to the unbounded gradients when…

Distributed sparse learning with a cluster of multiple machines has attracted much attention in machine learning, especially for large-scale applications with high-dimensional data. One popular way to implement sparse learning is to use…

Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…