Related papers: A Dimension Reduction Technique for Large-scale St…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data…
With the growing interest and applications in machine learning and data science, finding an efficient method to sparse analysis the high-dimensional data and optimizing a dimension reduction model to extract lower dimensional features has…
In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods…
Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity…
The remarkable success of Large Language Models (LLMs) relies heavily on their substantial scale, which poses significant challenges during model deployment in terms of latency and memory consumption. Recently, numerous studies have…
Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the…
Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…
Attributed graph clustering, which aims to group the nodes of an attributed graph into disjoint clusters, has made promising advancements in recent years. However, most existing methods face challenges when applied to large graphs due to…
This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of…
Sparse system identification problems often exist in many applications, such as echo interference cancellation, sparse channel estimation, and adaptive beamforming. One of popular adaptive sparse system identification (ASSI) methods is…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
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…
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex…
Convex optimization is a powerful tool for resource allocation and signal processing in wireless networks. As the network density is expected to drastically increase in order to accommodate the exponentially growing mobile data traffic,…