相关论文: K-Deep Simplex: Deep Manifold Learning via Local D…

Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to…

Recent years, analysis dictionary learning (ADL) and its applications for classification have been well developed, due to its flexible projective ability and low classification complexity. With the learned analysis dictionary, test samples…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

Dictionary learning has recently emerged as a promising approach for mechanistic interpretability of large transformer models. Disentangling high-dimensional transformer embeddings requires algorithms that scale to high-dimensional data…

Machine learning models have emerged as powerful tools in physics and engineering. Although flexible, a fundamental challenge remains on how to connect new machine learning models with known physics. In this work, we present an autoencoder…

We develop a dictionary learning algorithm by minimizing the $\ell_1$ distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization…

This paper extends our previous work on regularization of neural networks using Eigenvalue Decay by employing a soft approximation of the dominant eigenvalue in order to enable the calculation of its derivatives in relation to the synaptic…

We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…

Given an undirected graph and a size parameter $k$, the Densest $k$-Subgraph (D$k$S) problem extracts the subgraph on $k$ vertices with the largest number of induced edges. While D$k$S is NP--hard and difficult to approximate, penalty-based…

The Densest $k$-Subgraph (D$k$S) is a fundamental combinatorial problem known for its theoretical hardness and breadth of applications. Recently, Lu et al. (AAAI 2025) introduced a penalty-based non-convex relaxation that achieves promising…

In this paper we present a new approach of incorporating kernels into dictionary learning. The kernel K-SVD algorithm (KKSVD), which has been introduced recently, shows an improvement in classification performance, with relation to its…

In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error…

Local feature frameworks are difficult to learn in an end-to-end fashion, due to the discreteness inherent to the selection and matching of sparse keypoints. We introduce DISK (DIScrete Keypoints), a novel method that overcomes these…

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…