相关论文: Sparse Quantized Spectral Clustering

This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to…

Self-supervision is key to extending use of deep learning for label scarce domains. For most of self-supervised approaches data transformations play an important role. However, up until now the impact of transformations have not been…

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.…

A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…

A widely used paradigm to improve the generalization performance of high-capacity neural models is through the addition of auxiliary unsupervised tasks during supervised training. Tasks such as similarity matching and input reconstruction…

A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

Diffusion models are one of the key architectures of generative AI. Their main drawback, however, is the computational costs. This study indicates that the concept of sparsity, well known especially in statistics, can provide a pathway to…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…

Semi-supervised clustering seeks to augment traditional clustering methods by incorporating side information provided via human expertise in order to increase the semantic meaningfulness of the resulting clusters. However, most current…

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…