Related papers: Sparse eigenbasis approximation: multiple feature …
In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
Dimension of the encoder output (i.e., the code layer) in an autoencoder is a key hyper-parameter for representing the input data in a proper space. This dimension must be carefully selected in order to guarantee the desired reconstruction…
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…
Spectral techniques are popular and robust approaches to data analysis. A prominent example is the use of eigenvectors of a Laplacian, constructed from data affinities, to identify natural data groupings or clusters, or to produce a…
Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…
Sparse autoencoders (SAEs) have become a central tool for interpreting language models. However, two key SAE analyses that remain difficult to scale are (1) matching semantically similar features across multi-layers and (2) compressing…
Scientific archives now contain hundreds of petabytes of data across genomics, ecology, climate, and molecular biology that could reveal undiscovered patterns if systematically analyzed at scale. Large-scale, weakly-supervised datasets in…
We propose a sparse-coding framework for activity recognition in ubiquitous and mobile computing that alleviates two fundamental problems of current supervised learning approaches. (i) It automatically derives a compact, sparse and…
Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…
We introduce point affiliation into feature upsampling, a notion that describes the affiliation of each upsampled point to a semantic cluster formed by local decoder feature points with semantic similarity. By rethinking point affiliation,…
Autoencoding has achieved great empirical success as a framework for learning generative models for natural images. Autoencoders often use generic deep networks as the encoder or decoder, which are difficult to interpret, and the learned…
In this paper, we propose a simple but effective semantic-based aggregation (SBA) method. The proposed SBA utilizes the discriminative filters of deep convolutional layers as semantic detectors. Moreover, we propose the effective…
Hyperspectral data acquired through remote sensing are invaluable for environmental and resource studies. While rich in spectral information, various complexities such as environmental conditions, material properties, and sensor…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…