Related papers: A Note on Spectral Clustering and SVD of Graph Dat…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…
Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
We develop an Iterative version of the Singular Value Decomposition (ISVD) that jointly analyzes a finite number of data matrices to identify signals that correlate among the rows of matrices. It will be illustrated how the supervised…
Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to…
Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…
Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…