Related papers: Dimensionality Reduction of Massive Sparse Dataset…
We describe two algorithms for computing a sparse solution to a least-squares problem where the coefficient matrix can have arbitrary dimensions. We show that the solution vector obtained by our algorithms is close to the solution vector…
Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in…
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…
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…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional…
This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a models…
Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
We consider the problem of constructing small coresets for $k$-Median in Euclidean spaces. Given a large set of data points $P\subset \mathbb{R}^d$, a coreset is a much smaller set $S\subset \mathbb{R}^d$, so that the $k$-Median costs of…
We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…
Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…
In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…
The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data…