Related papers: Sparse PCA via $l_{2,p}$-Norm Regularization for U…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
Feature selection is an essential problem in computer vision, important for category learning and recognition. Along with the rapid development of a wide variety of visual features and classifiers, there is a growing need for efficient…
We present two practical improvement techniques for unsupervised segmentation learning. These techniques address limitations in the resolution and accuracy of predicted segmentation maps of recent state-of-the-art methods. Firstly, we…
Self-similarity learning has been recognized as a promising method for single image super-resolution (SR) to produce high-resolution (HR) image in recent years. The performance of learning based SR reconstruction, however, highly depends on…
Hyperspectral remote sensing is a prominent research topic in data processing. Most of the spectral unmixing algorithms are developed by adopting the linear mixing models. Nonnegative matrix factorization (NMF) and its developments are used…
High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…
In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
Major complications arise from the recent increase in the amount of high-dimensional data, including high computational costs and memory requirements. Feature selection, which identifies the most relevant and informative attributes of a…
We study the meta-learning for support (i.e. the set of non-zero entries) recovery in high-dimensional Principal Component Analysis. We reduce the sufficient sample complexity in a novel task with the information that is learned from…
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
We propose a meta-parameter free, off-the-shelf, simple and fast unsupervised feature learning algorithm, which exploits a new way of optimizing for sparsity. Experiments on STL-10 show that the method presents state-of-the-art performance…
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR…