相关论文: NP-Hardness and Inapproximability of Sparse PCA

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…

Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted…

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…

The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…

We study a variant of the sparse PCA (principal component analysis) problem in the "hard" regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio,…

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…

Sparse PCA (SPCA) is a fundamental model in machine learning and data analytics, which has witnessed a variety of application areas such as finance, manufacturing, biology, healthcare. To select a prespecified-size principal submatrix from…

In this paper, we will find a pseudopolynomial algorithm to solve $Qm \mid \mid L_{\max}$ and then we will prove that it is impossible to get any constant-factor approximation in polynomial time, and thus also impossible to have a PTAS for…

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a…

In clinical and biomedical research, multiple high-dimensional datasets are nowadays routinely collected from omics and imaging devices. Multivariate methods, such as Canonical Correlation Analysis (CCA), integrate two (or more) datasets to…

Face recognition is the very significant field in pattern recognition area. It has multiple applications in military and finance, to name a few. In this paper, the combination of the sparse PCA with the nearest-neighbor method (and with the…

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…