Related papers: Robust PCA in High-dimension: A Deterministic Appr…
The study of stability and sensitivity of statistical methods or algorithms with respect to their data is an important problem in machine learning and statistics. The performance of the algorithm under resampling of the data is a…
Principal component analysis (PCA) is not only a fundamental dimension reduction method, but is also a widely used network anomaly detection technique. Traditionally, PCA is performed in a centralized manner, which has poor scalability for…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
This paper uses network packet capture data to demonstrate how Robust Principal Component Analysis (RPCA) can be used in a new way to detect anomalies which serve as cyber-network attack indicators. The approach requires only a few…
The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…
In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with…
We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces…
We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…