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Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade…

For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal…

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…

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…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

Low-rank and sparse decomposition based methods find their use in many applications involving background modeling such as clutter suppression and object tracking. While Robust Principal Component Analysis (RPCA) has achieved great success…

We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, $p$-dimensional samples are presented sequentially, and the goal is to produce the $k$-dimensional subspace that…

In this work, we study the online robust principal components' analysis (RPCA) problem. In recent work, RPCA has been defined as a problem of separating a low-rank matrix (true data), $L$, and a sparse matrix (outliers), $S$, from their…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…

Privacy-preserving data mining has become an important topic. People have built several multi-party-computation (MPC)-based frameworks to provide theoretically guaranteed privacy, the poor performance of real-world algorithms have always…

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…