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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…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
Environmental health researchers often aim to identify sources/behaviors that give rise to potentially harmful exposures. We adapted principal component pursuit (PCP)-a robust technique for dimensionality reduction in computer vision and…
In the past decades, exactly recovering the intrinsic data structure from corrupted observations, which is known as robust principal component analysis (RPCA), has attracted tremendous interests and found many applications in computer…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Particle Image Velocimetry (PIV) data processing procedures are adversely affected by light reflections and backgrounds as well as defects in the models and sticky particles that occlude the inner walls of the boundaries. In this paper, a…
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.…
This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…
Deep learning models hold state of the art performance in many fields, yet their design is still based on heuristics or grid search methods that often result in overparametrized networks. This work proposes a method to analyze a trained…
In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Latency is one of the most critical performance metrics for a wide range of applications. Therefore, it is important to understand the underlying mechanisms that give rise to the observed latency values and diagnose the ones that are…
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case…
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…