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Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…
The present paper applied Principal Component Analysis (PCA) for grouping of machines and parts so that the part families can be processed in the cells formed by those associated machines. An incidence matrix with binary entries has been…
This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where…
Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in the existing literature. To address this issue and achieve robustness, we propose an…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…
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…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
High-resolution spectroscopy of strong chromospheric absorption lines delivers nowadays several millions of spectra per observing day, when using fast scanning devices to cover large regions on the solar surface. Therefore, fast and robust…
Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other…
The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…
In the current data-intensive era, big data has become a significant asset for Artificial Intelligence (AI), serving as a foundation for developing data-driven models and providing insight into various unknown fields. This study navigates…
The present paper attempts to generate visual clustering and data extraction of cell formation problem using both principal component analysis (PCA) and self organizing map (SOM) from input of sequence based machine-part incidence matrix.…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…