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When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying…
This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of…
We present qrpca, a fast and scalable QR-decomposition principal component analysis package. The software, written in both R and python languages, makes use of torch for internal matrix computations, and enables GPU acceleration, when…
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
Fast Approximate Nearest Neighbor (ANN) search technique for high-dimensional feature indexing and retrieval is the crux of large-scale image retrieval. A recent promising technique is Product Quantization, which attempts to index…
We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method. We also discuss the dependent case where the covariance matrix $\Sigma$ is not…
Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes…
This work includes all the technical details of the Sequential Principal Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear and invertible feature extraction technique. The identified curvilinear features can be…
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…
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…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
Model identification is a crucial problem in chemical industries. In recent years, there has been increasing interest in learning data-driven models utilizing partial knowledge about the system of interest. Most techniques for model…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure…