Related papers: Axes that matter: PCA with a difference
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Data collection often results in records that have missing values or variables. This investigation compares 3 different data imputation models and identifies their merits by using accuracy measures. Autoencoder Neural Networks, Principal…
The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to…
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…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…
Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In…
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…
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…
Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
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…
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…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
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…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…