Related papers: Parameterized Principal Component Analysis
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…
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…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local…
Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
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…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…
The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs). However, when used as a precursor to independent component analysis (ICA) for…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…