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Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized…
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…
Handwritten digit images lie in a high-dimensional pixel space but exhibit strong geometric and statistical structure. This paper investigates the latent organization of handwritten digits in the MNIST dataset using three complementary…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
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…
This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…
Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…
In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of…
With the development of modern technologies such as IFUs, it is possible to obtain data cubes in which one produces images with spectral resolution. To extract information from them can be quite complex, and hence the development of new…
We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra corresponding to the symmetry group of the underlying manifold. We…