Related papers: Nonlinear Dimensionality Reduction for Discriminat…
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…
Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…
Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience.…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust…
We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…
Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…
Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…
As an unsupervised dimensionality reduction method, principal component analysis (PCA) has been widely considered as an efficient and effective preprocessing step for hyperspectral image (HSI) processing and analysis tasks. It takes each…
Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…