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Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…
Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. It extends principal component analysis (PCA) and can extract important and complicated components with small…
Reducing dimensionality is a key preprocessing step in many data analysis applications to address the negative effects of the curse of dimensionality and collinearity on model performance and computational complexity, to denoise the data or…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
Neural networks enjoy widespread use, but many aspects of their training, representation, and operation are poorly understood. In particular, our view into the training process is limited, with a single scalar loss being the most common…
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…
Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…
Recent years have seen growing interest in learning disentangled representations, in which distinct features, such as size or shape, are represented by distinct neurons. Quantifying the extent to which a given representation is disentangled…
For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world…
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…
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,…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…
Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…