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Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
Stochastic modelling provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. In practice, the common challenge is to calibrate a large number of model parameters against the…
Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…
The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate…
Recent research demonstrated that training large language models involves memorization of a significant fraction of training data. Such memorization can lead to privacy violations when training on sensitive user data and thus motivates 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…
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…
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…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
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…
Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In many…
Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…