Related papers: Dimensionality reduction, and function approximati…
High-dimensional measurements are often correlated which motivates their approximation by factor models. This holds also true when features are engineered via low-dimensional interactions or kernel tricks. This often results in over…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
The high dimensional nature of genomics data complicates feature selection, in particular in low sample size studies - not uncommon in clinical prediction settings. It is widely recognized that complementary data on the features, `co-data',…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and…
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…
Structured width pruning of GLU-MLP layers, guided by the Maximum Absolute Weight (MAW) criterion, reveals a systematic dichotomy in how reducing the expansion ratio affects different model capabilities. While performance on tasks relying…
Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…
Globally, chronic liver disease continues to be a major health concern that requires precise predictive models for prompt detection and treatment. Using the Indian Liver Patient Dataset (ILPD) from the University of California at Irvine's…
Data dimension reduction (DDR) is all about mapping data from high dimensions to low dimensions, various techniques of DDR are being used for image dimension reduction like Random Projections, Principal Component Analysis (PCA), the…
Predicting the dissolution rates of silicate glasses in aqueous conditions is a complex task as the underlying mechanism(s) remain poorly understood and the dissolution kinetics can depend on a large number of intrinsic and extrinsic…
In this paper, we apply the Logistic PCA (LPCA) as a dimensionality reduction tool for visualizing patterns and characterizing the relevance of mathematics abilities from a given population measured by a large-scale assessment. We establish…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…
Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neural networks (CNNs) and linear discriminant analysis (LDA) as…