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Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction.…

Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…

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…

Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a…

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…

High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…

Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…

Bibliometric mapping and visualization techniques represent one of the main pillars in the field of scientometrics. Traditionally, the main methodologies employed for representing data are Multi-Dimensional Scaling, Principal Component…

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…

Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…

This study investigates privacy leakage in dimensionality reduction methods through a novel machine learning-based reconstruction attack. Employing an informed adversary threat model, we develop a neural network capable of reconstructing…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…

The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…

Vector Symbolic Architecture (VSA) is emerging in machine learning due to its efficiency, but they are hindered by issues of hyperdimensionality and accuracy. As a promising mitigation, the Low-Dimensional Computing (LDC) method…

The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…