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Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches…

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…

Anomaly detection is challenging, especially for large datasets in high dimensions. Here we explore a general anomaly detection framework based on dimensionality reduction and unsupervised clustering. We release DRAMA, a general python…

Representational Similarity Analysis (RSA) aims to explore similarities between neural activities of different stimuli. Classical RSA techniques employ the inverse of the covariance matrix to explore a linear model between the neural…

Dimensionality reduction (DR) offers a useful representation of complex high-dimensional data. Recent DR methods focus on hyperbolic geometry to derive a faithful low-dimensional representation of hierarchical data. However, existing…

We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…

Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (obser- vations), makes…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Previous studies on image classification have mainly focused on the performance of the networks, not on real-time operation or model compression. We propose a Gaussian Deep Recurrent visual Attention Model (GDRAM)- a reinforcement learning…

We propose a new dimensionality reduction toolkit designed to address some of the challenges faced by traditional methods like UMAP and tSNE such as loss of global structure and computational efficiency. Built on the JAX framework, DiRe…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

We introduce a new approximate multiresolution analysis (MRA) using a single Gaussian as the scaling function, which we call Gaussian MRA (GMRA). As an initial application, we employ this new tool to accurately and efficiently compute the…

Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…

Stereo depth estimation is used for many computer vision applications. Though many popular methods strive solely for depth quality, for real-time mobile applications (e.g. prosthetic glasses or micro-UAVs), speed and power efficiency are…

Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their…

Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…

Motivation: Microarray experiments result in large scale data sets that require extensive mining and refining to extract useful information. We have been developing an efficient novel algorithm for nonmetric multidimensional scaling (nMDS)…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…

Computer-assisted diagnosis (CAD) based on deep learning has become a crucial diagnostic technology in the medical industry, effectively improving diagnosis accuracy. However, the scarcity of brain tumor Magnetic Resonance (MR) image…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…