Related papers: nD-PDPA: nDimensional Probability Density Profile …

Nuclear magnetic resonance (NMR) spectroscopy is one of the leading techniques for protein studies. The method features a number of properties, allowing to explain macromolecular interactions mechanistically and resolve structures with…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a…

Traditional approaches to elucidation of protein structures by NMR spectroscopy rely on distance restraints also known as nuclear Overhauser effects (NOEs). The use of NOEs as the primary source of structure determination by NMR…

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

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…

Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Proteins are essential for maintaining life. For example, knowing the structure of a protein, cell regulatory mechanisms of organisms can be modeled, supporting the development of disease treatments or the understanding of relationships…

The advent of highly accurate protein structure prediction methods has fueled an exponential expansion of the protein structure database. Consequently, there is a rising demand for rapid and precise structural homolog search. Traditional…

While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…

Despite the constant evolution of similarity searching research, it continues to face the same challenges stemming from the complexity of the data, such as the curse of dimensionality and computationally expensive distance functions.…

Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data. However, we argue that it is possible to have reconstructed data identically distributed as the original…

Proteins perform much of the work in living organisms, and consequently the development of efficient computational methods for protein representation is essential for advancing large-scale biological research. Most current approaches…

Learning meaningful protein representation is important for a variety of biological downstream tasks such as structure-based drug design. Having witnessed the success of protein sequence pretraining, pretraining for structural data which is…

Protein structure reconstruction from Nuclear Magnetic Resonance (NMR) experiments largely relies on computational algorithms. Recently, some effective low-rank matrix completion (MC) methods, such as ASD and ScaledASD, have been…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Traditional approaches to elucidation of protein structures by NMR spectroscopy rely on distance restraints also know as nuclear Overhauser effects (NOEs). The use of NOEs as the primary source of structure determination by NMR spectroscopy…