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Within scientific and real life problems, classification is a typical case of extremely complex tasks in data-driven scenarios, especially if approached with traditional techniques. Machine Learning supervised and unsupervised paradigms,…

The latent class model is a widely used mixture model for multivariate discrete data. Besides the existence of qualitatively heterogeneous latent classes, real data often exhibit additional quantitative heterogeneity nested within each…

Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In…

Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…

Structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function. CryoEM provides direct visualization of individual macromolecules sampling different conformational and compositional states.…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

The identification of different homogeneous groups of observations and their appropriate analysis in PLS-SEM has become a critical issue in many appli- cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all units on…

Quantifying local structures in self-assembled systems is a central challenge in soft matter and materials science. When no a priori knowledge of the relevant structures is available, traditional order parameters often fall short.…

In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…

In high-energy heavy-ion collisions, structures in the initial collision zone are a matter of intense investigation, both from theory and experimental points of view. A large number of models have been developed to represent the initial…

We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…

From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous…

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in…

We describe a robust, fast, and memory-efficient procedure that can cluster millions of structures derived from molecular dynamics simulations. The essence of the method is based on a peak-picking algorithm applied to three- and…

The relationship between structure and dynamics in glassy fluids remains an intriguing open question. Recent work has shown impressive advances in our ability to predict local dynamics using structural features, most notably due to the use…

We use the ``isoconfigurational ensemble'' [Phys. Rev. Lett. {\bf 93}, 135701 (2004)] to analyze both dynamical and structural properties in simulations of a glass forming molecular liquid. We show that spatially correlated clusters of low…