Related papers: Discovering Phases, Phase Transitions and Crossove…

We investigate the two-dimensional melting of deformable polymeric particles with multi-body interactions described by the Voronoi model. We report machine learning evidence for the existence of the intermediate hexatic phase in this…

Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

The main question raised in the article is whether a neural network trained on a spin lattice model in one universality class can be used to test a model in another universality class. The quantities of interest are the critical phase…

Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degrees of freedom undergoes a second-order…

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…

Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries also from noisy and imperfect data and…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

As one of the newest members in the field of artificial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data,…

The phase transitions in the transverse field Ising model in a competing spatially modulated (periodic and oscillatory) longitudinal field are studied numerically. There is a multiphase point in absence of the transverse field where the…

In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

We show that the ground-state quantum correlations of an Ising model can be detected by monitoring the time evolution of a single spin alone, and that the critical point of a quantum phase transition is detected through a maximum of a…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

We propose a novel exemplar selection approach based on Principal Component Analysis (PCA) and median sampling, and a neural network training regime in the setting of class-incremental learning. This approach avoids the pitfalls due to…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…