相关论文: Learning phase transitions: comparing PCA and SVM

We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with…

A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…

In this paper, we use support vector machines (SVM) to develop a machine learning framework to discover phase space structures that distinguish between distinct reaction pathways. The SVM model is trained using data from trajectories of…

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection…

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…

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions…

Machine learning algorithms provide a new perspective on the study of physical phenomena. In this paper, we explore the nature of quantum phase transitions using multi-color convolutional neural-network (CNN) in combination with quantum…

Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…

We propose a two-stage approach Spec PC-CP to identify change points in multivariate time series. In the first stage, we obtain a low-dimensional summary of the high-dimensional time series by Spectral Principal Component Analysis…

In this paper, we analyze the applicability of the principal component analysis (PCA) as a tool to extract the Sq variation of the geomagnetic field. We tested different geomagnetic field components and used data measured at different…

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and…

Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…

We devise new quantum algorithms that exponentially speeds up the training and prediction procedures of twin support vector machines (TSVM). To train TSVMs using quantum methods, we demonstrate how to prepare the desired input states…

Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Learning many-body quantum states and quantum phase transitions remains a major challenge in quantum many-body physics. Classical machine learning methods offer certain advantages in addressing these difficulties. In this work, we propose a…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…