scholarly journals Principal Component Analysis Applied to Gradient Fields in Band Gap Optimization Problems for Metamaterials

2021 ◽  
Vol 2015 (1) ◽  
pp. 012047
Author(s):  
Giorgio Gnecco ◽  
Andrea Bacigalupo ◽  
Francesca Fantoni ◽  
Daniela Selvi
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Band Gap ◽  
Optimization Problems ◽  
Principal Component ◽  
Component Analysis ◽  
Physical Models ◽  
Supervised Machine Learning ◽  
Iterative Optimization ◽  
Gradient Based

Abstract A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based iterative optimization algorithms to the numerical solution of such problems is typically highly demanding, due to the complexity of the underlying physical models. Nevertheless, supervised machine learning techniques can reduce such a computational effort, e.g., by replacing the original objective functions of such optimization problems with more-easily computable approximations. In this framework, the present article describes the application of a related unsupervised machine learning technique, namely, principal component analysis, to approximate the gradient of the objective function of a band gap optimization problem for an acoustic metamaterial, with the aim of making the successive application of a gradient-based iterative optimization algorithm faster. Numerical results show the effectiveness of the proposed method.

Classification of Observations through Combination of the Dimension Reduction and the Cluster Analysis

2017 ◽  
Vol 7 (8) ◽  
pp. 30
Author(s):  
Hyeuk Kim
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Cluster Analysis ◽  
Unsupervised Learning ◽  
Principal Component ◽  
Component Analysis ◽  
Baseball Players ◽  
Partitioning Around Medoids ◽  
Different Characteristics

Unsupervised learning in machine learning divides data into several groups. The observations in the same group have similar characteristics and the observations in the different groups have the different characteristics. In the paper, we classify data by partitioning around medoids which have some advantages over the k-means clustering. We apply it to baseball players in Korea Baseball League. We also apply the principal component analysis to data and draw the graph using two components for axis. We interpret the meaning of the clustering graphically through the procedure. The combination of the partitioning around medoids and the principal component analysis can be used to any other data and the approach makes us to figure out the characteristics easily.

Analysis of the Bath Motion in the MM-SQC Dynamics Using Unsupervised Machine Learning Dimensionality Reduction Approaches: Principal Component Analysis

2020 ◽  
Author(s):  
Jiawei Peng ◽  
Yu Xie ◽  
Deping Hu ◽  
Zhenggang Lan
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Collective Motion ◽  
Principal Component ◽  
Component Analysis ◽  
Nonadiabatic Dynamics ◽  
Trajectory Data ◽  
Unsupervised Machine Learning ◽  
Physical Knowledge ◽  
Vibronic Couplings

The system-plus-bath model is an important tool to understand nonadiabatic dynamics for large molecular systems. The understanding of the collective motion of a huge number of bath modes is essential to reveal their key roles in the overall dynamics. We apply the principal component analysis (PCA) to investigate the bath motion based on the massive data generated from the MM-SQC (symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian) nonadiabatic dynamics of the excited-state energy transfer dynamics of Frenkel-exciton model. The PCA method clearly clarifies that two types of bath modes, which either display the strong vibronic couplings or have the frequencies close to electronic transition, are very important to the nonadiabatic dynamics. These observations are fully consistent with the physical insights. This conclusion is obtained purely based on the PCA understanding of the trajectory data, without the large involvement of pre-defined physical knowledge. The results show that the PCA approach, one of the simplest unsupervised machine learning methods, is very powerful to analyze the complicated nonadiabatic dynamics in condensed phase involving many degrees of freedom.

scholarly journals Criteria for choosing the number of dimensions in a principal component analysis: An empirical assessment

2020 ◽  
Author(s):  
Renata Silva ◽  
Daniel Oliveira ◽  
Davi Pereira Santos ◽  
Lucio F.D. Santos ◽  
Rodrigo Erthal Wilson ◽  
...  
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Hypothesis Test ◽  
Feature Learning ◽  
Principal Component ◽  
Component Analysis ◽  
Scree Plot ◽  
Open Issue ◽  
Chained Tasks ◽  
High Dimensional Datasets

Principal component analysis (PCA) is an efficient model for the optimization problem of finding d' axes of a subspace Rd' ⊆ Rd so that the mean squared distances from a given set R of points to the axes are minimal. Despite being steadily employed since 1901 in different scenarios, e.g., mechanics, PCA has become an important link in machine learning chained tasks, such as feature learning and AutoML designs. A frequent yet open issue that arises from supervised-based problems is how many PCA axes are required for the performance of machine learning constructs to be tuned. Accordingly, we investigate the behavior of six independent and uncoupled criteria for estimating the number of PCA axes, namely Scree-Plot %, Scree Plot Gap, Kaiser-Guttman, Broken-Stick, p-Score, and 2D. In total, we evaluate the performance of those approaches in 20 high dimensional datasets by using (i) four different classifiers, and (ii) a hypothesis test upon the reported F-Measures. Results indicate Broken-Stick and Scree-Plot % criteria consistently outperformed the competitors regarding supervised-based tasks, whereas estimators Kaiser-Guttman and Scree-Plot Gap delivered poor performances in the same scenarios.

Tropical principal component analysis on the space of phylogenetic trees

2020 ◽  
Vol 36 (17) ◽  
pp. 4590-4598
Author(s):  
Robert Page ◽  
Ruriko Yoshida ◽  
Leon Zhang
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Phylogenetic Trees ◽  
Principal Component ◽  
Component Analysis ◽  
Fixed Number ◽  
Supplementary Information ◽  
Gene Trees ◽  
Learning Methods ◽  
Machine Learning Methods

Abstract Motivation Due to new technology for efficiently generating genome data, machine learning methods are urgently needed to analyze large sets of gene trees over the space of phylogenetic trees. However, the space of phylogenetic trees is not Euclidean, so ordinary machine learning methods cannot be directly applied. In 2019, Yoshida et al. introduced the notion of tropical principal component analysis (PCA), a statistical method for visualization and dimensionality reduction using a tropical polytope with a fixed number of vertices that minimizes the sum of tropical distances between each data point and its tropical projection. However, their work focused on the tropical projective space rather than the space of phylogenetic trees. We focus here on tropical PCA for dimension reduction and visualization over the space of phylogenetic trees. Results Our main results are 2-fold: (i) theoretical interpretations of the tropical principal components over the space of phylogenetic trees, namely, the existence of a tropical cell decomposition into regions of fixed tree topology; and (ii) the development of a stochastic optimization method to estimate tropical PCs over the space of phylogenetic trees using a Markov Chain Monte Carlo approach. This method performs well with simulation studies, and it is applied to three empirical datasets: Apicomplexa and African coelacanth genomes as well as sequences of hemagglutinin for influenza from New York. Availability and implementation Dataset: http://polytopes.net/Data.tar.gz. Code: http://polytopes.net/tropica_MCMC_codes.tar.gz. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Multivariate Analysis and Machine Learning for Ripeness Classification of Cape Gooseberry Fruits

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 928 ◽  
Author(s):  
Miguel De-la-Torre ◽  
Omar Zatarain ◽  
Himer Avila-George ◽  
Mirna Muñoz ◽  
Jimy Oblitas ◽  
...  
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Feature Selection ◽  
Principal Component ◽  
Component Analysis ◽  
Support Vector ◽  
Color Spaces ◽  
Combination Methods ◽  
Fruit Samples ◽  
Cape Gooseberry

This paper explores five multivariate techniques for information fusion on sorting the visual ripeness of Cape gooseberry fruits (principal component analysis, linear discriminant analysis, independent component analysis, eigenvector centrality feature selection, and multi-cluster feature selection.) These techniques are applied to the concatenated channels corresponding to red, green, and blue (RGB), hue, saturation, value (HSV), and lightness, red/green value, and blue/yellow value (L*a*b) color spaces (9 features in total). Machine learning techniques have been reported for sorting the Cape gooseberry fruits’ ripeness. Classifiers such as neural networks, support vector machines, and nearest neighbors discriminate on fruit samples using different color spaces. Despite the color spaces being equivalent up to a transformation, a few classifiers enable better performances due to differences in the pixel distribution of samples. Experimental results show that selection and combination of color channels allow classifiers to reach similar levels of accuracy; however, combination methods still require higher computational complexity. The highest level of accuracy was obtained using the seven-dimensional principal component analysis feature space.

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