Search

The clustering of categorical data is a common and important task in computer science, offering profound implications across a spectrum of applications. Unlike purely numerical data, categorical data often lack inherent ordering as in nominal data, or have varying levels of order as in ordinal data, thus requiring specialized methodologies for efficient organization and analysis. This review provides a comprehensive synthesis of categorical data clustering in the past twenty-five years, starting from the introduction of K-modes. It elucidates the pivotal role of categorical data clustering in diverse fields such as health sciences, natural sciences, social sciences, education, engineering and economics. Practical comparisons are conducted for algorithms having public implementations, highlighting distinguishing clustering methodologies and revealing the performance of recent algorithms on several benchmark categorical datasets. Finally, challenges and opportunities in the field are discussed.

As interdisciplinary science is flourishing because of materials informatics and additional factors; a systematic way is required for expressing knowledge and facilitating communication between scientists in various fields. A function decomposition tree is such a representation, but domain scientists face difficulty in constructing it. Thus, this study cites the general problems encountered by beginners in generating function decomposition trees and proposes a new function decomposition representation method based on a causality-first perspective for resolution of these problems. The causality-first decomposition tree was obtained from a workflow expressed according to the processing sequence. Moreover, we developed a program that performed automatic conversion using the features of the causality-first decomposition trees. The proposed method was applied to materials informatics to demonstrate the systematic representation of expert knowledge and its usefullness., Comment: 41 page, 13 figures

We propose a data-driven method to extract dissimilarity between materials, with respect to a given target physical property. The technique is based on an ensemble method with Kernel ridge regression as the predicting model; multiple random subset sampling of the materials is done to generate prediction models and the corresponding contributions of the reference training materials in detail. The distribution of the predicted values for each material can be approximated by a Gaussian mixture model. The reference training materials contributed to the prediction model that accurately predicts the physical property value of a specific material, are considered to be similar to that material, or vice versa. Evaluations using synthesized data demonstrate that the proposed method can effectively measure the dissimilarity between data instances. An application of the analysis method on the data of Curie temperature (TC) of binary 3d transition metal 4f rare earth binary alloys also reveals meaningful results on the relations between the materials. The proposed method can be considered as a potential tool for obtaining a deeper understanding of the structure of data, with respect to a target property, in particular., Comment: 10 pages, 3 figures

New Nd-Fe-B crystal structures can be formed via the elemental substitution of LATX host structures, including lanthanides LA, transition metals T, and light elements X as B, C, N, and O. The 5967 samples of ternary LATX materials that are collected are then used as the host structures. For each host crystal structure, a substituted crystal structure is created by substituting all lanthanide sites with Nd, all transition metal sites with Fe, and all light element sites with B. High throughput first-principles calculations are applied to evaluate the phase stability of the newly created crystal structures, and 20 of them are found to be potentially formable. A data driven approach based on supervised and unsupervised learning techniques is applied to estimate the stability and analyze the structure stability relationship of the newly created NdFeB crystal structures. For predicting the stability for the newly created NdFeB structures, three supervised learning models, kernel ridge regression, logistic classification, and decision tree model, are learned from the LATX host crystal structures; the models achieve the maximum accuracy and recall scores of 70.4 and 68.7 percent, respectively. On the other hand, our proposed unsupervised learning model based on the integration of descriptor-relevance analysis and a Gaussian mixture model achieves accuracy and recall score of 72.9 and 82.1 percent, respectively, which are significantly better than those of the supervised models. While capturing and interpreting the structure stability relationship of the NdFeB crystal structures, the unsupervised learning model indicates that the average atomic coordination number and coordination number of the Fe sites are the most important factors in determining the phase stability of the new substituted NdFeB crystal structures., Comment: 14 pages, 7 figures

In this study, we investigate the structure-stability relationship of hypothetical Nd-Fe-B crystal structures using descriptor-relevance analysis and the t-SNE dimensionality reduction method. 149 hypothetical Nd-Fe-B crystal structures are generated from 5967 LA-T-X host structures in Open Quantum Materials Database by using the elemental substitution method, with LA denoting lanthanides, T denoting transition metals, and X denoting light elements such as B, C, N and O. A hypothetical crystal structure is created by substituting all lanthanide sites with Nd, all transition metal sites with Fe, and all light element sites with B. High-throughput first-principle calculations are applied to evaluate the phase stability of these structures. Twenty of them are found to be potentially formable. The descriptor-relevance analysis on the orbital field matrix (OFM) materials' descriptor reveals the average atomic coordination number as the essential factor in determining the structure stability of these substituted Nd-Fe-B crystal structures. 19 among 20 hypothetical structures that are found potentially formable have an average coordination number larger than 6.5. In addition, all the local structures represented by the OFM descriptors are integrated into a visible space to study the detailed correlation between their characteristics and the stability of the crystal structure to which they belong. We discover that unstable substituted structures frequently carry Nd and Fe local structures with two prominent points: low average coordination numbers and fully occupied B neighboring atoms. Moreover, there are only three popular forms of B local structures appearing on all potentially formable substituted structures: cage networks, planar networks, and interstitial sites. The discovered relationships are promising to speed up the screening process for the new formable crystal structures., Comment: 12 pages, 8 figures

We propose a framework called HyperVAE for encoding distributions of distributions. When a target distribution is modeled by a VAE, its neural network parameters \theta is drawn from a distribution p(\theta) which is modeled by a hyper-level VAE. We propose a variational inference using Gaussian mixture models to implicitly encode the parameters \theta into a low dimensional Gaussian distribution. Given a target distribution, we predict the posterior distribution of the latent code, then use a matrix-network decoder to generate a posterior distribution q(\theta). HyperVAE can encode the parameters \theta in full in contrast to common hyper-networks practices, which generate only the scale and bias vectors as target-network parameters. Thus HyperVAE preserves much more information about the model for each task in the latent space. We discuss HyperVAE using the minimum description length (MDL) principle and show that it helps HyperVAE to generalize. We evaluate HyperVAE in density estimation tasks, outlier detection and discovery of novel design classes, demonstrating its efficacy., Comment: Accepted ECML-2021

In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that reflect their nature well. We perform a case study with a dataset of rare-earth transition metal crystalline compounds represented using the Orbital Field Matrix descriptor and the Coulomb Matrix descriptor. We perform predictions of the formation energies using k-nearest neighbors regression, ridge regression, and kernel ridge regression. Through detailed analyses of the yield prediction accuracy, we examine the relationship between the characteristics of the material representation and similarity measures, and the complexity of the energy function they can capture. Empirical experiments and theoretical analysis reveal that similarity measures and kernels that minimize the loss of materials distinctiveness improve the prediction performance.

We analyze Curie temperatures of rare-earth transition metal binary alloys with machine learning method. In order to select important descriptors and descriptor groups, we introduce newly developed subgroup relevance analysis and adopt the hierarchical clustering in the representation. We execute the exhaustive search and successfully illustrate the importance of descriptors and descriptor groups. We execute the exhaustive search and illustrate that our approach indeed leads to the successful selection of important descriptors and descriptor groups. It helps us to choose the combination of the descriptors and to understand the meaning of the selected combination of descriptors., Comment: 16 pages, 8 figures

We developed a method for measuring the similarity between materials, focusing on specific physical properties. The obtained information can be utilized to understand the underlying mechanisms and to support the prediction of the physical properties of materials. The method consists of three steps: variable evaluation based on non-linear regression, regression-based clustering, and similarity measurement with a committee machine constructed from the clustering results. Three datasets of well-characterized crystalline materials represented by critical atomic predicting variables are used as test beds. Herein, we focus on the formation energy, lattice parameter, and Curie temperature of the examined materials. Based on the information obtained on the similarities between the materials, a hierarchical clustering technique is applied to learn the cluster structures of the materials that facilitate interpreting the mechanism, and an improvement of regression models is introduced for predicting the physical properties of the materials. Our experiments show that rational and meaningful group structures can be obtained and that the prediction accuracy of the materials physical properties can be significantly increased, confirming the rationality of the proposed similarity measure., Comment: 13 pages

We propose a novel representation of crystalline materials named orbital-field matrix (OFM) based on the distribution of valence shell electrons. We demonstrate that this new representation can be highly useful in mining material data. Our experiment shows that the formation energies of crystalline materials, the atomization energies of molecular materials, and the local magnetic moments of the constituent atoms in transition metal--rare-earth metal bimetal alloys can be predicted with high accuracy using the OFM. Knowledge regarding the role of coordination numbers of transition-metal and rare-earth metal elements in determining the local magnetic moment of transition metal sites can be acquired directly from decision tree regression analyses using the OFM., Comment: 10 pages

The Curie temperature ($T_C$) of binary alloy compounds consisting of 3$d$ transition-metal and 4$f$ rare-earth elements is analyzed by a machine learning technique. We first demonstrate that nonlinear regression can accurately reproduce $T_C$ of the compounds. The prediction accuracy for $T_C$ is maximized when five to ten descriptors are selected, with the rare-earth concentration being the most relevant. We then discuss an attempt to utilize a regression-based model selection technique to learn the relation between the descriptors and the actuation mechanism of the corresponding physical phenomenon, i.e., $T_C$ in the present case., Comment: 4 pages