The observation matrix is approximated by a non-negative matrix factorization as the product of the base matrix and the coefficient matrix. Since the coefficient vector differs between individuals, the coefficient matrix is represented as the product of the parameter and covariate matrices. In general, the use of a covariate matrix reduces the accuracy of the approximation, but in this paper, the use of a Gaussian kernel for the covariates suppresses this reduction.Gaussian kernels provide smooth coefficients and predictions for changes in covariates, making them easy to interpret. The usefulness of the proposed method is demonstrated by applying it to text data and longitudinal measures and comparing it to the case where the covariates are not used.

In material design, the establishment of a process-structure-property linkage is indispensable for developing a general methodology for inverse material design and understanding the physical mechanisms behind material microstructure generation. In recent years, deep learning based methods have received much attention in the field of computational material design. Thus, we developed the general deep learning methodology for extraction of a process-structure-property linkage.Our approach can be divided into two parts: characterization of material microstructures by a vector quantized variational auto-encoder, and determination of the correlation between the extracted microstructure characterizations and the given conditions, such as processing parameters and/or material properties, by a pixel convolutional neural network. In this work, we present the following three our recent results: (i) extraction of the process-structure relationship of structural material by our deep learning framework, (ii) identification of a part of microstructures critically affecting the target property without giving the background physics, and (iii) molecular structure optimization by PixelCNN.

Clustering is an unsupervised learning method, which aims to classify objects according to differences in their underlying generative mechanisms. When classification predictions differ for objects depending on the selected features, a multiple clustering method which performs feature selection and object clustering simultaneously is particularly useful. In this paper, we focus on a specific type of clustering method (MCW), which performs multiple clustering for correlation matrices based on matrix partitioning. MCW is formalized as an extension of Wishart mixture models, and can identify multiple cluster solutions by inferring the block diagonalized structure of correlation matrices. In this study, we applied MCW to the seismic station selection problem for effectively detecting low-frequency earthquakes, which are local events occurring ubiquitously. To date, no solutions have been found for this problem. We applied MCW to the correlation matrices of spectrograms of low-frequency earthquake waveforms obtained from multiple seismic stations, which produced an optimal partitioning of seismic stations in terms of multiple clustering. As a result, a spatial correspondence between the selected seismic stations and the epicenters of low-frequency earthquakes was found, and the low-frequency earthquakes were classified into several clusters. Further, good reproducibility of the detection rate of low-frequency earthquakes was confirmed for specific selected seismic stations using validation data.