Factor Analysis on a Graph

Masayuki Karasuyama, Hiroshi Mamitsuka
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1117-1126, 2018.

Abstract

Graph is a common way to represent relationships among a set of objects in a variety of application areas of machine learning. We consider the case that the input data is not only a graph but also numerical features in which one of the given features corresponds to a node in the graph. Then, the primary importance is often in understanding interactions on the graph nodes which effect on covariance structure of the numerical features. We propose a Gaussian based analysis which is a combination of graph constrained covariance matrix estimation and factor analysis (FA). We show that this approach, called graph FA, has desirable interpretability. In particular, we prove the connection between graph FA and a graph node clustering based on a perspective of kernel method. This connection indicates that graph FA is effective not only on the conventional noise-reduction explanation of the observation by FA but also on identifying important subgraphs. The experiments on synthetic and real-world datasets demonstrate the effectiveness of the approach.

Cite this Paper


BibTeX
@InProceedings{pmlr-v84-karasuyama18a, title = {Factor Analysis on a Graph}, author = {Masayuki Karasuyama and Hiroshi Mamitsuka}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1117--1126}, year = {2018}, editor = {Amos Storkey and Fernando Perez-Cruz}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/karasuyama18a/karasuyama18a.pdf}, url = { http://proceedings.mlr.press/v84/karasuyama18a.html }, abstract = {Graph is a common way to represent relationships among a set of objects in a variety of application areas of machine learning. We consider the case that the input data is not only a graph but also numerical features in which one of the given features corresponds to a node in the graph. Then, the primary importance is often in understanding interactions on the graph nodes which effect on covariance structure of the numerical features. We propose a Gaussian based analysis which is a combination of graph constrained covariance matrix estimation and factor analysis (FA). We show that this approach, called graph FA, has desirable interpretability. In particular, we prove the connection between graph FA and a graph node clustering based on a perspective of kernel method. This connection indicates that graph FA is effective not only on the conventional noise-reduction explanation of the observation by FA but also on identifying important subgraphs. The experiments on synthetic and real-world datasets demonstrate the effectiveness of the approach.} }
Endnote
%0 Conference Paper %T Factor Analysis on a Graph %A Masayuki Karasuyama %A Hiroshi Mamitsuka %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-karasuyama18a %I PMLR %P 1117--1126 %U http://proceedings.mlr.press/v84/karasuyama18a.html %V 84 %X Graph is a common way to represent relationships among a set of objects in a variety of application areas of machine learning. We consider the case that the input data is not only a graph but also numerical features in which one of the given features corresponds to a node in the graph. Then, the primary importance is often in understanding interactions on the graph nodes which effect on covariance structure of the numerical features. We propose a Gaussian based analysis which is a combination of graph constrained covariance matrix estimation and factor analysis (FA). We show that this approach, called graph FA, has desirable interpretability. In particular, we prove the connection between graph FA and a graph node clustering based on a perspective of kernel method. This connection indicates that graph FA is effective not only on the conventional noise-reduction explanation of the observation by FA but also on identifying important subgraphs. The experiments on synthetic and real-world datasets demonstrate the effectiveness of the approach.
APA
Karasuyama, M. & Mamitsuka, H.. (2018). Factor Analysis on a Graph. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1117-1126 Available from http://proceedings.mlr.press/v84/karasuyama18a.html .

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