Abstract-In graph-based learning models, entities are often represented as vertices in an undirected graph with weighted edges describing the relationships between entities. In many real-world applications, however, entities are often associated with relations of different types and/or from different sources, which can be well captured by multiple undirected graphs over the same set of vertices. How to exploit such multiple sources of information to make better inferences on entities remains an interesting open problem. In this paper, we focus on the problem of clustering the vertices based on multiple graphs in both unsupervised and semi-supervised settings. As one of our contributions, we propose Linked Matrix Factorization (LMF) as a novel way of fusing information from multiple graph sources. In LMF, each graph is approximated by matrix factorization with a graph-specific factor and a factor common to all graphs, where the common factor provides features for all vertices. Experiments on SIAM journal data show that (1) we can improve the clustering accuracy through fusing multiple sources of information with several models, and (2) LMF yields superior or competitive results compared to other graph-based clustering methods.

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An elderly population refers to the proportion of persons age 65 years or older out of the total population. The World Health Organization (WHO) and the United Nations define an "aging society" as one in which more than 7% of the population is 65 years or older, an "aged society" as a society in which more than 14% of the population is 65 years or older, and a "super-aged society" as a society in which more than 21% of the population is 65 years or older (1,2). Japan is experiencing population aging that is unprecedented. The elderly population (65 years or older) in Japan only accounted for about 5% of the total population in 1950, but that proportion exceeded 7% in 1970 and 14% in 1994. The rate of aging has continued to increase, reaching 21.5% in 2007 (3) and 28.1% in 2018 (4). The elderly population of Japan is forecast to continue to grow in the future and is expected to account for 33.3% of the population in 2036 and 38.4% in 2065 (Figure 1). In other words, 1 in 2.6 persons in the Japanese population will be elderly in 2065 (4). At the same time, progress in medical technology has decreased mortality rates, prolonging the mean life Summary Japan is experiencing unprecedented aging of its population. People age 65 years or older accounted for 28.1% of the total population in 2018, and that proportion is expected to reach 33.3% in 2036 and 38.4% in 2065. In 2017, the average life expectancy in Japan was 81.09 years for men and 87.26 years for women. By 2065, it is expected to reach 84.95 years for men and 91.35 years for women. Population aging affects health and long-term care systems. The government proposed the establishment of "a community-based integrated care system" by 2025 with the purpose of comprehensively ensuring the provision of health care, nursing care, preventive care, housing, and livelihood support. This will require health care and nursing care professionals who are capable of fully understanding the physical and mental characteristics of elderly people and the fostering of organic collaboration with others professionals in the community-based integrated care system. A department of gerontology or geriatric medicine is desired to be established in each medical school to teach students medicine and efficient medical care, to conduct research, and to develop personnel to facilitate this paradigm shift. In 2018, there were 263 colleges of nursing with an admissions capacity of 23,667. In Japan, Certified Nurse Specialists can specialize in 13 areas as of December 2016. The number of Certified Nurse Specialists increased to 2,279 as of December 2018. One hundred and forty-four of those specialists specialized in Gerontological Nursing while 53 specialized in Home Care Nursing. The number of nurses specializing in Gerontological Nursing and Home Care Nursing is desired to be increased in order to implement and improve community-based comprehensive care.

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