| 研究実績の概要 |
In this year, we are working on representation of data that are faithful to the original features as well as having cluster structures. We investigated the method of convex clustering to obtain a representation using a convex program, which is efficient and globally optimal.
The key idea is to assume that data follows cluster structures. For that, we cluster the data using convex clustering. The advantage of convex clustering is that it is a convex program that guarantees optimality. Another advantage is that it offers a relaxation of k-means and agglomerative clustering algorithms, offering potential advantages of the two algorithms.
Our main work here is to analyze analytically what are the clusters that are obtained by convex clustering, pros and cons compared to the other two algorithms. We found that convex cluster only can learn convex clusters. This is similar to k-means and different from agglomerative clustering. We also found that the clusters can be bounded in balls, making them round-shaped. These clusters are found to have gaps between them. These properties show that convex clustering found rather specific types of clusters, rather inflexible compare to the other algorithms.
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