位相情報を保持したアトラス学習
Topologically-Informed Atlas Learning
穴を持つ多様体を単一チャートで埋め込む従来法の限界を克服するため、小さなチャートを位相的に問題のない範囲で統合してアトラスを構築する手法を提案し、合成多様体や人間の動作・関節物体の運動学モデルで有効性を示した。
著者: Thomas Cohn, Nikhil Devraj, Odest Chadwicke Jenkins
分類: cs.RO, cs.AI, cs.LG
原文アブストラクト
We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional Euclidean space by learning a coordinate chart, but it requires that the entire manifold can be embedded in a single chart. This is impossible for manifolds with holes. In such cases, it is necessary to learn an atlas: a collection of charts that collectively cover the entire manifold. We begin with many small charts, and combine them in a bottom-up approach, where charts are only combined if doing so will not introduce problematic topological features. When it is no longer possible to combine any charts, each chart is individually embedded with standard manifold learning techniques, completing the construction of the atlas. We show the efficacy of our method by constructing atlases for challenging synthetic manifolds; learning human motion embeddings from motion capture data; and learning kinematic models of articulated objects.
