Discover the Semantic Topology in High-Dimensional Data

Discovering the homogeneous concept groups in the high-dimensional data sets and clustering them accordingly are contemporary challenge. Conventional clustering techniques often based on Euclidean metric. However, the metric is ad hoc not intrinsic to the semantic of the documents. In this paper, we are proposing a novel approach, in which the semantic space of high-dimensional data is structured as a simplicial complex of Euclidean space (a hypergraph but with different focus). Such a simplicial structure intrinsically captures the semantic of the data; for example, the coherent topics of documents will appear in the same connected component. Finally, we cluster the data by the structure of concepts, which is organized by such a geometry.