Affinity aggregation for spectral clustering

Spectral clustering makes use of spectral-graph structure of an affinity matrix to partition data into disjoint meaningful groups. Because of its elegance, efficiency and good performance, spectral clustering has become one of the most popular clustering methods. Traditional spectral clustering assumes a single affinity matrix. However, in many applications, there could be multiple potentially useful features and thereby multiple affinity matrices. To apply spectral clustering for these cases, a possible way is to aggregate the affinity matrices into a single one. Unfortunately, affinity measures constructed from different features could have different characteristics. Careless aggregation might make even worse clustering performance. This paper proposes an affinity aggregation spectral clustering (AASC) algorithm which extends spectral clustering to a setting with multiple affinities available. AASC seeks for an optimal combination of affinity matrices so that it is more immune to ineffective affinities and irrelevant features. This enables the construction of similarity or distance-metric measures for clustering less crucial. Experiments show that AASC is effective in simultaneous clustering and feature fusion, thus enhancing the performance of spectral clustering by employing multiple affinities.