ReD-SFA: Relation Discovery Based Slow Feature Analysis for Trajectory Clustering

For spectral embedding/clustering, it is still an open problem on how to construct an relation graph to reflect the intrinsic structures in data. In this paper, we proposed an approach, named Relation Discovery based Slow Feature Analysis (ReD-SFA), for feature learning and graph construction simultaneously. Given an initial graph with only a few nearest but most reliable pairwise relations, new reliable relations are discovered by an assumption of reliability preservation, i.e., the reliable relations will preserve their reliabilities in the learnt projection subspace. We formulate the idea as a cross entropy (CE) minimization problem to reduce the discrepancy between two Bernoulli distributions parameterized by the updated distances and the existing relation graph respectively. Furthermore, to overcome the imbalanced distribution of samples, a Boosting-like strategy is proposed to balance the discovered relations over all clusters. To evaluate the proposed method, extensive experiments are performed with various trajectory clustering tasks, including motion segmentation, time series clustering and crowd detection. The results demonstrate that ReD-SFA can discover reliable intra-cluster relations with high precision, and competitive clustering performance can be achieved in comparison with state-of-the-art.