Dynamic affinity graph construction for spectral clustering using multiple features

Spectral clustering (SC) has been widely applied to various computer vision tasks, where the key is to construct a robust affinity matrix for data partitioning. With the increase in visual features, conventional SC methods are facing two challenges: 1) how to effectively generate an affinity matrix based on multiple features? and 2) how to deal with high-dimensional visual features which could be redundant? To address these issues mentioned earlier, we present a new approach to: 1) learn a robust affinity matrix using multiple features, allowing us to simultaneously determine optimal weights for each feature; and 2) decide a set of optimal projection matrices, one for each feature, that decide the lower dimensional space, as well as the optimal affinity weight of each data pair in the lower dimensional space. There are two major advantages of our new approach over the existing clustering techniques. First, our approach assigns affinity weights for data points on a per-data-pair basis. The learning procedure avoids the explicit specification of the size of the neighborhood in the affinity matrix, and the bandwidth parameter required to compute the Gaussian kernel, both of which are sensitive and yet difficult to determine beforehand. Second, the affinity weights are based on the distances in a lower dimensional space, while the low-dimensional space is inferred according to the optimized affinity weights. Both variables are jointly optimized so as to leverage mutual benefits. The experimental results outperform the compared alternatives, which indicate that the proposed method is effective in simultaneously learning the affinity graph and feature fusion, resulting in better clustering results.