Estimating Cluster Overlap on Manifolds and its Application to Neuropsychiatric Disorders

Although it is usually assumed in many pattern recognition problems that different patterns are distinguishable, some patterns may have inseparable overlap. For example, some facial expressions involve subtle muscle movements, and are difficult to separate from other expressions or neutral faces. In this paper, we consider such overlapped patterns as "clusters", and present a novel method to quantify cluster overlap based on the Bayes error estimation on manifolds. Our method first applies a manifold learning method, ISOMAP, to discover the intrinsic structure of data, and then measures the overlap of different clusters using the k-NN Bayes error estimation on the learned manifolds. Due to the ISOMAP"s capability of preserving geodesic distances and k-NN\´s localized estimation, the method can provide an accurate measure of the overlap between clusters, as demonstrated by our simulation experiments. The method is further applied for an analysis of a specific type of facial expression impairment in schizophrenia, i.e.,"flat effect", which refers to a severe reduction in emotional expressiveness. In this study, we capture facial expressions of individuals, and quantify their expression flatness by estimating overlap between different facial expressions. The experimental results show that the patient group has much larger facial expression overlap than the control group, and demonstrate that the flat affect is an important symptom in diagnosing schizophrenia patients.