Diffusion Map Approach to Classifying Early Stage Cardiac Dysfunction

Magnetic resonance (MR) tagging technology can assist us in determining the motions of the myocardial pixels in a sequence of MR images. This paper presents a semi-supervised algorithm that processes these motion maps and classifies automatically myocardial dysfunctional motions. In distinction with other methods, our algorithm requires that only a few normal motions are labeled a priori. This is significant because, while normal motions can be confidently labeled by a human expert, abnormal motions are very difficult to label with high reliability by an operator. We use a graph to capture the motion map of the left ventricle. The normalized weighted adjacency matrix of the graph is interpreted as a stochastic matrix. Performing random walks, or diffusion, on the graph determines how similar myocardial motions are. Similar motions on the graph are represented by the diffusion maps framework as closer vectors in a Euclidean space. In the Euclidean space, we adopt eigen-analysis on a small portion of labeled normal motions. The analysis leads to a hyperelliptic surface that classifies the remaining cardiac motions as normal or dysfunctional.