Spectral analysis of cell-graphs of cancer

In this paper, we investigate the properties of the cell-graphs by using the spectral graph theory. The spectral analysis is performed on (i) the adjacency matrix of a cell-graph, and (ii) the normalized Laplacian of the cell-graph. We show that the spectra of the cell-graphs of cancerous tissues are unique and the features extracted from these spectra distinguish the cancerous (malignant glioma) tissues from the healthy and benign reactive/inflammatory processes. Our experiments on 646 brain biopsy samples of 60 different patients demonstrate that by using spectral features defined on the normalized Laplacian of the graph, we achieve 100% accuracy in the classification of cancerous and healthy tissues. In the classification of cancerous and benign tissues, our experiments yield 92% and 89% accuracy on the testing set for the cancerous and benign tissues. We also analyze graph spectra to identify the distinctive spectral features of the cancerous tissues to conclude that (i) the features representing the cellular density are the most distinctive features to distinguish the cancerous and healthy tissues, (ii) and the number of the eigenvalues in the normalized Laplacian spectrum that have a value of 0 is the most distinctive feature to distinguish the cancerous and benign tissues. ∗ Present address: Oregon Health and Science University, Department of Pathology, Portland, OR. Technical report, Rensselaer Polytechnic Institute, Department of Computer Science, TR-04-17.