A Statistical Approach to Set Classification by Feature Selection with Applications to Classification of Histopathology Images

摘要

Set classification problems arise when classification tasks are based on setsof observations as opposed to individual observations. In set classification, aclassification rule is trained with $N$ sets of observations, where each set islabeled with class information, and the prediction of a class label isperformed also with a set of observations. Data sets for set classificationappear, for example, in diagnostics of disease based on multiple cell nucleusimages from a single tissue. Relevant statistical models for set classificationare introduced, which motivate a set classification framework based oncontext-free feature extraction. By understanding a set of observations as anempirical distribution, we employ a data-driven method to choose those featureswhich contain information on location and major variation. In particular, themethod of principal component analysis is used to extract the features of majorvariation. Multidimensional scaling is used to represent features asvector-valued points on which conventional classifiers can be applied. Theproposed set classification approaches achieve better classification resultsthan competing methods in a number of simulated data examples. The benefits ofour method are demonstrated in an analysis of histopathology images of cellnuclei related to liver cancer.