Principal components null space analysis for image and video classification

We present a new classification algorithm, principal component null space analysis (PCNSA), which is designed for classification problems like object recognition where different classes have unequal and nonwhite noise covariance matrices. PCNSA first obtains a principal components subspace (PCA space) for the entire data. In this PCA space, it finds for each class "i," an Mi-dimensional subspace along which the class' intraclass variance is the smallest. We call this subspace an approximate null space (ANS) since the lowest variance is usually "much smaller" than the highest. A query is classified into class "i" if its distance from the class' mean in the class' ANS is a minimum. We derive upper bounds on classification error probability of PCNSA and use these expressions to compare classification performance of PCNSA with that of subspace linear discriminant analysis (SLDA). We propose a practical modification of PCNSA called progressive-PCNSA that also detects "new" (untrained classes). Finally, we provide an experimental comparison of PCNSA and progressive PCNSA with SLDA and PCA and also with other classification algorithms-linear SVMs, kernel PCA, kernel discriminant analysis, and kernel SLDA, for object recognition and face recognition under large pose/expression variation. We also show applications of PCNSA to two classification problems in video--an action retrieval problem and abnormal activity detection.