Principal Component Null Space Analysis for Image / Video Classification

We present a new classification algorithm, Principal Component Null Space Analysis (PCNSA), which is designed for “apples from oranges” type classification problems like object recognition where different classes have unequal and non-white noise covariance matrices. PCNSA first obtains a principal components subspace (PCA space) for the entire data in order to maximize the between-class variance. In this PCA space, it finds for each class ‘ i’, n Mi dimensional subspace along which the class’s intra-class 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’s mean in the class’s ANS is a minimum. We derive tight upper bounds on classification error probability. We use these expressions to compare classification performance of PCNSA with that of Subspace Linear Discriminant Analysis (SLDA) [1]. We propose a practical modification of PCNSA called progressive-PCNSA that also detects ‘new’ (untrained classes). Finally, we provide a brief experimental comparison of PCNSA, progressive-PCNSA and SLDA for three image classification problems object recognition, facial feature matching and face recognition under large pose/expression variation. We also show application of PCNSA to two classification problems in video an abnormal activity detection problem and an action retrieval problem.