High-Order Measurements for Residual Classifiers

Residual classifiers are common in dictionary-based multiclass classification. This paper proposes the concept of performance functions for residual classifiers. A performance function for multiclass classifications is a conceptual measurement function that combines local and global measurements. In general, the performance function is nonlinear. To explore the properties of the performance function, we employ the Taylor series expansion technique and derive a family of measurement functions. Specifically, the linear measurement and the quadratic measurement (QM) are derived. By exploiting the effect of the higher order terms in the performance function as well as the fundamental nondecreasing constrain, we derive the normalized QM (NQM). We present the classifier for multiclass classification using the proposed measurements. The proposed algorithms are tested against frontal faces and handwritten digit recognition tasks. Our tests show that the QM classifier achieves competitive classification results compared with baseline methods. NQM shows better stability with different parameter configurations.