Null Space Analysis for Class-Specific Discriminant Learning

In this paper, we carry out null space analysis for Class-Specific Discriminant Analysis (CSDA) and formulate a number of solutions based on the analysis. We analyze both theoretically and experimentally the significance of each algorithmic step. The innate subspace dimensionality resulting from the proposed solutions is typically quite high and we discuss how the need for further dimensionality reduction changes the situation. Experimental evaluation of the proposed solutions shows that the straightforward extension of null space analysis approaches to the class-specific setting can outperform the standard CSDA method. Furthermore, by exploiting a recently proposed out-of-class scatter definition encoding the multi-modality of the negative class naturally appearing in class-specific problems, null space projections can lead to a performance comparable to or outperforming the most recent CSDA methods.