Building on Chap. 9, this chapter extends projection-based methods from one-class to binary and multi-class classification for fault diagnosis. In the binary case, two process models (nominal and faulty) with corresponding SIRs are used to construct projection systems and make classification decisions. A key challenge arises when projections onto the image subspaces of both systems are similar. In the first part of this chapter, properties of the similarity are analysed with the aid of operator theory. It reveals that the binary fault classification problem is hard to solve as the system operates in a transitional phase from fault-free to faulty operations. To mitigate this, two approaches are proposed: The chapter also covers multi-class extensions for fault isolation. Finally, noticing that the projection-based classification methods might become less efficient, when the gap metric-based threshold setting is too conservative, a method is proposed to integrate projection-based classification with data-driven algorithms to tighten threshold settings and improve detection performance.