A new two-layer mixture of factor analyzers with joint factor loading model for the classification of small dataset problems

Dimensionality Reduction (DR) is a fundamental topic of pattern classification and machine learning. For classification tasks, DR is typically employed as a pre-processing step, succeeded by an independent classifier training stage. However, such independent operation of the two stages often limits the final classification performance notably, as the generated subspace may not be maximally beneficial or appropriate to the learning task at hand. This problem is further accentuated for high-dimensional data classification in situations of the limited number of samples. To address this problem, we develop a novel joint learning model for classification, referred to as two-layer mixture of factor analyzers with joint factor loading (2L-MJFA). Specifically, the model adopts a special two-layer mixture or a mixture of mixtures structure, where each component represents each specific class as a mixture of factor analyzers (MFA). Importantly, all the involved factor analyzers are intentionally designed so that they share the same loading matrix. This, apart from operating as the DR matrix, largely reduces the parameters and makes the proposed algorithm very suitable to small dataset situations. Additionally, we propose a modified expectation maximization algorithm to train the proposed model. A series of simulation experiments demonstrate that what we propose significantly outperforms other state-of-the-art algorithms on various benchmark datasets. Finally, since factor analyzers are closely linked with Auto-encoder networks, the proposed idea could be of particular utility to the community of neural networks.