Supervised dimensionality reduction for multi-dimensional classification
Bin-Bin Jia, MinLing ZHANG · Scientia Sinica Informationis · 2023
Compared to traditional multi-class classification, each object in multi-dimensional classification is also represented by a single instance while associated with multiple class variables. Here, each class variable corresponds to one heterogeneous class space characterizing an object's semantics from one dimension. Dimensionality reduction effectively alleviates the curse of dimensionality and expedites model training. Existing multi-dimensional classification studies aim at designing learning algorithms with better performance, while the problem of dimensionality reduction for multi-dimensional classification has not been investigated. According to the correlation between feature space and semantic space, this paper makes a first attempt at designing a supervised linear dimensionality reduction method called SDeM for multi-dimensional classification. SDeM measures the correlation between two spaces with the Hilbert-Schmidt independence criterion and determines the projection matrix by maximizing the correlation between the projected feature space and the semantic space under this metric. Experimental results show that the reduced features obtained by SDeM are more conducive than those obtained by unsupervised dimensionality reduction methods to achieve better generalization performance for multi-dimensional classification methods.