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Supervised dimensionality reduction strategies have been of great interest.However, current supervised dimensionality reduction approaches are difficultto scale for situations characterized by large datasets given the highcomputational complexities associated with such methods. While stochasticapproximation strategies have been explored for unsupervised dimensionalityreduction to tackle this challenge, such approaches are not well-suited foraccelerating computational speed for supervised dimensionality reduction.Motivated to tackle this challenge, in this study we explore a novel directionof directly learning optimal class-aware embeddings in a supervised manner viathe notion of supervised random projections (SRP). The key idea behind SRP isthat, rather than performing spectral decomposition (or approximations thereof)which are computationally prohibitive for large-scale data, we instead performa direct decomposition by leveraging kernel approximation theory and thesymmetry of the Hilbert-Schmidt Independence Criterion (HSIC) measure ofdependence between the embedded data and the labels. Experimental results onfive different synthetic and real-world datasets demonstrate that the proposedSRP strategy for class-aware embedding learning can be very promising inproducing embeddings that are highly competitive with existing superviseddimensionality reduction methods (e.g., SPCA and KSPCA) while achieving 1-2orders of magnitude better computational performance. As such, such anefficient approach to learning embeddings for dimensionality reduction can be apowerful tool for large-scale data analysis and visualization.

SRP: Efficient class-aware embedding learning for large-scale data via supervised random projections