End-to-End Data Visualization by Metric Learning and Coordinate Transformation

This paper presents a deep nonlinear metric learning framework for data visualization on an image dataset. We propose the Triangular Similarity and prove its equivalence to the Cosine Similarity in measuring a data pair. Based on this novel similarity, a geometrically motivated loss function - the triangular loss - is then developed for optimizing a metric learning system comprising two identical CNNs. It is shown that this deep nonlinear system can be efficiently trained by a hybrid algorithm based on the conventional backpropagation algorithm. More interestingly, benefiting from classical manifold learning theories, the proposed system offers two different views to visualize the outputs, the second of which provides better classification results than the state-of-the-art methods in the visualizable spaces.