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PixelSNE: Visualizing Fast with Just Enough Precision via Pixel-Aligned Stochastic Neighbor Embedding
Mar 03, 2017
Embedding and visualizing large-scale high-dimensional data in a two-dimensional space is an important problem since such visualization can reveal deep insights out of complex data. Most of the existing embedding approaches, however, run on an excessively high precision, ignoring the fact that at the end, embedding outputs are converted into coarse-grained discrete pixel coordinates in a screen space. Motivated by such an observation and directly considering pixel coordinates in an embedding optimization process, we accelerate Barnes-Hut tree-based t-distributed stochastic neighbor embedding (BH-SNE), known as a state-of-the-art 2D embedding method, and propose a novel method called PixelSNE, a highly-efficient, screen resolution-driven 2D embedding method with a linear computational complexity in terms of the number of data items. Our experimental results show the significantly fast running time of PixelSNE by a large margin against BH-SNE, while maintaining the minimal degradation in the embedding quality. Finally, the source code of our method is publicly available at https://github.com/awesome-davian/PixelSNE
Manifold Regularized Deep Neural Networks using Adversarial Examples
Jan 14, 2016
Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the most popular training protocols. Based on that, more advanced methods (i.e., Maxout and Batch Normalization) have been proposed in recent years, but most still suffer from performance degradation caused by small perturbations, also known as adversarial examples. To address this issue, we propose manifold regularized networks (MRnet) that utilize a novel training objective function that minimizes the difference between multi-layer embedding results of samples and those adversarial. Our experimental results demonstrated that MRnet is more resilient to adversarial examples and helps us to generalize representations on manifolds. Furthermore, combining MRnet and dropout allowed us to achieve competitive classification performances for three well-known benchmarks: MNIST, CIFAR-10, and SVHN.