Auto-encoder based dimensionality reduction

Auto-encoder—a tricky three-layered neural network, known as auto-association before, constructs the “building block” of deep learning, which has been demonstrated to achieve good performance in various domains. In this paper, we try to investigate the dimensionality reduction ability of auto-encoder, and see if it has some kind of good property that might accumulate when being stacked and thus contribute to the success of deep learning.Based on the above idea, this paper starts from auto-encoder and focuses on its ability to reduce the dimensionality, trying to understand the difference between auto-encoder and state-of-the-art dimensionality reduction methods. Experiments are conducted both on the synthesized data for an intuitive understanding of the method, mainly on two and three-dimensional spaces for better visualization, and on some real datasets, including MNIST and Olivetti face datasets. The results show that auto-encoder can indeed learn something different from other methods. Besides, we preliminarily investigate the influence of the number of hidden layer nodes on the performance of auto-encoder and its possible relation with the intrinsic dimensionality of input data.