# 2006 ReducingtheDimensionalityofData

- (Hinton & Salakhutdinov, 2006) ⇒ Geoffrey E. Hinton, and Ruslan R. Salakhutdinov. (2006). “Reducing the Dimensionality of Data with Neural Networks.” In: Science, 313(5786). doi:10.1126/science.1127647

**Subject Headings:** Autoencoder, Feature Detector.

## Notes

- Supporting online material: http://www.sciencemag.org/content/suppl/2006/08/04/313.5786.504.DC1/Hinton.SOM.pdf

## Cited By

## Quotes

### Abstract

High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such "autoencoder" networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data.

### Introduction

Dimensionality reduction facilitates the classification, visualization, communication, and storage of high-dimensional data. A simple and widely used method is principal components analysis (PCA), which finds the directions of greatest variance in the data set and represents each data point by its coordinates along each of these directions. We describe a nonlinear generalization of PCA that uses an adaptive, multilayer "encoder" network …

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Starting with random weights in the two networks, they can be trained together by minimizing the discrepancy between the original data and its reconstruction. The required gradients are easily obtained by using the chain rule to backpropagate error derivatives first through the decoder network and then through the encoder network (1). The whole system is called an "autoencoder" and is depicted in Fig. 1.

It is difficult to optimize the weights in nonlinear autoencoders that have multiple hidden layers (2–4). With large initial weights, autoencoders typically find poor local minima; with small initial weights, the gradients in the early layers are tiny, making it infeasible to train autoencoders with many hidden layers. If the initial weights are close to a good solution, gradient descent works well, but finding such initial weights requires a very different type of algorithm that learns one layer of features at a time. We introduce this "pretraining" procedure for binary data, generalize it to real-valued data, and show that it works well for a variety of data sets.

An ensemble of binary vectors (e.g., images) can be modeled using a two-layer network called a "restricted Boltzmann machine" (RBM) (5, 6) in which stochastic, binary pixels are connected to stochastic, binary feature detectors using symmetrically weighted connections. The pixels correspond to "visible" units of the RBM because their states are observed; the feature detectors correspond to "hidden" units. A joint configuration [math]\displaystyle{ (\mathbf{v}, \mathbf{h}) }[/math] of the visible and hidden units has an energy (7) given by...

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## References

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Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
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2006 ReducingtheDimensionalityofData | Geoffrey E. Hinton Ruslan Salakhutdinov | Reducing the Dimensionality of Data with Neural Networks | 10.1126/science.1127647 |