# Representation Learning

## Why we need representation learning?

The success of machine learning algorithms generally depends on data representation [1], although specific domain knowledge can be used to help design representations, sometimes it is difficult to manuelly craft features from raw data collected. Especially when ….

Representation Learning aims to learn representations from data that make it easier to extract useful information for various tasks [2].

According to [3], a good example is that when you are asked to divide CCX by VI, you would begin by converting the numbers to the Arabic numeral representation. That is the importance of representation.

We can think of the suprevised training of feedforward networks as performing a kind of representation learning where in the last hidden layer we can get some more seperable representation of the raw data.

## How to conduct representation learning?

### Auto-encoders

An autoencoder is a type of artificial neural network used to learn efficient data codings in an unsupervised manner. The aim of an autoencoder is to learn a representation (encoding) for a set of data, typically for dimensionality reduction, by training the network to ignore signal “noise”.

The network may be viewed as consisting of two parts: an encoder function $$\pmb{h}=f(\pmb{x})$$ and a decoder that produces a reconstruction $$\pmb{r}=g(\pmb{h})$$.

For undercomplete auto encoders, the learning process is described simply as minimizing a loss function

$L(\pmb{x},g(f(\pmb{x})))$

Simple autoencoder may fail in extracting useful information from the dataset due to overfitting, some regularized autoencoders can somehow fix the problem:

• Sparse Autoencoders: $$L(\pmb{x},g(f(\pmb{x})))+\Omega(\pmb{h})$$, where $$\Omega(\pmb{h})$$ is a sparsity penalty over the code layer $$\pmb{h}$$.
• Denoising Autoencoders (DAE): $$L(\pmb{x},g(f(\pmb{\tilde x})))$$, where $$\pmb{\tilde x}$$ is a copy of $$\pmb{x}$$ that has been corrupted by some form of noise.

## Ref.

[1] Bengio, Y., Courville, A., & Vincent, P. (2013). Representation learning: A review and new perspectives. IEEE transactions on pattern analysis and machine intelligence, 35(8), 1798-1828.

[2] Li, Y., Fu, K., Wang, Z., Shahabi, C., Ye, J., & Liu, Y. (2018, July). Multi-task representation learning for travel time estimation. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (pp. 1695-1704). ACM.

[3] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press.