# Data Preprocessing

### From Ufldl

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* Per-example mean subtraction (a.k.a. remove DC) | * Per-example mean subtraction (a.k.a. remove DC) | ||

* Feature Standardization (zero-mean and unit variance for each feature across the dataset) | * Feature Standardization (zero-mean and unit variance for each feature across the dataset) | ||

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=== Simple Rescaling === | === Simple Rescaling === | ||

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If your data is ''stationary'' (i.e., the statistics for each data dimension follow the same distribution), then you might want to consider subtracting the mean-value for each example (computed per-example). | If your data is ''stationary'' (i.e., the statistics for each data dimension follow the same distribution), then you might want to consider subtracting the mean-value for each example (computed per-example). | ||

- | '''Example:''' In images, this normalization has the property of removing the average brightness (intensity) of the data point. In many cases, we are not interested in the illumination conditions of the image, but more so in the content; removing the average pixel value per data point makes sense here. | + | '''Example:''' In images, this normalization has the property of removing the average brightness (intensity) of the data point. In many cases, we are not interested in the illumination conditions of the image, but more so in the content; removing the average pixel value per data point makes sense here. '''Note:''' While this method is generally used for images, one might want to take more care when applying this to color images. In particular, the stationarity property does not generally apply across pixels in different color channels. |

=== Feature Standardization === | === Feature Standardization === | ||

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'''Example: ''' When working with audio data, it is common to use [http://en.wikipedia.org/wiki/Mel-frequency_cepstrum MFCCs] as the data representation. However, the first component (representing the DC) of the MFCC features often overshadow the other components. Thus, one method to restore balance to the components is to standardize the values in each component independently. | '''Example: ''' When working with audio data, it is common to use [http://en.wikipedia.org/wiki/Mel-frequency_cepstrum MFCCs] as the data representation. However, the first component (representing the DC) of the MFCC features often overshadow the other components. Thus, one method to restore balance to the components is to standardize the values in each component independently. | ||

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== PCA/ZCA Whitening == | == PCA/ZCA Whitening == | ||

- | + | After doing the simple normalizations, whitening is often the next preprocessing step employed that helps make our algorithms work better. In practice, many deep learning algorithms rely on whitening to learn good features. | |

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+ | In performing PCA/ZCA whitening, it is pertinent to first zero-mean the features (across the dataset) to ensure that <math> \frac{1}{m} \sum_i x^{(i)} = 0 </math>. Specifically, this should be done before computing the covariance matrix. '''The only exception is when per-example mean subtraction is performed and the data is stationary across dimensions/pixels.''' | ||

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+ | {{quote| | ||

+ | Note: When working in a classification framework, one should compute the PCA/ZCA whitening matrices based only on the training set. The following parameters used be saved for use with the test set: (a) average vector that was used to zero-mean the data, (b) whitening matrices. The test set should undergo the same preprocessing steps using these saved values. }} | ||

== Large Images == | == Large Images == |

## Revision as of 06:30, 29 April 2011

## Contents |

## Overview

Data preprocessing plays a very important in many deep learning algorithms. In practice, many methods work best after the data has been normalized and whitened. However, the exact parameters for data preprocessing are usually not immediately apparent unless one has much experience working with the algorithms. In this page, we hope to demystify some of the preprocessing methods and also provide tips (and a "standard pipeline") for preprocessing data.

Tip: When approaching a dataset, the first thing to do is to look at the data itself and observe its properties. While the techniques here apply generally, you might want to opt to do certain things differently given your dataset. For example, one standard preprocessing trick is to subtract the mean of each data point from itself (also known as remove DC, local mean subtraction, subtractive normalization). While this makes sense for data such as natural images, it is less obvious for data with with a natural "zero" point such as MNIST images (where all data points use the same value of 0 to represent an empty background).

## Data Normalization

A standard first step to data preprocessing is data normalization. While there are a few possible approaches, this step is usually clear depending on the data. The common methods for feature normalization are:

- Simple Rescaling
- Per-example mean subtraction (a.k.a. remove DC)
- Feature Standardization (zero-mean and unit variance for each feature across the dataset)

### Simple Rescaling

In simple rescaling, our goal is to rescale the data along each data dimension (possibly independently) so that the final data vectors lie in the range [0,1] or [ − 1,1] (depending on your dataset). This is useful for later processing as many *default* parameters (e.g., epsilon in PCA-whitening) treat the data as if it has been scaled to a reasonable range.

**Example: ** When processing natural images, we often obtain pixel values in the range [0,255]. It is a common operation to rescale these values to [0,1] by dividing the data by 255.

### Per-example mean subtraction

If your data is *stationary* (i.e., the statistics for each data dimension follow the same distribution), then you might want to consider subtracting the mean-value for each example (computed per-example).

**Example:** In images, this normalization has the property of removing the average brightness (intensity) of the data point. In many cases, we are not interested in the illumination conditions of the image, but more so in the content; removing the average pixel value per data point makes sense here. **Note:** While this method is generally used for images, one might want to take more care when applying this to color images. In particular, the stationarity property does not generally apply across pixels in different color channels.

### Feature Standardization

Feature standardization refers to (independently) setting each dimension of the data to have zero-mean and unit-variance. This is the most common method for normalization and is generally used widely (e.g., when working with SVMs, feature standardization is often recommended as a preprocessing step). In practice, one achieves this by first computing the mean of each dimension (across the dataset) and subtracts this from each dimension. Next, each dimension is divided by its standard deviation.

**Example: ** When working with audio data, it is common to use MFCCs as the data representation. However, the first component (representing the DC) of the MFCC features often overshadow the other components. Thus, one method to restore balance to the components is to standardize the values in each component independently.

## PCA/ZCA Whitening

After doing the simple normalizations, whitening is often the next preprocessing step employed that helps make our algorithms work better. In practice, many deep learning algorithms rely on whitening to learn good features.

In performing PCA/ZCA whitening, it is pertinent to first zero-mean the features (across the dataset) to ensure that . Specifically, this should be done before computing the covariance matrix. **The only exception is when per-example mean subtraction is performed and the data is stationary across dimensions/pixels.**

Note: When working in a classification framework, one should compute the PCA/ZCA whitening matrices based only on the training set. The following parameters used be saved for use with the test set: (a) average vector that was used to zero-mean the data, (b) whitening matrices. The test set should undergo the same preprocessing steps using these saved values.

## Large Images

1/f Whitening