PCA (Java Statistical Analysis Tool 0.0.8 API)

java.lang.Object
- jsat.datatransform.PCA

All Implemented Interfaces:

Serializable, Cloneable, DataTransform
```
public class PCA
extends Object
implements DataTransform
```
Principle Component Analysis is a method that attempts to create a basis of the given space that maintains the variance in the data set while eliminating correlation of the variables.
When a full basis is formed, the dimensionality will remain the same, but the data will be transformed to a new space.
PCA is particularly useful when a small number of basis can explain most of the variance in the data set that is not related to noise, maintaining information while reducing the dimensionality of the data.

PCA works only on the numerical attributes of a data set.
For PCA to work correctly, a ZeroMeanTransform should be applied to the data set first. If not done, the first dimension of PCA may contain noise and become uninformative, possibly throwing off the computation of the other PCs

Author:

Edward Raff

See Also:

ZeroMeanTransform, Serialized Form

Constructor Summary

Constructors
Constructor and Description
`PCA()` Creates a new object for performing PCA that stops at 50 principal components.
`PCA(DataSet dataSet)` Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
`PCA(DataSet dataSet, int maxPCs)` Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
`PCA(DataSet dataSet, int maxPCs, double threshold)` Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
`PCA(int maxPCs)` Creates a new object for performing PCA
`PCA(int maxPCs, double threshold)` Creates a new object for performing PCA

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`DataTransform`	`clone()`
`void`	`fit(DataSet dataSet)` Fits this transform to the given dataset.
`int`	`getMaxPCs()`
`double`	`getThreshold()`
`void`	`setMaxPCs(int maxPCs)` sets the maximum number of principal components to learn
`void`	`setThreshold(double threshold)`
`DataPoint`	`transform(DataPoint dp)` Returns a new data point that is a transformation of the original data point.

Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - PCA
```
public PCA()
```
    Creates a new object for performing PCA that stops at 50 principal components. This may not be optimal for any particular dataset
  - PCA
```
public PCA(DataSet dataSet)
```
    Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
    
    NOTE: The maximum number of PCs will be learned until a convergence threshold is meet. It is possible that the number of PCs computed will be equal to the number of dimensions, meaning no dimensionality reduction has occurred, but a transformation of the dimensions into a new space.
    
    Parameters:
    
    dataSet - the data set to learn from
  - PCA
```
public PCA(DataSet dataSet,
           int maxPCs)
```
    Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
    
    Parameters:
    
    dataSet - the data set to learn from
    
    maxPCs - the maximum number of Principal Components to let the algorithm learn. The algorithm may stop earlier if all the variance has been explained, or the convergence threshold has been met. Note, the computable maximum number of PCs is limited to the minimum of the number of samples and the number of dimensions.
  - PCA
```
public PCA(int maxPCs)
```
    Creates a new object for performing PCA
    
    Parameters:
    
    maxPCs - the maximum number of Principal Components to let the algorithm learn. The algorithm may stop earlier if all the variance has been explained, or the convergence threshold has been met. Note, the computable maximum number of PCs is limited to the minimum of the number of samples and the number of dimensions.
  - PCA
```
public PCA(int maxPCs,
           double threshold)
```
    Creates a new object for performing PCA
    
    Parameters:
    
    maxPCs - the maximum number of Principal Components to let the algorithm learn. The algorithm may stop earlier if all the variance has been explained, or the convergence threshold has been met. Note, the computable maximum number of PCs is limited to the minimum of the number of samples and the number of dimensions.
    
    threshold - a convergence threshold, any small value will work. Smaller values will not produce more accurate results, but may make the algorithm take longer if it would have terminated before maxPCs was reached.
  - PCA
```
public PCA(DataSet dataSet,
           int maxPCs,
           double threshold)
```
    Performs PCA analysis using the given data set, so that transformations may be performed on future data points.
    
    Parameters:
    
    dataSet - the data set to learn from
    
    maxPCs - the maximum number of Principal Components to let the algorithm learn. The algorithm may stop earlier if all the variance has been explained, or the convergence threshold has been met. Note, the computable maximum number of PCs is limited to the minimum of the number of samples and the number of dimensions.
    
    threshold - a convergence threshold, any small value will work. Smaller values will not produce more accurate results, but may make the algorithm take longer if it would have terminated before maxPCs was reached.
- Method Detail
  - fit
```
public void fit(DataSet dataSet)
```
    Description copied from interface: DataTransform
    
    Fits this transform to the given dataset. Some transforms can only be learned from classification or regression datasets. If an incompatible dataset type is given, a FailedToFitException exception may be thrown.
    
    Specified by:
    
    fit in interface DataTransform
    
    Parameters:
    
    dataSet - the dataset to fir this transform to
  - setMaxPCs
```
public void setMaxPCs(int maxPCs)
```
    sets the maximum number of principal components to learn
    
    Parameters:
    
    maxPCs - the maximum number of principal components to learn
  - getMaxPCs
```
public int getMaxPCs()
```
    Returns:
    
    maximum number of principal components to learn
  - setThreshold
```
public void setThreshold(double threshold)
```
    Parameters:
    
    threshold - the threshold for convergence of the algorithm
  - getThreshold
```
public double getThreshold()
```
  - transform
```
public DataPoint transform(DataPoint dp)
```
    Description copied from interface: DataTransform
    
    Returns a new data point that is a transformation of the original data point. This new data point is a different object, but may contain the same references as the original data point. It is not guaranteed that you can mutate the transformed point without having a side effect on the original point.
    
    Specified by:
    
    transform in interface DataTransform
    
    Parameters:
    
    dp - the data point to apply a transformation to
    
    Returns:
    
    a transformed data point
  - clone
```
public DataTransform clone()
```
    Specified by:
    
    clone in interface DataTransform
    
    Overrides:
    
    clone in class Object

Class PCA

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PCA

PCA

PCA

PCA

PCA

PCA

Method Detail

fit

setMaxPCs

getMaxPCs

setThreshold

getThreshold

transform

clone