com.imsl.datamining.neural

Class ScaleFilter

java.lang.Object

com.imsl.datamining.neural.ScaleFilter

All Implemented Interfaces:

Serializable

public class ScaleFilter
extends Object
implements Serializable

Scales or unscales continuous data prior to its use in neural network training, testing, or forecasting.

Bounded scaling is used to ensure that the values in the scaled array fall between a lower and upper bound. The scale limits have the following interpretation:

Argument	Interpretation
realMin	The lowest value expected in x.
realMax	The largest value expected in x.
targetMin	The lower bound for the values in the scaled data.
targetMax	The upper bound for the values in the scaled data.

The scale limits are set using the method setBounds.

The specific scaling used is controlled by the argument scalingMethod used when constructing the filter object. If scalingMethod is NO_SCALING, then no scaling is performed on the data.

If the scalingMethod is BOUNDED_SCALING then the bounded method of scaling and unscaling is applied to x. The scaling operation is conducted using the scale limits set in method setBounds, using the following calculation: $$z = r(x - \text{realMin}) + \text{targetMin},$$ where $$r = \frac{\text{targetMax} - \text{targetMin}}{\text{realMax} - \text{realMin}}.$$

If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV, or BOUNDED_Z_SCORE_SCALING_MEAN_STDEV, then \(a\) and \(b\) are the arithmetic average and sample standard deviation of the training data.

If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD or BOUNDED_Z_SCORE_SCALING_MEDIAN_MAD, then \(a\) and \(b\) are the median and \(\tilde{s}\), where \(\tilde{s}\) is a robust estimate of the population standard deviation: $$\tilde{s} = \frac{\mbox{MAD}}{0.6745}$$ where MAD is the Mean Absolute Deviation $$\mbox{MAD} = \text{median} \{ \mid x - \text{median}\{x\}\mid \}$$ The Mean Absolute Deviation is a robust measure of spread calculated by finding the median of the absolute value of differences between each non-missing value for the \(i\)th variable and the median of those values.

If the method decode is called then an unscaling operation is conducted by inverting using: $$x = \frac{(z - \text{targetMin})}{r} + \text{realMin}.$$

Unbounded z-score Scaling

If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV or UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD, then a scaling operation is conducted using the z-score calculation: $$z = \frac{(x - center)}{spread},$$ If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV then \(center\) is set equal to the arithmetic average \(\bar{x}\) of x, and \(spread\) is set equal to the sample standard deviation of x. If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD then \(center\) is set equal to the median \(\tilde{m}\) of x, and \(spread\) is set equal to the Mean Absolute Difference (MAD).

The method decode can be used to unfilter data using the the inverse calculation for the above equation: $$x = spread \cdot z + center.$$

Bounded z-score Scaling

This method is essentially the same as the z-score calculation described above with additional scaling or unscaling using the scale limits set in method setBounds. The scaling operation is conducted using the well known z-score calculation: $$z = \frac{r \cdot (x - center)} {spread} - r \cdot realMin + targetMin.$$ If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV then \(center\) is set equal to the arithmetic average \(\bar{x}\) of x, and \(spread\) is set equal to the sample standard deviation of x. If scalingMethod is UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD then \(center\) is set equal to the median \(\tilde{m}\) of x, and \(spread\) is set equal to the Mean Absolute Difference (MAD).

The method decode can be used to unfilter data using the the inverse calculation for the above equation: $$x = \frac{spread \cdot (z - \text{targetMin})}{r} + spread \cdot \text{realMin} + center$$

See Also:

Example, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	BOUNDED_SCALING Flag to indicate bounded scaling.
static int	BOUNDED_Z_SCORE_SCALING_MEAN_STDEV Flag to indicate bounded z-score scaling using the mean and standard deviation.
static int	BOUNDED_Z_SCORE_SCALING_MEDIAN_MAD Flag to indicate bounded z-score scaling using the median and mean absolute difference.
static int	NO_SCALING Flag to indicate no scaling.
static int	UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV Flag to indicate unbounded z-score scaling using the mean and standard deviation.
static int	UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD Flag to indicate unbounded z-score scaling using the median and mean absolute difference.

Constructor Summary

Constructors

Constructor and Description
ScaleFilter(int scalingMethod) Constructor for ScaleFilter.

Method Summary

Modifier and Type	Method and Description
double	decode(double z) Unscales a value.
double[]	decode(double[] z) Unscales an array of values.
void	decode(int columnIndex, double[][] z) Unscales a single column of a two dimensional array of values.
double	encode(double x) Scales a value.
double[]	encode(double[] x) Scales an array of values.
void	encode(int columnIndex, double[][] x) Scales a single column of a two dimensional array of values.
double[]	getBounds() Retrieves bounds used during bounded scaling.
double	getCenter() Retrieves the measure of center to be used during z-score scaling.
double	getSpread() Retrieves the measure of spread to be used during scaling.
void	setBounds(double realMin, double realMax, double targetMin, double targetMax) Sets bounds to be used during bounded scaling and unscaling.
void	setCenter(double center) Set the measure of center to be used during z-score scaling.
void	setSpread(double spread) Set the measure of spread to be used during z-score scaling.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

NO_SCALING

public static final int NO_SCALING

Flag to indicate no scaling.

See Also:

Constant Field Values

BOUNDED_SCALING

public static final int BOUNDED_SCALING

Flag to indicate bounded scaling.

See Also:

Constant Field Values

UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV

public static final int UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV

Flag to indicate unbounded z-score scaling using the mean and standard deviation.

See Also:

Constant Field Values

UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD

public static final int UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD

Flag to indicate unbounded z-score scaling using the median and mean absolute difference.

See Also:

Constant Field Values

BOUNDED_Z_SCORE_SCALING_MEAN_STDEV

public static final int BOUNDED_Z_SCORE_SCALING_MEAN_STDEV

Flag to indicate bounded z-score scaling using the mean and standard deviation.

See Also:

Constant Field Values

BOUNDED_Z_SCORE_SCALING_MEDIAN_MAD

public static final int BOUNDED_Z_SCORE_SCALING_MEDIAN_MAD

Flag to indicate bounded z-score scaling using the median and mean absolute difference.

See Also:

Constant Field Values

Constructor Detail

ScaleFilter

public ScaleFilter(int scalingMethod)

Constructor for ScaleFilter.

Parameters:

scalingMethod - An int specifying the scaling method to be applied. scalingMethod is specified by: NO_SCALING, BOUNDED_SCALING, UNBOUNDED_Z_SCORE_SCALING_MEAN_STDEV, UNBOUNDED_Z_SCORE_SCALING_MEDIAN_MAD, BOUNDED_Z_SCORE_SCALING_MEAN_STDEV, or BOUNDED_Z_SCORE_SCALING_MEDIAN_MAD.

Method Detail

setBounds

public void setBounds(double realMin,
                      double realMax,
                      double targetMin,
                      double targetMax)

Sets bounds to be used during bounded scaling and unscaling. This method is normally called prior to calls to encode or decode. Otherwise the default bounds are realMin = 0, realMax = 1, targetMin = 0, and targetMax = 1. These bounds are ignored for unbounded scaling.

Parameters:

realMin - A double containing the lowest expected value in the data to be filtered.

realMax - A double containing the largest expected value in the data to be filtered.

targetMin - A double containing the lowest allowed value in the filtered data.

targetMax - A double containing the largest allowed value in the filtered data.

getBounds

public double[] getBounds()

Retrieves bounds used during bounded scaling.

Returns:

A double array of length 4 containing the values

i	result[i]
0	realMin. Lowest expected value in the data to be filtered.
1	realMax. Largest expected value in the data to be filtered.
2	targetMin. Lowest allowed value in the filtered data.
3	targetMax. Largest allowed value in the filtered data.

setCenter

public void setCenter(double center)

Set the measure of center to be used during z-score scaling.

Parameters:

center - A double containing the measure of center to be used during scaling. If this method is not called then the measure of center is computed from the data.

getCenter

public double getCenter()

Retrieves the measure of center to be used during z-score scaling.

Returns:

A double containing the measure of center to be used during z-score scaling.

setSpread

public void setSpread(double spread)

Set the measure of spread to be used during z-score scaling.

Parameters:

spread - A double containing the measure of spread to be used during z-score scaling. If this method is not called then the measure of spread is computed from the data.

getSpread

public double getSpread()

Retrieves the measure of spread to be used during scaling.

Returns:

a double containing the measure of spread to be used during scaling.

encode

public double encode(double x)

Scales a value.

Parameters:

x - A double containing the value to be scaled.

Returns:

A double containing the scaled value.

encode

public double[] encode(double[] x)

Scales an array of values.

Parameters:

x - A double array containing the data to be scaled.

Returns:

A double array containing the scaled data.

encode

public void encode(int columnIndex,
                   double[][] x)

Scales a single column of a two dimensional array of values.

Parameters:

columnIndex - An int specifying the index of the column of x to scale. Indexing is zero-based.

x - A double matrix containing the value to be scaled. Its columnIndex-th column is modified in place.

decode

public double decode(double z)

Unscales a value.

Parameters:

z - A double containing the value to be unscaled.

Returns:

A double containing the filtered data.

decode

public double[] decode(double[] z)

Unscales an array of values.

Parameters:

z - A double array of values to be unscaled.

Returns:

A double array containing the filtered data.

decode

public void decode(int columnIndex,
                   double[][] z)

Unscales a single column of a two dimensional array of values.

Parameters:

columnIndex - An int specifying the index of the column of z to unscale. Indexing is zero-based.

z - A double matrix containing the values to be unscaled. Its columnIndex-th column is modified in place.