de.lmu.ifi.dbs.elki.math

Class MeanVariance

java.lang.Object

de.lmu.ifi.dbs.elki.math.Mean

de.lmu.ifi.dbs.elki.math.MeanVariance

Direct Known Subclasses:

MeanVarianceMinMax

@Reference(authors="Erich Schubert, Michael Gertz",title="Numerically Stable Parallel Computation of (Co-)Variance",booktitle="Proc. 30th Int. Conf. Scientific and Statistical Database Management (SSDBM 2018)",url="https://doi.org/10.1145/3221269.3223036",bibkey="DBLP:conf/ssdbm/SchubertG18") @Reference(authors="E. A. Youngs, E. M. Cramer",title="Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms",booktitle="Technometrics 13(3)",url="https://doi.org/10.1080/00401706.1971.10488826",bibkey="doi:10.1080/00401706.1971.10488826") @Reference(authors="B. P. Welford",title="Note on a method for calculating corrected sums of squares and products",booktitle="Technometrics 4(3)",url="https://doi.org/10.2307/1266577",bibkey="doi:10.2307/1266577") @Reference(authors="D. H. D. West",title="Updating Mean and Variance Estimates: An Improved Method",booktitle="Communications of the ACM 22(9)",url="https://doi.org/10.1145/359146.359153",bibkey="DBLP:journals/cacm/West79")
public class MeanVariance
extends Mean

Do some simple statistics (mean, variance) using a numerically stable online algorithm.

This class can repeatedly be fed with data using the add() methods, the resulting values for mean and average can be queried at any time using Mean.getMean() and getSampleVariance().

Make sure you have understood variance correctly when using getNaiveVariance() - since this class is fed with samples and estimates the mean from the samples, getSampleVariance() is often the more appropriate version.

As experimentally studied in

Erich Schubert, Michael Gertz
Numerically Stable Parallel Computation of (Co-)Variance
Proc. 30th Int. Conf. Scientific and Statistical Database Management (SSDBM 2018)

the current approach is based on:

E. A. Youngs and E. M. Cramer
Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms
Technometrics 13(3), 1971

We have originally experimented with:

B. P. Welford
Note on a method for calculating corrected sums of squares and products
Technometrics 4(3), 1962

D. H. D. West
Updating Mean and Variance Estimates: An Improved Method
Communications of the ACM 22(9)

Since:

0.2

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field and Description
protected double	m2 n times Variance

Fields inherited from class de.lmu.ifi.dbs.elki.math.Mean

n, sum

Constructor Summary

Constructors

Constructor and Description
MeanVariance() Empty constructor
MeanVariance(MeanVariance other) Constructor from other instance

Method Summary

Modifier and Type	Method and Description
double	getNaiveStddev() Return standard deviation using the non-sample variance Note: usually, you should be using getSampleStddev() instead!
double	getNaiveVariance() Return the naive variance (not taking sampling into account) Note: usually, you should be using getSampleVariance() instead!
double	getSampleStddev() Return standard deviation
double	getSampleVariance() Return sample variance.
double	getSumOfSquares() Get the sum of squares.
static MeanVariance[]	newArray(int dimensionality) Create and initialize a new array of MeanVariance
void	put(double val) Add a single value with weight 1.0
MeanVariance	put(double[] vals) Add values with weight 1.0
MeanVariance	put(double[] vals, double[] weights) Add values with weight 1.0
void	put(double val, double weight) Add data with a given weight.
void	put(Mean other) Join the data of another MeanVariance instance.
void	reset() Reset the value.
java.lang.String	toString()

Methods inherited from class de.lmu.ifi.dbs.elki.math.Mean

getCount, getMean, highPrecision, of

Methods inherited from class java.lang.Object

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

Field Detail

m2

protected double m2

n times Variance

Constructor Detail

MeanVariance

public MeanVariance()

Empty constructor

MeanVariance

public MeanVariance(MeanVariance other)

Constructor from other instance

Parameters:

other - other instance to copy data from.

Method Detail

put

public void put(double val)

Add a single value with weight 1.0

Overrides:

put in class Mean

Parameters:

val - Value

put

public void put(double val,
                double weight)

Add data with a given weight.

Overrides:

put in class Mean

Parameters:

val - data

weight - weight

put

public void put(Mean other)

Join the data of another MeanVariance instance.

Overrides:

put in class Mean

Parameters:

other - Data to join with

put

public MeanVariance put(double[] vals)

Add values with weight 1.0

Overrides:

put in class Mean

Parameters:

vals - Values

Returns:

this

put

public MeanVariance put(double[] vals,
                        double[] weights)

Description copied from class: Mean

Add values with weight 1.0

Overrides:

put in class Mean

Parameters:

vals - Values

Returns:

this

getNaiveVariance

public double getNaiveVariance()

Return the naive variance (not taking sampling into account) Note: usually, you should be using getSampleVariance() instead!

Returns:

variance

getSampleVariance

public double getSampleVariance()

Return sample variance.

Returns:

sample variance

getSumOfSquares

public double getSumOfSquares()

Get the sum of squares.

Returns:

sum of squared deviations

getNaiveStddev

public double getNaiveStddev()

Return standard deviation using the non-sample variance Note: usually, you should be using getSampleStddev() instead!

Returns:

stddev

getSampleStddev

public double getSampleStddev()

Return standard deviation

Returns:

stddev

newArray

public static MeanVariance[] newArray(int dimensionality)

Create and initialize a new array of MeanVariance

Parameters:

dimensionality - Dimensionality

Returns:

New and initialized Array

toString

public java.lang.String toString()

Overrides:

toString in class Mean

reset

public void reset()

Description copied from class: Mean

Reset the value.

Overrides:

reset in class Mean