de.lmu.ifi.dbs.elki.math.statistics.dependence

Class HSMDependenceMeasure

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.dependence.AbstractDependenceMeasure

de.lmu.ifi.dbs.elki.math.statistics.dependence.HSMDependenceMeasure

All Implemented Interfaces:

DependenceMeasure

@Priority(value=-100)
 @Reference(authors="A. Tatu, G. Albuquerque, M. Eisemann, P. Bak, H. Theisel, M. A. Magnor, D. A. Keim",
           title="Automated Analytical Methods to Support Visual Exploration of High-Dimensional Data",
           booktitle="IEEE Trans. Visualization and Computer Graphics",
           url="https://doi.org/10.1109/TVCG.2010.242",
           bibkey="DBLP:journals/tvcg/TatuAEBTMK11")
public class HSMDependenceMeasure
extends AbstractDependenceMeasure

Compute the "interestingness" of dimension connections using the hough transformation. This is a very visual approach, designed to find certain patterns in parallel coordinates visualizations. The patterns detected here occur mostly if you have mutliple clusters of linear patterns as far as we understood the approach (which is not easy to use, unfortunately).

Reference:

A. Tatu, G. Albuquerque, M. Eisemann, P. Bak, H. Theisel, M. A. Magnor, D. A. Keim.
Automated Analytical Methods to Support Visual Exploration of High-Dimensional Data.
IEEE Trans. Visualization and Computer Graphics

FIXME: while the plots look reasonable, this fails to find interesting associations. This needs closer investigation.

Since:

0.5.5

Author:

Erich Schubert, Robert Rödler

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	HSMDependenceMeasure.Parameterizer Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
private int	resolution Resolution of image.
static HSMDependenceMeasure	STATIC Static instance.
private static int	STEPS Angular resolution.
private static SinCosTable	table Precompute sinus and cosinus

Constructor Summary

Constructors

Constructor and Description
HSMDependenceMeasure()

Method Summary

Modifier and Type	Method and Description
private int	countAboveThreshold(int[][] mat, double threshold) Count the number of cells above the threshold.
<A,B> double	dependence(NumberArrayAdapter<?,A> adapter1, A data1, NumberArrayAdapter<?,B> adapter2, B data2) Measure the dependence of two variables.
private static void	drawLine(int x0, int y0, int x1, int y1, boolean[][] pic) Draw a line onto the array, using the classic Bresenham algorithm.
private int[][]	houghTransformation(boolean[][] mat) Perform a hough transformation on the binary image in "mat".
private long	sumMatrix(int[][] mat) Compute the sum of a matrix.

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.dependence.AbstractDependenceMeasure

clamp, computeNormalizedRanks, discretize, index, ranks, ranks, size, size, sortedIndex

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.lmu.ifi.dbs.elki.math.statistics.dependence.DependenceMeasure

dependence, dependence, dependence

Field Detail

STATIC

public static final HSMDependenceMeasure STATIC

Static instance.

STEPS

private static final int STEPS

Angular resolution. Best if divisible by 4: smaller tables. The original publication used 50.

See Also:

Constant Field Values

resolution

private final int resolution

Resolution of image.

See Also:

Constant Field Values

table

private static final SinCosTable table

Precompute sinus and cosinus

Constructor Detail

HSMDependenceMeasure

public HSMDependenceMeasure()

Method Detail

dependence

public <A,B> double dependence(NumberArrayAdapter<?,A> adapter1,
                               A data1,
                               NumberArrayAdapter<?,B> adapter2,
                               B data2)

Description copied from interface: DependenceMeasure

Measure the dependence of two variables. This is the more flexible API, which allows using different internal data representations.

Type Parameters:

A - First array type

B - Second array type

Parameters:

adapter1 - First data adapter

data1 - First data set

adapter2 - Second data adapter

data2 - Second data set

Returns:

Dependence measure

sumMatrix

private long sumMatrix(int[][] mat)

Compute the sum of a matrix.

Parameters:

mat - Matrix

Returns:

Sum of all elements

countAboveThreshold

private int countAboveThreshold(int[][] mat,
                                double threshold)

Count the number of cells above the threshold.

Parameters:

mat - Matrix

threshold - Threshold

Returns:

Number of elements above the threshold.

houghTransformation

private int[][] houghTransformation(boolean[][] mat)

Perform a hough transformation on the binary image in "mat".

Parameters:

mat - Binary image

Returns:

Hough transformation of image.

drawLine

private static void drawLine(int x0,
                             int y0,
                             int x1,
                             int y1,
                             boolean[][] pic)

Draw a line onto the array, using the classic Bresenham algorithm.

Parameters:

x0 - Start X

y0 - Start Y

x1 - End X

y1 - End Y

pic - Picture array