Correlations

Full name Microsoft.VisualBasic.Math.Correlations.Correlations Assembly Microsoft.VisualBasic.Runtime Members 16

计算两个数据向量之间的相关度的大小

01 Syntax

Microsoft.VisualBasic.Math.Correlations.Correlations

02 Methods

Name	Overloads	Summary
JaccardIndex	1	The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally coined coefficient de communauté by Paul Jaccard), is a statistic used…
JaccardIndex	2
SW	1	Sandelin-Wasserman similarity function.
JSD	1	Jensen–Shannon divergence（J-S散度） is a method of measuring the similarity between two probability distributions.
KLD	1	Kullback-Leibler divergence, (KL散度/相对熵)
rankKendallTauBeta	1	Provides rank correlation coefficient metrics Kendall tau
kendallTauBeta	1	Provides rank correlation coefficient metrics Kendall tau
GetPearson	2
TestStats	1
Spearman	1	This method should not be used in cases where the data set is truncated; that is, when the Spearman correlation coefficient is desired for the top X records (whether by pre-chang…
CorrelationMatrix	1	输入的数据为一个对象属性的集合，默认的compute计算方法为Correlations.GetPearson())

03 Properties

Name	Overloads	Summary
PearsonDefault	1	默认使用Pearson相似度

04 Fields

Name	Overloads	Summary
TINY	2	will regularize the unusual case of complete correlation

05 Members

method JaccardIndex #

JaccardIndex``1(IEnumerable(Of ``0), IEnumerable(Of ``0), Func(Of Object, Object, Boolean))

The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally coined coefficient de communauté by Paul Jaccard), is a statistic used for comparing the similarity and diversity of sample sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets.

https://en.wikipedia.org/wiki/Jaccard_index

Type Parameters

Name	Description
`T`

Parameters

Name	Type	Description
`a`	IEnumerable(Of ``0)	-
`b`	IEnumerable(Of ``0)	-
`equal`	`Func(Of Object, Object, Boolean)`	-

method JaccardIndex overload 2 #

JaccardIndex(IReadOnlyCollection(Of String), IReadOnlyCollection(Of String))

https://en.wikipedia.org/wiki/Jaccard_index

Parameters

Name	Type	Description
`a`	`IReadOnlyCollection(Of String)`	-
`b`	`IReadOnlyCollection(Of String)`	-

method SW #

SW(Double(), Double())

Sandelin-Wasserman similarity function. (假若所有的元素都是0-1之间的话，结果除以2可以得到相似度)

Parameters

Name	Type	Description
`x`	`Double()`	-
`y`	`Double()`	-

method JSD #

JSD(Double(), Double())

Jensen–Shannon divergence（J-S散度） is a method of measuring the similarity between two probability distributions. It is based on the Kullback–Leibler divergence（K-L散度）, with some notable (and useful) differences, including that it is symmetric and it is always a finite value.

Parameters

Name	Type	Description
`P`	`Double()`	-
`Q`	`Double()`	-

Returns

jsd value is not in range [0,1], value maybe in any real number.

method KLD #

KLD(Double(), Double())

Kullback-Leibler divergence, (KL散度/相对熵)

Remarks

计算 D_KL(P || Q) = Σ P(i) * ln(P(i) / Q(i))

Parameters

Name	Type	Description
`x`	`Double()`	x和y必须是等长的
`y`	`Double()`	-

method rankKendallTauBeta #

rankKendallTauBeta(Double(), Double())

Provides rank correlation coefficient metrics Kendall tau

Remarks

https://github.com/felipebravom/RankCorrelation

Parameters

Name	Type	Description
`x`	`Double()`	-
`y`	`Double()`	-

method kendallTauBeta #

kendallTauBeta(Double(), Double())

Provides rank correlation coefficient metrics Kendall tau

Remarks

https://github.com/felipebravom/RankCorrelation

Parameters

Name	Type	Description
`x`	`Double()`	-
`y`	`Double()`	-

method GetPearson #

GetPearson(Double(), Double(), Double, Double, Double, Double, Double, Boolean)

Remarks

checked by Excel

Parameters

Name	Type	Description
`x`	`Double()`	-
`y`	`Double()`	-
`prob`	`Double`	p-value in R `cor.test` function.
`prob2`	`Double`	-
`z`	`Double`	fisher's z trasnformation
`df`	`Double`	degree of freedom
`t`	`Double`	student's t probability

method GetPearson overload 2 #

GetPearson(Double(), Double())

Pearson correlations

Remarks

计算 Pearson 相关系数

Parameters

Name	Type	Description
`x#`	`Double()`	-
`y#`	`Double()`	-

method TestStats #

TestStats(Double, Int32, Double, Double, Double, Double, Double, Boolean)

Remarks

Fisher's z 变换，主要用于皮尔逊相关系数的非线性修正上面。因为普通皮尔逊相关系数在0-1上并不服从正态分布，相关系数的绝对值越趋近1时，概率变得非常非常小。相关系数的分布非常像断了两头的正态分布。所以需要通过Fisherz-transformation对皮尔逊相关系数进行修正，使得满足正态分布。

Parameters

Name	Type	Description
`cor`	`Double`	-
`n`	`Int32`	should be the length of x or y vector
`z`	`Double`	-
`pvalue`	`Double`	-
`prob2`	`Double`	-
`t`	`Double`	-
`df`	`Double`	-
`throwMaxIterError`	`Boolean`	-

method Spearman #

Spearman(Double(), Double())

This method should not be used in cases where the data set is truncated; that is, when the Spearman correlation coefficient is desired for the top X records (whether by pre-change rank or post-change rank, or both), the user should use the Pearson correlation coefficient formula given above. (斯皮尔曼相关性)

Remarks

https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient spearman rho checked!

Parameters

Name	Type	Description
`X`	`Double()`	-
`Y`	`Double()`	-

method CorrelationMatrix #

CorrelationMatrix(IEnumerable(Of NamedValue(Of Double())), ICorrelation)

输入的数据为一个对象属性的集合，默认的compute计算方法为Correlations.GetPearson()

Parameters

Name	Type	Description
`data`	`IEnumerable(Of NamedValue(Of Double()))`	`[ID, properties]`
`compute`	ICorrelation	Using pearson method as default if this parameter is nothing. (默认的计算形式为Correlations.GetPearson())

property PearsonDefault #

PearsonDefault

默认使用Pearson相似度

field TINY #

TINY

will regularize the unusual case of complete correlation

Remarks

A this tiny value for avoid divid ZERO

field TINY overload 2 #

TINY

method JaccardIndex #

JaccardIndex(IEnumerable(Of T), IEnumerable(Of T), Func(Of Object, Object, Boolean))