System (hierarchical) clustering method and SPSS implementation

Catalog

One . Definition

Two . thought

3、 ... and . give an example

Four . Systematic clustering method Spss Realization

5、 ... and . Conclusion

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One . Definition

Systematic clustering (hierarchjcal cluster method) One translation " Hierarchical clustering method ". A method of cluster analysis . The method is to treat each sample as a class at the beginning , Then take the nearest sample ( That is, the group with the smallest distance ) First, it is grouped into small categories , Then press the aggregated subclass Distance between classes Re merger , Keep going , Finally, all subclasses are aggregated into a large class .

notes ： Distance between classes and distance between samples

Here is my own understanding ： Classes can consist of one or more samples , So if the class consists of only one sample , The distance between classes is equal to the distance between samples ; If the class consists of multiple samples , Then we need to define the distance between classes . The main definitions are as follows ：

1. The shortest distance method

2. The longest distance method

3. Group average connection method

4. Intra group average connection method

5. Barycenter method

6. Variable average method

7. The sum of squares of deviations

ad locum （ Systematic clustering ） When calculating the distance between classes, we use the shortest distance method ：

As shown in the figure , The category on the left contains five points , The right contains three points , among 1 Point and 2 The distance between the points Is the smallest distance between all points , therefore 1 Point and 2 The distance between points is the shortest distance of these two kinds .

Naturally , We think of , How to calculate 1 Point and 2 The distance between points ？

This is the distance between samples just mentioned , The most commonly used definition is Euclidean distance (EuclideanDistance), From the distance formula between two points in Euclidean space .

Euclidean distance formula in two-dimensional space

Such as ： Definition a=[1,5],b=[2,1], solve a And b Euclidean distance between vectors （ Use matlab Realization ）

a=[1,5],b=[2,1];
c=[a;b];
pdist(c,'euclidean')

Euclidean distance formula in three-dimensional space

n Euclidean distance formula of dimensional space

n Dimensional Euclidean space It's a set of points , Every point of it  X  It can be expressed as (x[1]x[2]…x[n]), Then set points X1(x[1]x[2]…x[n]) With the point X2(y[1]y[2]…y[n]) The distance between them can be expressed as

Two . thought

For the idea of systematic clustering , I use flow chart to show ：

Let the initial sample have n individual , Each sample falls into its own category .

3、 ... and . give an example

Set the available quality indicators of milk production in a certain place X To measure , There are five bottles of fresh milk ,X The values of are 1.5,2.5,5,6.5,8.5. Please use the system clustering method to classify five bottles of milk .

Explain ： Let the distance between samples use Euclidean distance , Use the shortest distance between classes , And record the samples as X1、X2、X3、X4、X5.

1） The calculated distance is shown in the table

class	X1	X2	X3	X4	X5
X1	0	1	3.5	5	7
X2		0	2.5	4	6
X3			0	1.5	3.5
X4				0	2
X4					0

2） take X1 And X2 Group together , Write it down as N1

class	N1	X3	X4	X5
N1	0	2.5	4	6
X3		0	1.5	2.5
X4			0	2
X5				0

3） take X3 And X4 Group together , Write it down as N2

class	N1	N2	X5
N1	0	2.5	6
N2		0	2
X5			0

4） take N2 And X5 Group together , Write it down as N3

class	N1	N3
N1	0	2.5
N3		0

5） take N1 And N3 Group together , end

6） Draw a genealogical structure （ It is complicated to process data and draw pictures by yourself , Let's skip , The next part uses Spss Simulate and draw ）

Four . Systematic clustering method Spss Realization

1) Data import （ This data has no practical significance, only for demonstration ）

This is us. excel Data in table , The file named “milk.xlsx"

  Then we turn on Spss24（ If the version is too low, some functions may not be realized ）

  Now we have successfully imported the data , It's time to move on .

2） You can start clustering

We take the liberty of correcting a small problem ,Spss Set our several clusters under the classification column , But in fact, we know that clustering and classification are completely different concepts .

choice V2 As a variable ,V1 Mark the basis for the case .

 

  stay ” chart “ Check “ Genealogy ”

3） Generate analysis results

Case summary a,b
individual case
It works		defect		A total of
Number of cases	percentage	Number of cases	percentage	Number of cases	percentage
5	100.0	0	.0	5	100.0

a.   Square Euclidean distance In the use

b. Average connection （ Intergroup ）

 

Here, the vertical icicle diagram is also generated by default , But in general, it is of little reference significance .

5、 ... and . Conclusion

Here, the sharing of systematic clustering is over .

I wish ： Always happy .