How can I use multidimensional matrices as input for clustering in MATLAB?

Hi all,

I am trying to cluster 2-dimensional time series signals with a similarity measure (maybe corr2).

For example, suppose I have the following signals (1st column is time, 2nd column is amplitude):

A = [1.2,1.5; 2.4,0.5; 3.2,1.5; 4.1,1.0]

B = [1.0,1.0; 2.0,0; 3.0,1.0; 4.0,0.5]

C = [1.1,1.2; 2.2,1.3; 3.3,1.5; 4.2,1.7]

D = [1.3,1.3; 2.1,1.4; 3.2,1.7; 4.3, 2.0]

E = [1.3,1.8; 2.3,0.4; 3.1,1.6; 4.3,0.8]

After applying a clustering technique, such as K-means (hard partition) or Fuzzy (soft partition) or something else, I am expecting 2 clusters like this:

Cluster 1 (A, B, E: see figure 1) and cluster 2 (C, D: see figure 2)

Plot of A, B, E

Plot of C, D

I have been searching for a way to cluster 2-dimensional matrices but I have not found any MATLAB code I can adopt to cluster my matrices.

How can I use multidimensional matrices like A, B, C, D and E as input for clustering in MATLAB?

Answer 1

[Ameer Hamza]

You can first convert each matrix to a linear array and then apply a clustering algorithm. Since the corresponding element of each matrix have the same unit, so the shape and order of input do not matter to the clustering algorithm. For example,

A = [1.2,1.5; 2.4,0.5; 3.2,1.5; 4.1,1.0];
B = [1.0,1.0; 2.0,0; 3.0,1.0; 4.0,0.5];
C = [1.1,1.2; 2.2,1.3; 3.3,1.5; 4.2,1.7];
D = [1.3,1.3; 2.1,1.4; 3.2,1.7; 4.3, 2.0];
E = [1.3,1.8; 2.3,0.4; 3.1,1.6; 4.3,0.8];

M = [A(:) B(:) C(:) D(:) E(:)]'; % each matrix A,B,...,E is now a row of matrix M

idx = kmeans(M, 2, 'Distance', 'correlation')

result:

idx =

     1
     1
     2
     2
     1

It identified 1st, 2nd, and 5th row are one cluster, 3rd and fourth are other cluster.

[SOPAE YI]

Hi Mr. Hamza,

Your answer is AWESOME!!

Thanks a million!!

I have learned something :--)

One more question,

Since most of my data have different lengths…

Can we cluster matrices of different sizes like following?

A = [1.2,1.5; 2.4,0.5; 3.2,1.5];

B = [1.0,1.0; 2.0,0; 3.0,1.0; 4.0,0.5];

C = [1.1,1.2; 2.2,1.3; 3.3,1.5];

D = [1.3,1.3; 2.1,1.4; 3.2,1.7; 4.3,2.0; 5.0,1.9];

E = [1.3,1.8; 2.3,0.4; 3.1,1.6; 4.3,0.8];

*** I noticed that ‘interp1’ is losing ‘time information’. The time (1st column) of each point is important in my research. I’d like to keep the time information of all matrices.

I do not have to keep the actual time values, I just want to keep the proportional time interval between points (points within 1st column). (e.g. Z = [1, 1.2; 6, 2.1; 8, 3.4 ] can be rewritten as ZZ = [1, 1.2; 4, 2.1; 5, 3.4 ] ). As they still have the same ratio (3 to 1) of time intervals, they have the same time information.

[Ameer Hamza]

The clustering algorithm must take data with a consistent dimension, so I am not sure is there an easy way to apply clustering in a situation where the size of input matrices is not equal. Please refer to my comment on your other question to see how you can avoid losing information in matrix B.