How to test the difference between 2 groups of 2D matrix?

Hi there, I have 2 groups of 2D matrix, which stand for two groups of points in 2D coordinate,i.e.

group1:[x1,y1],[x2,y2],[x3,y3]...
group2:[x'1,y'1],[x'2,y'2],[x'3,y'3]...

I want to test whether these two groups of data have a significant difference, could anyone tell me which method I should choose, thanks a lot!

Answer 1

[Star Strider]

If you have R2015a or later, the ismembertol function would be my choice, because if your values are floating-point, you will need to include a tolerance value.

If you are talking about a statistical significance between them, and your know they are normally distributed, one of the t-test functions would likely work.

If you want to use non-parametric statistics, the Wilcoxon ranksum or signrank tests would likely be best.

All the statistical tests are in the Statistics and Machine Learning Toolbox.

[Weiqian Jiang]

Thanks a lot for your kind response,but as far as I know, I only use t-test or ranksum test to test the difference between 2 array (1-dimension), but my data now are 2 matrix (2-dimensions), actually they are two groups of points which has x as well as y coordinate, I don't know whether and how ttest or ranksum test can do this?

[Star Strider]

I still don’t know enough about your data. If you want to do a linear fit and compare the parameters, this paper Comparing Correlation Coefficients, Slopes, and Intercepts seems to go into sufficient detail, and there are links to related papers from the same author. (These appear to be statistics class handouts.)

[Weiqian Jiang]

Sorry...I made my question a bit confused, maybe I should define my question as the classification problem, I want to find a line that can classify my points into two groups, I want to know whether this line (classifier) exists and how well it classify my points into two groups..

[Star Strider]

Then use the classify function. It implements a linear discriminant analysis.

[Weiqian Jiang]

I'll try soon later, thank you very much!

[Star Strider]

My pleasure!

Answer 2

[Image Analyst]

It would help if we had more context. For example, if they are two closed contours - perimeters around some shapes - and you want to see how well they compare, some people look at the non-overlapped area, and sometimes normalize it to the area of one of the blobs or the average of the two areas. So you could use poly2mask() to turn them into masks and count the non-overlapped pixels

mask1 = poly2mask(x1, y1, rows, columns);
mask2 = poly2mask(x2, y2, rows, columns);
nonOverlappedPixels = xor(mask1, mask2);
numNonOverlappedPixels = sum(nonOverlappedPixels(:));
percentMisMatch = 100 * numNonOverlappedPixels / mean([sum(mask1(:)), sum(mask2(:))]);

[Weiqian Jiang]

Thanks for your kind response, my data set are as follows(for example): group1: [0,0],[0,1],[1,0] group2:[1,1],[0.2,1],[1,0] as you see, there are some points that are very close in these two groups, I want to find a linear or non-linear classifier to distinguish these two groups, if this classifier is hard to find, I still want to know whether or not these two groups are different. Could you tell me the method to find a classifier or to distinguish these two groups? Thanks!

[Image Analyst]

Try the "Classification Learner" app on the Apps tab of the tool ribbon. From there you can try a bunch of different classification methods such as kmeans, SVM, Bayesian, etc. Try several of them with a wide range of your data and see which one works the best.

[Weiqian Jiang]

Sorry but I cannot find the tool ribbon in this website, could you please tell me where I can find this "classification learner"?