-1

I have two groups of data. Both groups have 25 variables and 114 observations.

The goal is to take one of the variables in either group, calculate the mahalanobis distance from both of the groups mean. The group with the smallest distance is the one that the variable belongs to.

I have implemented this in Octave and it "works". It gives an answer but thrown a singular matrix warning or a "warning: matrix singular to machine precision" error. For some reason the covarience matrix of either group is ending up singular, or it's a precision error.

I also implemented this in python. And it throws a singular matrix error. I ended up using the numpy pseudo inverse function (linalg.pinv) instead of taking the real inverse of the covarience matrix.

Questions

1) Why is my covariance matrix giving me this error when I take the inverse of it?

2) What is the proper way to handle this application?

3) Is using the numpy pseudo inverse still calculating close to the correct mahalanobis distance? I get very different values using it than what Octave spits out.

Code

Code for Octave and python can be found here: Code

Update

Instead of 25 variables and 114 observations, I reduced the data to have 25 variables and 25 observations and everything started to work.

Why does it matter?

Is this common?

How can I be able to have more observations than variables or more importantly more variables than observations? Is there anything that I can do to the data to pre-process it to work?

Python Code

Here is the working python code with the 25 variables and 25 observations edit.

#Group 1
#25 Variables with 114 observations each
S0 = [131, 133, 123, 123, 133, 135, 137, 136, 136, 140, 139, 137, 136, 134, 135, 136, 136, 137, 135, 133, 135, 136, 136, 139, 137, 132, 115, 80, 69, 95, 91, 60, 70, 94, 99, 79, 55, 71, 93, 108, 109, 107, 105, 102, 102, 107, 113, 116, 116, 118, 120, 115, 109, 110, 107, 91, 88, 101, 102, 105, 106, 101, 98, 100, 104, 105, 104, 103, 99, 88, 83, 86, 86, 88, 89, 99, 100, 98, 100, 99, 94, 90, 91, 99, 103, 103, 101, 96, 88, 81, 75, 69, 72, 82, 82, 71, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S1 = [127, 134, 125, 119, 126, 133, 134, 137, 140, 140, 140, 139, 136, 135, 135, 135, 136, 136, 135, 134, 134, 135, 135, 136, 136, 136, 134, 127, 103, 68, 75, 92, 79, 57, 74, 99, 97, 71, 57, 82, 105, 105, 103, 103, 101, 101, 105, 112, 119, 120, 121, 118, 111, 105, 109, 106, 89, 89, 101, 101, 105, 105, 100, 97, 101, 105, 105, 105, 103, 99, 89, 83, 85, 86, 87, 88, 96, 102, 99, 100, 101, 98, 91, 91, 96, 101, 103, 103, 99, 95, 88, 81, 74, 72, 78, 85, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S2 = [130, 134, 123, 120, 127, 136, 137, 140, 141, 141, 141, 139, 137, 135, 135, 136, 136, 136, 136, 132, 134, 134, 135, 136, 135, 135, 132, 123, 98, 67, 76, 92, 77, 59, 78, 100, 93, 63, 59, 85, 105, 105, 105, 103, 101, 102, 108, 113, 115, 115, 119, 118, 111, 106, 111, 105, 87, 90, 102, 103, 105, 105, 101, 99, 102, 105, 105, 103, 104, 101, 91, 85, 86, 87, 88, 88, 97, 102, 100, 101, 101, 98, 91, 91, 96, 101, 104, 103, 101, 96, 86, 80, 73, 70, 76, 85, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S3 = [129, 133, 124, 121, 130, 136, 136, 137, 140, 140, 140, 140, 136, 135, 135, 135, 135, 134, 134, 132, 133, 134, 136, 136, 136, 135, 133, 123, 95, 62, 79, 93, 73, 60, 86, 103, 92, 62, 62, 89, 105, 105, 104, 102, 101, 103, 109, 115, 117, 118, 121, 119, 110, 106, 110, 101, 85, 92, 101, 103, 105, 105, 101, 98, 101, 105, 106, 105, 104, 100, 91, 85, 88, 88, 89, 91, 100, 102, 101, 102, 99, 96, 89, 91, 98, 101, 103, 101, 98, 93, 85, 79, 72, 70, 79, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S4 = [126, 134, 127, 120, 126, 135, 136, 137, 139, 140, 139, 140, 139, 139, 137, 135, 135, 134, 133, 132, 132, 133, 135, 137, 139, 137, 133, 119, 89, 65, 86, 94, 68, 60, 89, 103, 85, 55, 70, 97, 105, 103, 103, 101, 101, 103, 109, 117, 119, 119, 121, 118, 109, 105, 108, 98, 85, 91, 99, 98, 101, 103, 97, 91, 99, 104, 105, 105, 103, 99, 88, 85, 90, 92, 92, 94, 101, 101, 100, 102, 102, 98, 96, 98, 101, 103, 103, 102, 100, 95, 86, 79, 73, 74, 85, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S5 = [123, 131, 131, 122, 123, 131, 136, 137, 139, 139, 140, 140, 139, 136, 136, 135, 134, 135, 134, 133, 134, 136, 137, 139, 139, 139, 135, 131, 106, 70, 69, 92, 83, 59, 76, 99, 90, 63, 65, 91, 105, 104, 102, 102, 101, 103, 105, 113, 121, 121, 122, 121, 113, 106, 109, 110, 96, 86, 94, 99, 97, 101, 101, 91, 89, 100, 105, 106, 105, 102, 92, 86, 89, 91, 93, 92, 99, 103, 101, 101, 102, 101, 98, 96, 99, 101, 101, 101, 101, 98, 92, 85, 77, 75, 85, 87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S6 = [125, 131, 131, 123, 125, 133, 135, 137, 137, 139, 140, 137, 136, 135, 135, 135, 137, 137, 139, 136, 137, 137, 139, 139, 139, 139, 135, 129, 103, 68, 74, 91, 73, 59, 83, 102, 87, 60, 63, 91, 106, 105, 105, 101, 101, 103, 109, 117, 119, 119, 121, 121, 114, 107, 108, 111, 101, 85, 90, 99, 98, 101, 103, 95, 94, 102, 105, 105, 105, 101, 91, 86, 89, 91, 93, 92, 99, 103, 102, 103, 103, 101, 97, 96, 98, 101, 102, 101, 101, 98, 91, 83, 74, 75, 87, 85, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S7 = [125, 133, 128, 121, 126, 133, 134, 136, 137, 137, 137, 136, 135, 135, 135, 136, 137, 137, 137, 136, 136, 136, 136, 137, 139, 139, 134, 118, 79, 68, 92, 89, 62, 68, 95, 101, 77, 55, 77, 101, 104, 105, 105, 102, 101, 104, 111, 116, 118, 118, 120, 120, 115, 107, 108, 108, 98, 84, 91, 95, 96, 101, 95, 87, 96, 105, 105, 105, 103, 99, 88, 85, 91, 93, 94, 94, 100, 103, 101, 101, 101, 99, 97, 98, 101, 103, 103, 103, 100, 94, 89, 79, 75, 83, 87, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S8 = [127, 133, 123, 120, 128, 134, 134, 136, 137, 139, 140, 140, 137, 137, 136, 136, 139, 139, 137, 136, 135, 136, 137, 137, 137, 134, 126, 101, 68, 79, 98, 89, 59, 76, 100, 92, 67, 55, 84, 103, 105, 105, 105, 101, 101, 104, 111, 117, 119, 117, 119, 121, 115, 107, 107, 105, 91, 90, 101, 102, 105, 105, 101, 99, 103, 106, 106, 105, 103, 97, 86, 85, 89, 88, 87, 91, 100, 101, 99, 100, 97, 91, 87, 91, 99, 102, 102, 99, 91, 84, 78, 71, 72, 80, 84, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S9 = [130, 133, 124, 120, 129, 133, 134, 136, 139, 140, 139, 137, 135, 135, 135, 135, 136, 136, 136, 136, 136, 136, 137, 137, 136, 133, 125, 100, 69, 80, 97, 76, 60, 84, 102, 93, 63, 57, 85, 105, 105, 105, 105, 101, 101, 102, 109, 113, 115, 113, 118, 121, 113, 105, 109, 100, 86, 91, 101, 100, 103, 103, 98, 98, 103, 105, 105, 105, 103, 95, 85, 85, 87, 88, 87, 93, 101, 99, 101, 101, 98, 92, 92, 99, 103, 104, 103, 99, 91, 85, 79, 72, 73, 84, 85, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S10 = [125, 132, 126, 121, 128, 134, 135, 137, 139, 140, 140, 139, 136, 136, 136, 137, 137, 137, 137, 137, 137, 137, 137, 137, 137, 136, 131, 113, 74, 67, 92, 96, 67, 62, 91, 103, 91, 63, 55, 80, 101, 105, 105, 104, 100, 99, 99, 107, 111, 112, 114, 119, 115, 108, 106, 107, 93, 84, 96, 99, 101, 104, 102, 96, 97, 103, 105, 105, 103, 100, 89, 85, 89, 89, 91, 95, 102, 100, 101, 102, 99, 94, 93, 98, 101, 103, 103, 101, 98, 91, 84, 76, 71, 75, 85, 81, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S11 = [127, 131, 124, 122, 131, 135, 135, 137, 139, 140, 140, 139, 137, 136, 136, 135, 135, 133, 134, 133, 133, 135, 136, 137, 139, 136, 130, 105, 70, 70, 93, 91, 65, 63, 92, 103, 88, 65, 59, 82, 103, 105, 104, 103, 101, 103, 107, 115, 118, 118, 120, 121, 114, 105, 108, 105, 88, 85, 96, 96, 98, 102, 97, 90, 97, 105, 105, 104, 101, 95, 85, 88, 91, 93, 93, 100, 102, 101, 102, 102, 99, 97, 98, 100, 103, 104, 102, 101, 97, 89, 84, 74, 72, 80, 86, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S12 = [128, 132, 124, 123, 133, 135, 136, 139, 141, 141, 139, 136, 134, 134, 134, 135, 134, 134, 134, 135, 135, 136, 137, 137, 137, 134, 128, 106, 73, 69, 92, 94, 72, 60, 81, 100, 91, 65, 60, 86, 105, 105, 103, 102, 101, 102, 108, 114, 117, 118, 121, 119, 112, 104, 107, 105, 89, 85, 98, 100, 102, 104, 99, 96, 102, 106, 106, 105, 101, 91, 85, 87, 87, 89, 91, 101, 103, 101, 102, 102, 98, 93, 92, 98, 102, 103, 103, 101, 95, 89, 83, 76, 72, 79, 88, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S13 = [125, 133, 128, 121, 130, 135, 135, 137, 137, 139, 137, 135, 133, 134, 133, 133, 136, 136, 135, 134, 134, 136, 136, 137, 137, 137, 134, 127, 103, 68, 72, 95, 92, 63, 67, 96, 100, 73, 55, 79, 104, 105, 105, 105, 101, 101, 105, 113, 117, 117, 118, 120, 116, 108, 105, 109, 99, 83, 91, 99, 99, 103, 99, 94, 100, 105, 105, 105, 103, 93, 85, 86, 90, 92, 92, 98, 103, 101, 101, 102, 100, 96, 93, 95, 101, 103, 103, 102, 100, 93, 86, 80, 73, 74, 85, 85, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S14 = [124, 133, 127, 123, 131, 134, 135, 136, 137, 139, 139, 137, 137, 137, 137, 137, 137, 140, 137, 135, 134, 137, 139, 139, 139, 140, 137, 127, 101, 68, 76, 101, 90, 59, 81, 104, 93, 63, 67, 88, 105, 105, 105, 105, 101, 101, 103, 109, 116, 119, 119, 121, 119, 110, 103, 103, 90, 85, 97, 93, 99, 101, 92, 92, 103, 107, 107, 106, 101, 91, 87, 91, 93, 95, 94, 99, 103, 103, 103, 103, 101, 98, 98, 101, 103, 105, 105, 103, 101, 95, 87, 79, 73, 80, 87, 85, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S15 = [129, 132, 123, 121, 131, 134, 134, 136, 137, 140, 139, 137, 137, 139, 139, 137, 137, 139, 139, 135, 135, 136, 137, 137, 137, 137, 136, 129, 105, 70, 77, 97, 80, 60, 82, 103, 92, 63, 60, 90, 106, 105, 104, 103, 101, 101, 105, 113, 117, 117, 119, 119, 112, 104, 107, 104, 88, 90, 101, 100, 104, 103, 98, 99, 105, 107, 106, 105, 101, 91, 87, 88, 89, 90, 90, 97, 103, 101, 101, 101, 100, 96, 92, 95, 101, 103, 103, 103, 99, 92, 84, 79, 72, 73, 85, 85, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S16 = [127, 131, 123, 124, 133, 135, 136, 139, 139, 141, 140, 137, 135, 135, 136, 137, 139, 137, 139, 137, 136, 136, 139, 140, 139, 137, 131, 122, 91, 67, 85, 98, 70, 60, 84, 101, 87, 55, 60, 88, 105, 105, 105, 105, 101, 100, 103, 110, 115, 115, 118, 119, 111, 104, 107, 100, 85, 94, 101, 101, 105, 103, 98, 101, 105, 107, 107, 105, 101, 93, 85, 86, 87, 89, 90, 97, 103, 101, 101, 102, 100, 95, 92, 97, 101, 105, 105, 103, 100, 93, 85, 78, 72, 75, 87, 85, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S17 = [119, 129, 131, 120, 121, 131, 133, 135, 137, 137, 139, 137, 137, 134, 134, 134, 135, 136, 136, 137, 136, 135, 134, 135, 136, 137, 136, 133, 126, 98, 67, 80, 95, 76, 60, 78, 101, 97, 69, 57, 79, 103, 104, 105, 104, 99, 99, 105, 112, 114, 115, 119, 117, 109, 105, 109, 102, 83, 91, 99, 100, 103, 101, 96, 97, 103, 107, 107, 105, 103, 97, 85, 86, 90, 91, 92, 97, 103, 102, 101, 103, 101, 98, 94, 97, 101, 104, 103, 103, 100, 93, 86, 79, 73, 74, 83, 85, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S18 = [119, 128, 131, 122, 125, 134, 136, 136, 139, 140, 141, 140, 140, 136, 137, 136, 136, 137, 139, 137, 137, 137, 139, 139, 140, 139, 137, 135, 121, 94, 67, 85, 98, 73, 60, 79, 102, 98, 68, 57, 82, 104, 105, 105, 104, 101, 100, 106, 115, 117, 117, 121, 118, 110, 105, 107, 96, 83, 94, 99, 99, 104, 102, 96, 97, 103, 107, 106, 105, 104, 96, 86, 85, 91, 92, 93, 98, 103, 103, 103, 103, 102, 98, 97, 99, 103, 105, 105, 103, 100, 94, 86, 80, 73, 73, 84, 86, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S19 = [128, 131, 122, 121, 131, 135, 135, 137, 137, 141, 141, 141, 139, 136, 135, 134, 136, 135, 133, 133, 134, 134, 136, 139, 139, 137, 133, 123, 98, 67, 77, 97, 80, 60, 74, 98, 98, 71, 57, 85, 104, 105, 104, 102, 100, 102, 108, 115, 117, 118, 119, 114, 106, 106, 109, 98, 83, 92, 101, 101, 105, 104, 99, 98, 103, 106, 106, 105, 104, 98, 87, 85, 90, 89, 90, 94, 101, 101, 100, 103, 102, 97, 92, 93, 99, 102, 103, 102, 99, 94, 87, 81, 74, 73, 83, 87, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S20 = [128, 131, 125, 123, 132, 136, 137, 139, 140, 140, 140, 139, 136, 135, 133, 133, 134, 135, 135, 134, 135, 136, 139, 140, 140, 139, 131, 118, 90, 67, 81, 98, 76, 60, 79, 99, 86, 59, 65, 91, 105, 104, 104, 101, 99, 103, 111, 117, 117, 119, 121, 114, 106, 104, 107, 97, 84, 95, 102, 101, 105, 104, 100, 99, 104, 107, 107, 106, 103, 95, 85, 85, 88, 88, 90, 96, 103, 101, 101, 101, 99, 93, 91, 94, 100, 104, 105, 103, 101, 96, 86, 79, 72, 73, 85, 86, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S21 = [132, 131, 122, 121, 131, 136, 137, 137, 136, 137, 139, 135, 133, 133, 133, 136, 137, 137, 137, 135, 136, 137, 139, 140, 140, 136, 131, 107, 73, 69, 96, 93, 59, 69, 95, 96, 67, 55, 84, 107, 109, 109, 107, 103, 103, 108, 113, 114, 115, 118, 120, 116, 109, 109, 105, 91, 88, 101, 102, 103, 105, 102, 98, 100, 105, 105, 105, 104, 99, 87, 84, 88, 87, 89, 91, 98, 101, 98, 100, 99, 96, 89, 88, 92, 99, 101, 101, 99, 92, 85, 79, 73, 70, 79, 84, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S22 = [126, 134, 127, 121, 127, 135, 137, 139, 139, 140, 140, 139, 137, 137, 135, 136, 137, 139, 139, 137, 137, 139, 140, 140, 141, 139, 133, 119, 80, 67, 92, 96, 55, 68, 96, 100, 71, 55, 84, 107, 108, 108, 107, 103, 103, 107, 114, 117, 117, 118, 120, 119, 115, 110, 108, 97, 86, 98, 103, 101, 106, 103, 99, 99, 104, 106, 106, 104, 99, 89, 84, 88, 89, 90, 91, 97, 101, 100, 99, 101, 99, 94, 90, 93, 99, 102, 102, 101, 96, 88, 81, 74, 70, 76, 84, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S23 = [128, 135, 127, 121, 131, 134, 135, 136, 137, 141, 140, 139, 135, 135, 135, 135, 136, 139, 140, 139, 137, 139, 140, 140, 140, 137, 129, 105, 73, 73, 99, 89, 62, 73, 100, 90, 59, 65, 94, 107, 108, 109, 106, 104, 105, 107, 113, 116, 115, 117, 119, 117, 111, 108, 109, 96, 85, 97, 103, 103, 106, 103, 99, 101, 103, 102, 102, 103, 99, 92, 86, 89, 90, 91, 90, 94, 100, 99, 99, 101, 99, 94, 91, 92, 100, 103, 103, 100, 95, 86, 80, 74, 71, 80, 85, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S24 = [129, 131, 123, 125, 131, 134, 137, 139, 139, 141, 141, 140, 137, 136, 137, 139, 141, 141, 139, 137, 137, 139, 139, 140, 137, 130, 116, 87, 67, 91, 102, 68, 62, 90, 94, 74, 54, 74, 98, 108, 111, 110, 107, 102, 101, 103, 109, 111, 108, 109, 113, 113, 110, 105, 105, 94, 87, 101, 104, 105, 108, 105, 103, 103, 105, 107, 103, 101, 97, 87, 82, 84, 85, 85, 84, 92, 100, 99, 99, 101, 98, 89, 88, 95, 101, 103, 103, 99, 91, 83, 77, 71, 72, 81, 83, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];


#Group 2
#25 Variables with 114 observations each
S20 = [115, 114, 125, 130, 131, 132, 132, 132, 131, 130, 130, 130, 128, 128, 129, 128, 128, 128, 129, 130, 130, 130, 124, 98, 76, 75, 80, 80, 84, 96, 104, 107, 108, 110, 109, 108, 107, 104, 105, 107, 105, 101, 98, 99, 98, 96, 97, 96, 94, 93, 97, 105, 111, 110, 101, 90, 82, 76, 72, 67, 63, 65, 77, 100, 108, 105, 94, 78, 70, 77, 86, 90, 86, 89, 95, 94, 94, 95, 92, 92, 96, 97, 96, 91, 84, 76, 73, 81, 84, 85, 88, 86, 89, 99, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S21 = [122, 112, 119, 129, 129, 130, 131, 131, 131, 131, 131, 131, 130, 130, 130, 131, 131, 131, 131, 130, 130, 130, 130, 128, 109, 80, 75, 80, 82, 85, 96, 105, 108, 109, 110, 109, 108, 105, 105, 107, 108, 105, 101, 99, 101, 99, 96, 98, 98, 95, 94, 97, 105, 111, 111, 101, 90, 80, 73, 69, 65, 63, 70, 88, 106, 108, 105, 93, 78, 70, 76, 85, 88, 86, 87, 94, 94, 94, 94, 93, 92, 96, 98, 97, 92, 85, 76, 72, 82, 84, 86, 89, 87, 92, 100, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S22 = [120, 112, 119, 128, 130, 131, 131, 132, 131, 131, 130, 130, 130, 129, 129, 131, 132, 132, 132, 131, 131, 131, 131, 128, 107, 75, 74, 81, 84, 86, 94, 101, 105, 107, 108, 108, 106, 103, 103, 105, 106, 104, 99, 96, 96, 94, 92, 94, 95, 94, 94, 99, 107, 112, 109, 98, 87, 81, 76, 71, 67, 65, 69, 85, 105, 108, 105, 95, 81, 71, 75, 84, 88, 86, 88, 94, 92, 92, 94, 93, 92, 95, 96, 94, 88, 82, 74, 73, 82, 84, 85, 87, 86, 92, 101, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S23 = [120, 111, 115, 127, 129, 130, 131, 131, 131, 131, 130, 130, 129, 128, 128, 128, 128, 128, 127, 128, 128, 128, 128, 128, 116, 90, 74, 79, 81, 81, 86, 96, 102, 105, 107, 107, 105, 103, 102, 104, 105, 104, 101, 97, 96, 96, 92, 92, 95, 92, 90, 92, 100, 108, 111, 108, 98, 86, 76, 71, 68, 65, 65, 70, 90, 105, 107, 101, 88, 73, 68, 76, 83, 86, 83, 88, 94, 92, 92, 91, 89, 90, 92, 95, 92, 87, 80, 72, 75, 80, 80, 85, 88, 86, 93, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S24 = [119, 112, 121, 130, 131, 131, 131, 131, 131, 130, 130, 130, 128, 127, 128, 130, 131, 131, 130, 129, 130, 130, 130, 128, 107, 81, 74, 78, 77, 76, 83, 97, 102, 105, 108, 108, 107, 104, 102, 102, 105, 103, 96, 94, 94, 92, 91, 94, 94, 93, 94, 99, 109, 113, 108, 94, 88, 90, 86, 79, 69, 65, 68, 82, 100, 108, 105, 96, 82, 70, 73, 82, 86, 84, 88, 94, 91, 92, 94, 94, 95, 97, 97, 94, 88, 81, 73, 73, 80, 84, 86, 87, 86, 90, 99, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S25 = [119, 111, 121, 130, 131, 132, 132, 131, 131, 131, 130, 130, 130, 130, 130, 131, 131, 130, 130, 130, 130, 131, 131, 128, 104, 82, 75, 78, 78, 77, 84, 99, 107, 108, 110, 110, 109, 107, 105, 105, 107, 105, 101, 98, 99, 98, 96, 97, 96, 95, 95, 99, 107, 113, 108, 96, 89, 93, 92, 82, 72, 67, 68, 81, 101, 109, 107, 99, 84, 72, 75, 86, 88, 86, 91, 96, 93, 92, 95, 96, 96, 98, 98, 94, 88, 81, 74, 72, 80, 88, 88, 88, 86, 88, 98, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S26 = [113, 114, 126, 128, 130, 132, 131, 131, 132, 131, 130, 130, 130, 128, 129, 130, 130, 131, 131, 131, 131, 130, 130, 125, 105, 77, 74, 80, 81, 83, 93, 102, 107, 108, 108, 108, 107, 105, 104, 106, 107, 105, 101, 99, 99, 97, 94, 96, 97, 93, 92, 98, 105, 111, 110, 101, 91, 82, 76, 71, 67, 63, 68, 86, 106, 108, 101, 86, 72, 72, 82, 89, 88, 87, 94, 94, 93, 94, 93, 92, 93, 96, 96, 92, 87, 80, 72, 74, 82, 84, 86, 88, 87, 89, 98, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S27 = [116, 116, 128, 130, 131, 132, 131, 131, 131, 131, 130, 129, 128, 130, 131, 132, 131, 131, 131, 131, 131, 130, 130, 121, 96, 74, 77, 82, 82, 83, 92, 100, 103, 105, 105, 105, 105, 102, 102, 105, 104, 99, 94, 94, 93, 92, 94, 95, 94, 93, 97, 104, 111, 113, 107, 94, 85, 82, 76, 70, 65, 67, 78, 100, 109, 105, 95, 78, 70, 75, 85, 88, 84, 89, 94, 92, 92, 93, 93, 92, 94, 96, 94, 90, 84, 76, 70, 75, 83, 84, 87, 88, 86, 94, 101, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S28 = [125, 116, 116, 128, 130, 131, 131, 131, 131, 131, 130, 131, 130, 130, 130, 131, 131, 130, 130, 131, 130, 130, 130, 130, 121, 96, 74, 77, 81, 84, 88, 97, 105, 108, 109, 108, 107, 106, 105, 105, 107, 107, 104, 101, 100, 100, 97, 95, 97, 95, 91, 92, 97, 105, 111, 110, 100, 86, 76, 70, 67, 63, 67, 81, 102, 108, 104, 91, 75, 70, 80, 86, 88, 84, 88, 94, 92, 93, 94, 91, 90, 92, 96, 96, 92, 86, 77, 71, 76, 82, 83, 87, 88, 86, 94, 102, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S29 = [119, 110, 119, 128, 130, 131, 131, 131, 131, 130, 130, 131, 130, 129, 130, 130, 130, 130, 130, 131, 131, 131, 131, 130, 119, 96, 74, 76, 81, 82, 86, 96, 104, 107, 108, 107, 105, 103, 103, 105, 105, 104, 99, 97, 97, 95, 92, 95, 96, 92, 91, 96, 104, 111, 113, 107, 94, 82, 74, 70, 67, 63, 68, 88, 107, 107, 99, 82, 70, 70, 79, 85, 86, 84, 90, 94, 92, 92, 93, 91, 92, 94, 96, 94, 90, 86, 77, 71, 76, 84, 85, 88, 88, 86, 94, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S210 = [114, 114, 127, 130, 130, 131, 131, 131, 130, 131, 131, 131, 130, 131, 131, 130, 131, 132, 131, 131, 131, 131, 131, 130, 115, 89, 75, 78, 80, 79, 88, 103, 108, 110, 110, 108, 108, 106, 105, 107, 107, 106, 101, 99, 101, 99, 95, 97, 97, 93, 92, 98, 105, 111, 108, 96, 86, 82, 77, 70, 67, 65, 77, 99, 108, 105, 96, 81, 71, 75, 84, 90, 87, 86, 93, 95, 92, 93, 94, 93, 94, 97, 96, 94, 88, 82, 74, 72, 80, 86, 88, 89, 88, 88, 98, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S211 = [114, 119, 128, 130, 130, 131, 131, 131, 131, 130, 130, 130, 130, 130, 131, 132, 132, 131, 131, 131, 131, 130, 130, 125, 98, 75, 76, 82, 82, 86, 95, 102, 104, 107, 107, 107, 105, 102, 102, 105, 105, 101, 96, 95, 94, 92, 92, 95, 94, 93, 96, 104, 111, 110, 98, 88, 86, 81, 74, 68, 65, 75, 94, 108, 108, 103, 90, 76, 70, 77, 86, 88, 84, 88, 93, 92, 92, 93, 94, 93, 95, 97, 95, 90, 85, 77, 71, 74, 81, 84, 85, 86, 85, 90, 99, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S212 = [120, 111, 119, 128, 128, 130, 130, 131, 131, 131, 130, 129, 128, 129, 129, 130, 131, 131, 131, 130, 130, 130, 130, 130, 125, 99, 74, 78, 83, 85, 92, 100, 107, 108, 109, 110, 108, 107, 105, 105, 108, 107, 105, 102, 101, 101, 99, 95, 98, 96, 92, 94, 101, 108, 111, 105, 93, 80, 72, 68, 65, 63, 73, 92, 108, 108, 102, 88, 75, 71, 78, 86, 88, 85, 88, 94, 93, 93, 94, 92, 91, 94, 97, 96, 93, 86, 80, 72, 76, 83, 84, 86, 88, 86, 91, 99, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S213 = [116, 115, 125, 128, 130, 131, 131, 131, 131, 131, 130, 130, 130, 129, 129, 130, 131, 130, 131, 130, 131, 130, 130, 127, 105, 78, 74, 80, 82, 84, 92, 99, 104, 105, 107, 107, 107, 104, 103, 104, 106, 105, 99, 95, 95, 93, 92, 94, 94, 93, 95, 102, 111, 111, 102, 88, 84, 80, 74, 68, 65, 68, 83, 104, 108, 105, 98, 82, 72, 73, 82, 88, 88, 86, 91, 93, 92, 94, 94, 94, 94, 97, 97, 94, 89, 82, 75, 70, 78, 84, 86, 87, 87, 87, 95, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S214 = [116, 113, 124, 130, 130, 131, 132, 132, 131, 131, 131, 131, 131, 130, 130, 131, 131, 131, 131, 131, 130, 130, 130, 130, 118, 91, 74, 78, 82, 83, 90, 100, 107, 109, 110, 110, 109, 108, 107, 106, 108, 107, 105, 101, 100, 101, 96, 98, 97, 94, 93, 98, 107, 112, 109, 99, 86, 78, 72, 68, 67, 65, 71, 90, 107, 109, 104, 91, 75, 70, 78, 87, 90, 86, 90, 96, 94, 94, 94, 92, 92, 94, 97, 96, 92, 87, 80, 72, 74, 82, 84, 86, 88, 87, 91, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S215 = [119, 111, 119, 129, 130, 131, 131, 131, 131, 131, 130, 130, 130, 129, 128, 130, 130, 131, 130, 130, 130, 130, 130, 130, 125, 104, 76, 74, 81, 83, 86, 94, 104, 107, 108, 108, 106, 105, 102, 102, 105, 105, 101, 97, 97, 96, 92, 94, 96, 92, 92, 98, 107, 111, 110, 103, 90, 79, 73, 70, 67, 63, 67, 79, 102, 108, 104, 93, 78, 68, 72, 81, 86, 85, 85, 94, 94, 92, 93, 92, 91, 92, 94, 96, 95, 91, 85, 77, 72, 78, 83, 83, 87, 88, 89, 98, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S216 = [115, 112, 124, 130, 131, 133, 133, 133, 132, 132, 131, 130, 131, 130, 129, 130, 130, 131, 131, 131, 131, 131, 131, 130, 117, 88, 74, 80, 84, 84, 90, 99, 107, 108, 109, 109, 109, 107, 105, 107, 107, 105, 101, 101, 101, 98, 98, 99, 96, 94, 96, 102, 110, 113, 110, 99, 88, 78, 72, 69, 67, 65, 72, 91, 107, 108, 102, 86, 74, 71, 80, 88, 90, 86, 90, 96, 94, 93, 94, 92, 90, 92, 96, 97, 94, 88, 81, 73, 75, 83, 84, 87, 88, 86, 94, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S217 = [119, 110, 118, 129, 130, 131, 131, 131, 131, 131, 131, 130, 130, 130, 130, 131, 130, 131, 131, 131, 131, 132, 132, 132, 122, 94, 74, 79, 83, 84, 90, 99, 107, 108, 108, 106, 105, 103, 103, 106, 105, 104, 101, 99, 98, 94, 94, 97, 96, 94, 93, 95, 101, 110, 111, 105, 94, 79, 71, 68, 68, 67, 71, 88, 105, 106, 101, 86, 73, 70, 74, 81, 85, 84, 84, 92, 92, 91, 92, 91, 88, 89, 92, 96, 94, 88, 81, 72, 75, 82, 82, 86, 87, 87, 96, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S218 = [120, 112, 118, 128, 130, 131, 130, 131, 131, 131, 131, 131, 130, 130, 131, 131, 131, 131, 130, 130, 131, 131, 131, 129, 107, 80, 74, 79, 80, 84, 96, 104, 106, 107, 109, 108, 107, 105, 106, 107, 105, 101, 98, 98, 97, 95, 97, 96, 96, 95, 98, 104, 111, 109, 98, 88, 87, 84, 77, 68, 63, 68, 87, 106, 109, 106, 97, 82, 73, 76, 84, 88, 86, 86, 93, 94, 91, 91, 93, 94, 95, 96, 96, 92, 87, 80, 72, 74, 82, 86, 88, 86, 85, 92, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S219 = [119, 111, 120, 129, 130, 131, 131, 130, 130, 130, 130, 129, 129, 129, 131, 131, 133, 133, 132, 131, 131, 130, 130, 127, 108, 79, 74, 81, 83, 86, 96, 104, 106, 108, 107, 105, 104, 104, 105, 105, 104, 100, 97, 98, 97, 93, 95, 96, 94, 92, 94, 102, 109, 111, 107, 96, 81, 72, 68, 67, 67, 68, 81, 102, 108, 104, 94, 78, 69, 73, 79, 85, 88, 84, 88, 94, 93, 94, 93, 90, 89, 92, 95, 94, 90, 83, 73, 72, 80, 81, 83, 87, 85, 92, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S220 = [124, 113, 114, 126, 130, 131, 131, 132, 131, 131, 131, 131, 131, 130, 130, 131, 132, 133, 132, 132, 132, 131, 131, 131, 127, 101, 74, 76, 82, 84, 91, 101, 108, 109, 110, 109, 108, 106, 105, 108, 107, 105, 102, 100, 101, 101, 97, 98, 98, 94, 93, 97, 104, 111, 112, 106, 91, 81, 74, 70, 67, 65, 68, 84, 105, 109, 106, 95, 80, 70, 73, 82, 87, 88, 86, 92, 94, 93, 94, 92, 90, 92, 95, 96, 94, 88, 80, 72, 74, 82, 82, 86, 88, 87, 96, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S221 = [120, 111, 120, 128, 128, 129, 130, 130, 130, 131, 130, 130, 130, 129, 129, 130, 131, 131, 131, 131, 131, 131, 131, 131, 119, 88, 74, 80, 82, 84, 93, 102, 106, 108, 107, 105, 104, 102, 104, 105, 105, 102, 99, 97, 98, 95, 92, 95, 95, 92, 92, 98, 106, 111, 110, 102, 89, 78, 72, 69, 67, 65, 68, 84, 105, 108, 103, 92, 78, 69, 73, 80, 86, 86, 85, 92, 94, 92, 94, 92, 91, 92, 96, 96, 93, 88, 79, 72, 78, 84, 84, 87, 88, 88, 97, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S222 = [116, 113, 124, 129, 130, 131, 131, 131, 131, 131, 131, 131, 131, 130, 130, 131, 132, 132, 131, 130, 131, 131, 131, 125, 98, 73, 78, 83, 83, 92, 101, 107, 107, 108, 107, 106, 104, 104, 105, 106, 105, 101, 98, 98, 98, 93, 94, 96, 94, 92, 94, 102, 110, 113, 107, 99, 84, 74, 70, 68, 67, 67, 78, 97, 108, 107, 99, 85, 72, 70, 76, 82, 87, 84, 89, 93, 92, 93, 91, 88, 88, 92, 96, 94, 88, 80, 72, 74, 81, 81, 84, 87, 86, 93, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S223 = [119, 111, 118, 128, 130, 131, 131, 131, 131, 131, 130, 130, 130, 130, 130, 130, 131, 131, 131, 131, 131, 131, 131, 125, 100, 75, 78, 80, 80, 84, 98, 105, 108, 109, 110, 110, 109, 107, 105, 107, 108, 106, 101, 99, 99, 98, 97, 98, 97, 96, 96, 102, 110, 113, 106, 91, 88, 88, 84, 74, 67, 65, 70, 90, 105, 108, 107, 99, 84, 72, 76, 86, 90, 86, 90, 96, 93, 92, 94, 95, 96, 98, 99, 95, 89, 81, 74, 72, 80, 86, 87, 88, 86, 90, 99, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
S224 = [113, 120, 129, 130, 131, 131, 132, 132, 132, 131, 131, 131, 130, 129, 130, 131, 131, 131, 130, 129, 130, 130, 122, 96, 74, 78, 81, 81, 85, 96, 104, 107, 108, 109, 110, 109, 106, 105, 106, 108, 105, 101, 98, 98, 96, 96, 98, 97, 95, 96, 101, 110, 113, 109, 94, 89, 87, 83, 75, 68, 65, 67, 78, 100, 110, 107, 97, 82, 71, 76, 86, 89, 86, 89, 95, 93, 92, 94, 94, 95, 97, 97, 95, 90, 83, 74, 72, 80, 86, 86, 88, 86, 90, 99, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];


#The variable to get the distance from the mean of each group
X = np.matrix(S25[:25]).transpose()
XSize = X.shape

#Group 1 
group1 = np.matrix([S0[:25],S1[:25],S2[:25],S3[:25],S4[:25],S5[:25],S6[:25],S7[:25],S8[:25],S9[:25],S10[:25],S11[:25],S12[:25],S13[:25],S14[:25],S15[:25],S16[:25],S17[:25],S18[:25],S19[:25],S20[:25],S21[:25],S22[:25],S23[:25],S24[:25]]) 
group1 = group1.transpose()
groupSize = group1.shape


#Group 2
group2 = np.matrix([S20[:25],S21[:25],S22[:25],S23[:25],S24[:25],S25[:25],S26[:25],S27[:25],S28[:25],S29[:25],S210[:25],S11[:25],S212[:25],S213[:25],S214[:25],S215[:25],S216[:25],S217[:25],S218[:25],S219[:25],S220[:25],S221[:25],S222[:25],S223[:25],S224[:25]])
group2 = group2.transpose()

#Group 1 Mean
g1_mean = np.mean(group1,1)
meanSize = g1_mean.shape

#Group 2 Mean
g2_mean = np.mean(group2,1)


#Group 1 COV
g1_cov = np.cov(group1, rowvar=1)
g1_cov = np.matrix(g1_cov) 
gcovSize = g1_cov.shape

#Group 2 COV
g2_cov = np.cov(group2, rowvar=1)
g2_cov = np.matrix(g2_cov)

#return XSize,groupSize,meanSize,gcovSize


#Fine the mahalanobis distance of X from group1 and group2
#The distance with the lowest value is the group X belongs to

#return g1_cov,g2_cov

#Mah for group1
Dm_g1 = maha(X,g1_mean,g1_cov)

#Mah for group2
Dm_g2 = maha(X,g2_mean,g2_cov)

#dm_c1 = mahalanobis(X, g1_mean,g1_cov.I)
#dm_c2 = mahalanobis(X, g2_mean,g2_cov.I)


return Dm_g1,Dm_g2



def maha(x,y,V):
    return np.sqrt((x-y).transpose() * V.I * (x-y))
guitardenver
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    Can you copy-paste the code snippets here? Adding links leads to the possibility of link rot, we don't get the benefit of code formatting and syntax highlighting, and it means less hops for everyone involved when the code is just right here. – Akshat Mahajan Jan 23 '17 at 22:05

1 Answers1

0

The problem is that Octave thinks you have 114 variables with 25 observations for each, not 25 variables with 114 observations for each. Its cov function computes covariance of the columns not of the rows. So, each variable should be in its own column, not in its own row.

In other words: use cov(X') and cov(X2') in your code.

I haven't tried the Python code; likely the issue is the same.

You can diagnose this yourself by printing the size of the covariance matrix: disp(size(S)) would tell you it's 114 by 114, which is obviously wrong.

  • Why is (114 by 114) wrong? If I use the X', the covariance matrix will end up being (25 by 25). And since the other two input vectors (The mean and Y) are (1 by 114) or (114 by 1) if the transpose is used. You can not multiply a (25 by 25) and a (1,114) matrix together when you do the mahalanobis equation. Could you elaborate? – guitardenver Jan 24 '17 at 13:20
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    Covariance is a thing between variables. If you have 25 variables, the covariance matrix is 25 by 25. And the means vector is of length 25. Please step away from Octave and Python, pull out paper and pencil, and review the mathematical meaning of what you are trying to do. –  Jan 24 '17 at 14:39