{"id":5588,"date":"2014-11-17T18:49:43","date_gmt":"2014-11-17T17:49:43","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=5588"},"modified":"2014-11-17T18:52:05","modified_gmt":"2014-11-17T17:52:05","slug":"solving-the-nearest-correlation-matrix-problem-using-python","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=5588","title":{"rendered":"Solving the nearest correlation matrix problem using Python"},"content":{"rendered":"

Given a symmetric matrix such as<\/p>\n

  <\/span>   <\/span>\"\light \[ \left( \begin{array}{ccc}<\/p>\n

What’s the nearest correlation matrix<\/a>? A 2002 paper by Manchester University’s Nick Higham<\/a> which answered this question has turned out to be rather popular! At the time of writing, Google tells me that it’s been cited 394 times.<\/p>\n

Last year, Nick wrote a blog post<\/a> about the algorithm he used and included some MATLAB code. He also included links to applications of this algorithm and implementations of various NCM algorithms in languages such as MATLAB, R and SAS as well as details of the superb commercial implementation by The Numerical algorithms group<\/a>.<\/p>\n

I noticed that there was no Python implementation of Nick’s code so I ported it myself<\/a>.<\/p>\n

Here’s an example IPython session using the module<\/p>\n

In [1]: from nearest_correlation import nearcorr\r\n\r\nIn [2]: import numpy as np\r\n\r\nIn [3]: A = np.array([[2, -1, 0, 0], \r\n   ...:               [-1, 2, -1, 0],\r\n   ...:               [0, -1, 2, -1], \r\n   ...:               [0, 0, -1, 2]])\r\n\r\nIn [4]: X = nearcorr(A)\r\n\r\nIn [5]: X\r\nOut[5]: \r\narray([[ 1.        , -0.8084125 ,  0.1915875 ,  0.10677505],\r\n       [-0.8084125 ,  1.        , -0.65623269,  0.1915875 ],\r\n       [ 0.1915875 , -0.65623269,  1.        , -0.8084125 ],\r\n       [ 0.10677505,  0.1915875 , -0.8084125 ,  1.        ]])<\/pre>\n
This module is in the early stages and there is a lot of work to be done. For example, I’d like to include a lot more examples in the test suite, add support for the commercial routines from NAG and implement other algorithms such as the one by Qi and Sun among other things.<\/p>\n
Hopefully, however, it is just good enough to be useful to someone. Help yourself and let me know if there are any problems. Thanks to Vedran Sego for many useful comments and suggestions.<\/p>\n