Showing posts with label correlation. Show all posts
Showing posts with label correlation. Show all posts

Sunday, March 25, 2012

Canonical Correlation Analysis for finding patterns in coupled fields

First CCA pattern of Sea Level Pressure (SLP) and Sea Surface Temperature (SST) monthly anomalies for the region between -180 °W to -70 °W and +30 °N to -30 °S.

The following post demonstrates the use of Canonical Correlation Analysis (CCA) for diagnosing coupled patterns in climate fields. The method produces similar results to that of  Maximum Covariance Analysis (MCA), but patterns reflect maximum correlation rather than maximum covariance. Furthermore, the output of the model is a combination of linear models that can be used for field prediction.

This particular method was illustrated by Barnett and Preisendorfer (1997) - it constructs a CCA model based on a truncated subset of EOF coefficients (i.e. "principle components") instead of using the original field (as with MCA). This truncation has several benefits for the fitting of the model - First, one reduces the amount of noise in the problem by eliminating the higher EOF modes, which represent poorly organized, small-scale features of the fields. Second, by using orthogonal functions, the algebra of the problem is simplified (see von Storch and Zweiers 1999 for details). Bretherton etal. (1992) reviewed several techniques for diagnosing coupled patterns and found the Barnett and Preisendorfer method (hereafter "BPCCA") and MCA to be the most robust.

Monday, December 19, 2011

Maximal Information Coefficient (MIC)

Pearson r correlation coefficients for various distributions of paired data (Credit: Denis Boigelot, Wikimedia Commons)

A paper published this week in Science outlines a new statistic called the maximal information coefficient (MIC), which is able to equally describe the correlation between paired variables regardless of linear or nonlinear relationship. In other words, as Pearson's r gives a measure of the noise surrounding a linear regression, MIC should give similar scores to equally noisy relationships regardless of type.