topic PCA Covariance Matrix not correct for standardized input in Data Management Questions https://community.esri.com/t5/data-management-questions/pca-covariance-matrix-not-correct-for-standardized/m-p/179141#M10108 <HTML><HEAD></HEAD><BODY><SPAN>Hello All,</SPAN><BR /><BR /><SPAN>I computed a Principal Component Analysis using the Multivariate Tool in ArcInfo 9.3.&nbsp; Input data were standardized by subtracting the mean and dividing by the standard deviation (Z-score) before PCA.&nbsp; The resulting output covariance matrix produces values of variance (for each input band to itself) that do not&nbsp; match the variance of that input band (should be ~ 1 in this case because the input bands have a standard deviation of ~1, but computed variance is approximately 0.42).&nbsp; The PCA computes the covariance matrix correctly for&nbsp; raw values (not standardized), but not for standardized data.&nbsp; It is necessary for me to standardize the data, as input bands are on very different scales/units.&nbsp; </SPAN><BR /><SPAN>Has anyone else had this problem?&nbsp; Any ideas of how to get around this?&nbsp;&nbsp; I am currently exploring the use of the correlation matrix instead of the covariance matrix using ERDAS.</SPAN><BR /><BR /><SPAN>Thanks for any help!</SPAN><BR /><BR /><SPAN>Regards,</SPAN><BR /><BR /><SPAN>Matt</SPAN></BODY></HTML> Mon, 13 Dec 2010 19:00:39 GMT MattLevi 2010-12-13T19:00:39Z PCA Covariance Matrix not correct for standardized input https://community.esri.com/t5/data-management-questions/pca-covariance-matrix-not-correct-for-standardized/m-p/179141#M10108 <HTML><HEAD></HEAD><BODY><SPAN>Hello All,</SPAN><BR /><BR /><SPAN>I computed a Principal Component Analysis using the Multivariate Tool in ArcInfo 9.3.&nbsp; Input data were standardized by subtracting the mean and dividing by the standard deviation (Z-score) before PCA.&nbsp; The resulting output covariance matrix produces values of variance (for each input band to itself) that do not&nbsp; match the variance of that input band (should be ~ 1 in this case because the input bands have a standard deviation of ~1, but computed variance is approximately 0.42).&nbsp; The PCA computes the covariance matrix correctly for&nbsp; raw values (not standardized), but not for standardized data.&nbsp; It is necessary for me to standardize the data, as input bands are on very different scales/units.&nbsp; </SPAN><BR /><SPAN>Has anyone else had this problem?&nbsp; Any ideas of how to get around this?&nbsp;&nbsp; I am currently exploring the use of the correlation matrix instead of the covariance matrix using ERDAS.</SPAN><BR /><BR /><SPAN>Thanks for any help!</SPAN><BR /><BR /><SPAN>Regards,</SPAN><BR /><BR /><SPAN>Matt</SPAN></BODY></HTML> Mon, 13 Dec 2010 19:00:39 GMT https://community.esri.com/t5/data-management-questions/pca-covariance-matrix-not-correct-for-standardized/m-p/179141#M10108 MattLevi 2010-12-13T19:00:39Z