Datahat: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
Calculates the model estimate and residuals of the data. | Calculates the model estimate and residuals of the data. | ||
===Synopsis=== | ===Synopsis=== | ||
:xhat = datahat(model); | :xhat = datahat(model); | ||
:[xhat,resids] = datahat(model,''data''); | :[xhat,resids] = datahat(model,''data''); | ||
===Description=== | ===Description=== | ||
Given a standard model structure model DATAHAT computes the model estimate of the data xhat. For example, if model is a PCA model of a matrix '''X'''<sub>cal</sub> such that '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''', then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup>. (i.e. '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''' = '''X'''<sub>hat</sub> + '''E'''). | Given a standard model structure model DATAHAT computes the model estimate of the data xhat. For example, if model is a PCA model of a matrix '''X'''<sub>cal</sub> such that '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''', then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup>. (i.e. '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''' = '''X'''<sub>hat</sub> + '''E'''). | ||
If optional input ''data'' is supplied then DATAHAT computes the model estimate of ''data'' that is output in xhat. For the PCA model of matrix '''X'''<sub>cal</sub>, and ''data'' is a data matrix '''X'''<sub>new</sub> then '''X'''<sub>hat</sub> = '''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''T'''<sub>new</sub>'''P'''<sup>T</sup>. The output resids is a matrix with the corresponding residuals '''E''' ['''E''' = '''X'''<sub>new</sub>-'''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''X'''<sub>new</sub>('''I'''-'''PP'''<sup>T</sup>)]. If ''data'' is '''X'''<sub>cal</sub> then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup> and resids is '''E''' = '''X'''<sub>cal</sub>('''I'''-'''PP'''<sup>T</sup>)]. | If optional input ''data'' is supplied then DATAHAT computes the model estimate of ''data'' that is output in xhat. For the PCA model of matrix '''X'''<sub>cal</sub>, and ''data'' is a data matrix '''X'''<sub>new</sub> then '''X'''<sub>hat</sub> = '''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''T'''<sub>new</sub>'''P'''<sup>T</sup>. The output resids is a matrix with the corresponding residuals '''E''' ['''E''' = '''X'''<sub>new</sub>-'''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''X'''<sub>new</sub>('''I'''-'''PP'''<sup>T</sup>)]. If ''data'' is '''X'''<sub>cal</sub> then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup> and resids is '''E''' = '''X'''<sub>cal</sub>('''I'''-'''PP'''<sup>T</sup>)]. | ||
Note that preprocessing in model will be performed before the residuals are calculated. If data is not provided, only xhat is available. | Note that preprocessing in model will be performed before the residuals are calculated. If data is not provided, only xhat is available. | ||
Note that DATAHAT works with almost all standard model structures. | Note that DATAHAT works with almost all standard model structures. | ||
===See Also=== | ===See Also=== | ||
[[analysis]], [[parafac]] | [[analysis]], [[parafac]] | ||
Revision as of 15:25, 3 September 2008
Purpose
Calculates the model estimate and residuals of the data.
Synopsis
- xhat = datahat(model);
- [xhat,resids] = datahat(model,data);
Description
Given a standard model structure model DATAHAT computes the model estimate of the data xhat. For example, if model is a PCA model of a matrix Xcal such that Xcal = TPT + E, then Xhat = TPT. (i.e. Xcal = TPT + E = Xhat + E).
If optional input data is supplied then DATAHAT computes the model estimate of data that is output in xhat. For the PCA model of matrix Xcal, and data is a data matrix Xnew then Xhat = XnewPPT = TnewPT. The output resids is a matrix with the corresponding residuals E [E = Xnew-XnewPPT = Xnew(I-PPT)]. If data is Xcal then Xhat = TPT and resids is E = Xcal(I-PPT)].
Note that preprocessing in model will be performed before the residuals are calculated. If data is not provided, only xhat is available.
Note that DATAHAT works with almost all standard model structures.