reverse engineering principal components...
- To: mathgroup at smc.vnet.net
- Subject: [mg128396] [mg128396] reverse engineering principal components...
- From: Richard Palmer <rhpalmer at gmail.com>
- Date: Fri, 12 Oct 2012 00:02:07 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
I would like to be able to take a large dataset, compute the principal components on a sufficient subset, and use the results to compute principal components on the remaining observations. So far, I haven't been able to figure out how it is done. Here is sample code (computed as a notebook expression). Can anyone tell me where I am going wrong? Notebook[{ Cell[CellGroupData[{ Cell["Reverse Engineering Principal Components", "Section", CellChangeTimes->{{3.558966707926651*^9, 3.5589667244925985`*^9}}], Cell["\<\ make a table of data and a table of the principal components using \ the Correllation method. Check to see that they have the requisite \ properties\ \>", "Text", CellChangeTimes->{{3.5589667304749403`*^9, 3.558966775500516*^9}, { 3.558966830268648*^9, 3.5589668439964333`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"RandomReal", "[", "]"}], ",", RowBox[{"{", "5", "}"}], ",", RowBox[{"{", "3", "}"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"princomponentst", "=", RowBox[{"PrincipalComponents", "[", RowBox[{"t", ",", RowBox[{"Method", "\[Rule]", "\"\<Correlation\>\""}]}], "]"}]}], ";"}], " "}], "\n", RowBox[{"Print", "[", RowBox[{"\"\<The mean of the set is \>\"", ",", RowBox[{ RowBox[{"Mean", "[", "princt", "]"}], "//", "Chop"}]}], "]"}], "\n", RowBox[{"Print", "[", RowBox[{"\"\<The variance of the set is \>\"", ",", RowBox[{"Variance", "[", "princt", "]"}]}], "]"}]}], "Input", CellChangeTimes->{{3.558943696585477*^9, 3.5589437436731706`*^9}, { 3.5589448723167253`*^9, 3.558944889147688*^9}, 3.5589452714125524`*^9, {3.558965740525318*^9, 3.558965743957515*^9}, 3.558966338325511*^9, { 3.5589667822939043`*^9, 3.558966817373911*^9}, { 3.558966862013464*^9, 3.5589669321494756`*^9}, { 3.558967927711418*^9, 3.558967942303253*^9}}], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"The mean of the set is \"\>", "\[InvisibleSpace]", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], SequenceForm["The mean of the set is ", {0, 0, 0}], Editable->False]], "Print", CellChangeTimes->{{3.558966925069071*^9, 3.558966932823514*^9}, { 3.558967933532751*^9, 3.5589679478705716`*^9}}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"The variance of the set is \"\>", "\[InvisibleSpace]", RowBox[{"{", RowBox[{ "1.4974734615741159`", ",", "0.9657686960146733`", ",", "0.5367578424112112`"}], "}"}]}], SequenceForm[ "The variance of the set is ", {1.4974734615741159`, 0.9657686960146733, 0.5367578424112112}], Editable->False]], "Print", CellChangeTimes->{{3.558966925069071*^9, 3.558966932823514*^9}, { 3.558967933532751*^9, 3.558967947872572*^9}}] }, Open ]] }, Open ]], Cell["\<\ Standardize the observations and compute a correlation matrix. \ Compute the eigenvectors.\ \>", "Text", CellChangeTimes->{{3.558966974924922*^9, 3.558967006484727*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"standardizet", "=", RowBox[{"Standardize", "[", "t", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"corrt", "=", RowBox[{"Correlation", "[", "standardizet", "]"}]}], ";"}], " "}], "\n", RowBox[{ RowBox[{ RowBox[{"eigenvectors", "=", RowBox[{"Eigenvectors", "[", "corrt", "]"}]}], ";"}], " "}]}], "Input", CellChangeTimes->{{3.5589449260758*^9, 3.5589449510202265`*^9}, { 3.5589454403162127`*^9, 3.5589454525239115`*^9}, 3.5589670144291816`*^9, 3.5589670498292065`*^9, { 3.5589711280694685`*^9, 3.5589711551900196`*^9}}], Cell["\<\ I think this is the multiplication. However, the variances are not \ correct since they do not decrease.\ \>", "Text", CellChangeTimes->{{3.5589677050376825`*^9, 3.5589677222526665`*^9}, { 3.558971033573064*^9, 3.558971044228673*^9}, {3.558971199412549*^9, 3.558971208188051*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"mypc2", "=", RowBox[{"standardizet", ".", "eigenvectors"}]}], ";"}], "\n", RowBox[{"Mean", "[", "mypc2", "]"}], "\n", RowBox[{"Variance", "[", "mypc2", "]"}]}], "Input", CellChangeTimes->{{3.5589661581992083`*^9, 3.5589662056929245`*^9}, 3.5589670948777833`*^9, 3.5589671263245816`*^9, { 3.558967191557313*^9, 3.558967192101344*^9}, { 3.5589677375095396`*^9, 3.558967776636778*^9}, 3.5589710607416177`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "2.4424906541753446`*^-16"}], ",", "3.108624468950438`*^-16", ",", RowBox[{"-", "3.7192471324942745`*^-16"}]}], "}"}]], "Output", CellChangeTimes->{{3.55897113613293*^9, 3.5589711629244623`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1.1977733239835728`", ",", "0.7727628961600694`", ",", "1.0294637798563568`"}], "}"}]], "Output", CellChangeTimes->{{3.55897113613293*^9, 3.558971162927462*^9}}] }, Open ]] }, Open ]] }, WindowSize->{707, 787}, WindowMargins->{{Automatic, 228}, {49, Automatic}}, ShowSelection->True, FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (October 6, \ 2011)", StyleDefinitions->"Default.nb" ] -- Richard Palmer Home 941 412 8828 Cell 508 982-7266