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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




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