{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "This Maple file reads in \+ 1) a file containing the inputs/class information, and 2) a file conta ining" }{TEXT -1 623 " parameters for a network trained on this data. \+ This was generated using the Java network simulator written by G. Orr . This Maple file assumes the net can have any number of layers and t hat each layer is either linear or sigmoid. For each input, the netwo rk output is generated and the output node with the largest positive o utput is taken to be the network's prediction of the class. This pred iction is compared with the true class. The data from each class is p lotted with a different color along all possible pairs of axes. If the prediction is correct, a circle is used to plot the point otherwise a cross is used." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "currentdir(\"C: \\\\orr\\\\classes\\\\NeuralNets\\\\MySimulator\\\\Maple\");\nfname := `..\\\\netParams.dat`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QLC:\\orr\\ classes\\NeuralNets\\MySimulator\\Maple6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&fnameG%1..\\netParams.datG" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 97 "Read in network parameters from the file netParams.data . This file was output by the Java neural " }}{PARA 0 "" 0 "" {TEXT -1 58 "net simulator when the \"save weights\" button is pressed. " } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "read fname:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 44 "sigmoid := proc(x) evalf(1./(1 + exp(-x) ));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(sigmoidGR6#%\"x G6\"F(F(-%&evalfG6#,$*&\"\"\"F.,&\"\"\"F0-%$expG6#,$9$!\"\"F0!\"\"$F0 \"\"!F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Given an input x, \+ calculate the output of the network. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 292 "f := proc(x) local i, w, nodesU, nodesL, y;\n y := x:\n for i from 1 to nops(wts) do \n w := wts[i];\n nodesU := nops(w) ;\n nodesL := nops(w[1]); \n \n if (actfun[i] = \"sigmoid \") then\n y := map(sigmoid,evalm(w &* y));\n else y := ev alm(w &* y); fi;\n od: \nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 7 "" 1 "" {TEXT -1 31 "Warning, premature end of input" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Read in classification data. The \+ first n-1 columns are the inputs followed by the class index in the " }}{PARA 0 "" 0 "" {TEXT -1 105 "last column. The array \"a\" contains some extraneous info at the top such as the number of input vectors. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fname := `..\\\\iris.dat`;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "with(plots):\ncols := 5;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "a := readdata(fname,cols):\nb := a[4..nop s(a)]:\nlen := nops(b);\ndim := cols-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&fnameG%,..\\iris.datG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%c olsG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$lenG\"$]\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dimG\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "The function pickClass picks out all vectors in array x t hat are in class i." }}{PARA 0 "" 0 "" {TEXT -1 77 "v is a list contai ning the class indices (no duplicates). The loop separates " }}{PARA 0 "" 0 "" {TEXT -1 44 "the different classes into their own arrays." } }{PARA 0 "" 0 "" {TEXT -1 76 "The array \"classes\" is a list of array s. There is one array for each class." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "pickClass := proc(x,i) is(x[dim+1]=i); end:\nv := sort(conve rt(\{op(map(u->u[dim+1], b))\},list));\nclasses := []:\nfor i from 1 t o nops(v) do \n classes := [ op(classes),select( pickClass, b,v[i]) ];\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%$\"\"\"\"\"!$\"\"#F ($\"\"$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Given a vector x, determine position of m ax element. return the corresponding element of v." }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 166 "getclass := proc(x,v) local c, m, i;\n m := ma x(op(x)): \n for i from 1 to nops(x) do \n if (m=x[i]) then c := i: \n fi;\n od:\n v[c];\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)getclassGR6$%\"xG%\"vG6%%\"cG%\"mG%\"iG6\"F-C%> 8%-%$maxG6#-%#opG6#9$?(8&\"\"\"F:-%%nopsGF6%%trueG@$/F0&F76#F9>8$F9&9% 6#FCF-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "classes[2,1,1 ..dim+1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'$\"#q!\"\"$\"#KF&$\"#ZF &$\"#9F&$\"\"#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "For each c lass, determine which inputs the network correctly classifies. Place" }}{PARA 0 "" 0 "" {TEXT -1 78 "these in the list called setCorrect and place the others in the list setWrong." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 514 "classes2 := []:setCorrect := []:setWrong := []:\nfor j from 1 to nops(v) do \n setCorrect := []; setWrong := [];\n for i from 1 to nops(classes[j]) do \n x1 := classes[j,i,1..dim]: \n x2 := [op(x1),1]: \n correctclass := classes[j,i,dim+1]:\n h := con vert(f(x2),list):\n netclass := getclass(h,v):\n if (correctc lass=netclass) then \n setCorrect := [ op(setCorrect),x1 ]: \n \+ else setWrong := [ op(setWrong),x1]:\n fi; \n od:\n class es2 := [op(classes2),setCorrect, setWrong]:\nod:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(plots): " }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 81 "This function takes two columns( n and m) and plot s them with each class being a " }}{PARA 0 "" 0 "" {TEXT -1 16 "differ ent color." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "myColors := [ blue, \+ red, black, green ];\nplotCut := proc(m,n) local i, mm, cc, fig;\n \+ fig := []:\n for i from 1 to 2*nops(v) do \n if (nops(classes2[ i])>0) then\n cc := floor((i+1)/2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 405 " mm := map(u->[ u[n],u[m] ], classes2[i]);\n \+ if (modp(i,2)=1) then \n fig := [op(fig),pointp lot(mm, symbol=CIRCLE,\n color=myColors[cc],labels=[`x x`.n,`xx`.m])]; \+ else \n fig := [op(fig),pointplot(mm, symbol=CROSS,\n \+ color=myColors[cc],labels=[`xx`.n,`xx`.m])];\n fi; \+ \n fi; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " od:\n fig;\nend :" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)myColorsG7&%%blueG%$redG%&blac kG%&greenG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "This function loops over all pairs of columns and plots them." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "all := []:\nfor i from 1 to dim do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 " for j from i+1 to dim do\n all := [op(a ll), plotCut(i,j)]; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " od; \+ " }}{PARA 0 "> " 0 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