linear discriminant analysis can i get some help doing this
I fallowed a tutorial and wrote most of the function and example data into c++.
http://people.revoledu.com/kardi/tutorial/LDA/Numerical%20Example.html
The discriminent Function that has fi in it I am having trouble and getting type mis mach.
I fallowed the code and their appears to be slight differences in rounding from the excel example.
The error I get before commenting out my fi line is ...
C:\Users\josheeg\Documents\c\test\test\main.cpp|157|error: cannot convert 'const Eigen::CwiseBinaryOp<Eigen::internal::scalar_difference_op<double>, const Eigen::ScaledProduct<Eigen::GeneralProduct<Eigen::Matrix<double, -0x000000001, -0x000000001, 0, -0x000000001, -0x000000001>, Eigen::Matrix<double, -0x000000001, -0x000000001, 0, -0x000000001, -0x000000001>, 5> >, const Eigen::GeneralProduct<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<double>, const Eigen::Matrix<double, -0x000000001, -0x000000001, 0, -0x000000001, -0x000000001> >, Eigen::Matri|

Code: Select all

#include <iostream>
#include <Eigen/Dense>
#include <Eigen/LU>
using Eigen::MatrixXd;
using namespace std;
int main()
{
cout << "Hello Pattern matching Linear Discriminent Analisis!" << endl;
cout << "" << endl;
cout << "x data" << endl;

//data matrix x row col
MatrixXd x(4,2);
//cur
x(0,0) = 2.95;//g0
x(1,0) = 2.53;
x(2,0) = 3.57;
x(3,0) = 3.16;

//dia
x(0,1) = 6.63;//g0
x(1,1) = 7.79;
x(2,1) = 5.65;
x(3,1) = 5.47;

std::cout << x << std::endl;
cout << "End of x data" << endl;
cout << "" << endl;

cout << "x1 data" << endl;

MatrixXd x1(3,2);

x1(0,0) = 2.58;//g1
x1(1,0) = 2.16;
x1(2,0) = 3.27;

x1(0,1) = 4.46;//g1
x1(1,1) = 6.22;
x1(2,1) = 3.52;

std::cout << x1 << std::endl;
cout << "End of x1 data" << endl;
cout << "" << endl;

//group adv
cout << "x data adverage ui" << endl;

MatrixXd ui(1,2);//group/feature
ui(0,0)=(x(0,0) + x(1,0) + x(2,0) + x(3,0))/4.0;
ui(0,1)=(x(0,1) + x(1,1) + x(2,1) + x(3,1))/4.0;
std::cout << ui << std::endl;
cout << "" << endl;

cout << "x1 data adverage ui1" << endl;

MatrixXd ui1(1,2);//group/feature

ui1(0,0)=(x1(0,0) + x1(1,0) + x1(2,0))/3.0;
ui1(0,1)=(x1(0,1) + x1(1,1) + x1(2,1))/3.0;
std::cout << ui1 << std::endl;
cout << "" << endl;

cout << "x & x1 data adverage u" << endl;
MatrixXd u(1,2);//all group/feature
u(0,0)=(x(0,0) + x(1,0) + x(2,0) + x(3,0) + x1(0,0) + x1(1,0) + x1(2,0))/7.0;

u(0,1)=(x(0,1) + x(1,1) + x(2,1) + x(3,1) + x1(0,1) + x1(1,1) + x1(2,1))/7.0;

std::cout << u << std::endl;
cout << "" << endl;


cout << "mean corrected data xig - u" << endl;
MatrixXd ximinu(4,2);
//cur
ximinu(0,0) = x(0,0) - u(0,0);//f0
ximinu(1,0) = x(1,0) - u(0,0);
ximinu(2,0) = x(2,0) - u(0,0);
ximinu(3,0) = x(3,0) - u(0,0);
//dia
ximinu(0,1) = x(0,1) - u(0,1);//f1
ximinu(1,1) = x(1,1) - u(0,1);
ximinu(2,1) = x(2,1) - u(0,1);
ximinu(3,1) = x(3,1) - u(0,1);
std::cout << ximinu << std::endl;
cout << "" << endl;

cout << "mean corrected data xi1 - u" << endl;


MatrixXd ximinu1(3,2);
//cur
ximinu1(0,0) = x1(0,0) - u(0,0);
ximinu1(1,0) = x1(1,0) - u(0,0);
ximinu1(2,0) = x1(2,0) - u(0,0);
//dia
ximinu1(0,1) = x1(0,1) - u(0,1);//g1
ximinu1(1,1) = x1(1,1) - u(0,1);
ximinu1(2,1) = x1(2,1) - u(0,1);

std::cout << ximinu1 << std::endl;

cout << " " << endl;

cout << "Transpose matricies" << endl;
cout << "xi - u T" << endl;

MatrixXd ximinut(4,2);
ximinut= ximinu.transpose();
std::cout << ximinut<< std::endl;
cout << " " << endl;

cout << "xi1 - u T" << endl;
MatrixXd ximinu1t(3,2);
ximinu1t= ximinu1.transpose();
std::cout << ximinu1t << std::endl;
cout << " " << endl;

cout << "Covariance matrix of group ci" << endl;
MatrixXd ci(2,2);
ci = ( ximinut * ximinu ) /4.0;
std::cout << ci << std::endl;
cout << "" << endl;

cout << "Covariance matrix of group ci1" << endl;
MatrixXd ci1(2,2);
ci1 = ( ximinu1t * ximinu1 ) /3.0;
std::cout << ci1 << std::endl;
cout << "" << endl;

cout << "Pooled within group Covariance matrix c" << endl;
MatrixXd c(2,2);
c(0,0) = 4.0/7.0 * ci(0,0) + 3.0/7.0 * ci1(0,0);
c(1,0) = 4.0/7.0 * ci(1,0) + 3.0/7.0 * ci1(1,0);
c(0,1) = 4.0/7.0 * ci(0,1) + 3.0/7.0 * ci1(0,1);
c(1,1) = 4.0/7.0 * ci(1,1) + 3.0/7.0 * ci1(1,1);
std::cout << c << std::endl;
cout << "" << endl;

cout << "inverse of Pooled within group Covariance matrix cinverse" << endl;
MatrixXd cinverse(2,2);
 cinverse=c.inverse();
std::cout << cinverse << std::endl;
cout << "" << endl;

cout << "Probability of a group" << endl;
cout << "x = 4/7 x1 = 3/7" << endl;

//create a vector of a probability...
cout << "" << endl;
//double fi  = 0;
//double fi1 = 0;
//double xk = 1;
//formula for calculatin likelyhood of data in a group...
//fi = uig  * cinverse xkt - 1/2uig cinverse uitg + ln probability
//fi  = ui  * cinverse * xk  - 1/2 * ui  * cinverse ui.transpose+.3;
//fi1 = ui1 * cinverse * x1.transpose() - 1/2 * ui1 * cinverse ui1.transpose + ln(3/7);
cout << "End of program!" << endl;

    return 0;
}


I did get a example to work for arduino with the linear algebra libraries.

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// Example By: RandomVibe
// Eigen Doc: http://eigen.tuxfamily.org/dox/
// Quick Reference: http://eigen.tuxfamily.org/dox/QuickRefPage.html

#include <Eigen312.h>     // Calls main Eigen3.1.2 matrix class library
#include <LU>             // Calls inverse, determinant, LU decomp., etc.
using namespace Eigen;    // Eigen related statement; simplifies syntax for declaration of matrices

void print_mtxf(const Eigen::MatrixXf& K);


void setup() {

    Serial.begin(9600);
   
    // DECLARE MATRICES
    //--------------------
    MatrixXf Pp(6,6);   // Produces 6x6 float matrix class
    MatrixXf H(6,6);    // Note: without "using namespace Eigen", declaration would be: Eigen::MatrixXf H(6,6);
    MatrixXf R(6,6);
    MatrixXf X(6,6);
    MatrixXf K(6,6);
    MatrixXf Z(6,6);

    // INPUT MATRICES (so-called comma-initialize syntax)
    //---------------------------------------------------------
    Pp << 0.3252,  0.3192,  1.0933, -0.0068, -1.0891, -1.4916,
         -0.7549,  0.3129,  1.1093,  1.5326,  0.0326, -0.7423,
          1.3703, -0.8649, -0.8637, -0.7697,  0.5525, -1.0616,
         -1.7115, -0.0301,  0.0774,  0.3714,  1.1006,  2.3505,
         -0.1022, -0.1649, -1.2141, -0.2256,  1.5442, -0.6156,
         -0.2414,  0.6277, -1.1135,  1.1174,  0.0859,  0.7481 ;

    H << 0.8147, 0.2785, 0.9572, 0.7922, 0.6787, 0.7060,
         0.9058, 0.5469, 0.4854, 0.9595, 0.7577, 0.0318,
         0.1270, 0.9575, 0.8003, 0.6557, 0.7431, 0.2769,
         0.9134, 0.9649, 0.1419, 0.0357, 0.3922, 0.0462,
         0.6324, 0.1576, 0.4218, 0.8491, 0.6555, 0.0971,
         0.0975, 0.9706, 0.9157, 0.9340, 0.1712, 0.8235;

    R << 0.3252,  0.3192,  1.0933, -0.0068, -1.0891, -1.4916,
        -0.7549,  0.3129,  1.1093,  1.5326,  0.0326, -0.7423,
         1.3703, -0.8649, -0.8637, -0.7697,  0.5525, -1.0616,
        -1.7115, -0.0301,  0.0774,  0.3714,  1.1006,  2.3505,
        -0.1022, -0.1649, -1.2141, -0.2256,  1.5442, -0.6156,
        -0.2414,  0.6277, -1.1135,  1.1174,  0.0859,  0.7481;


    // Kalman Gain Example; Matlab form:  K = Pp * H' * inv(H * Pp * H' + R)
    //-----------------------------------
    X  = H * Pp * H.transpose() + R;   
    K  = Pp * H.transpose() * X.inverse();   


    // Print Result
    //----------------------------
     print_mtxf(K);      // Print Matrix Result (passed by reference)
   
}




void loop() {
  // put your main code here, to run repeatedly:
 
}




// PRINT MATRIX (float type)
//-----------------------------
void print_mtxf(const Eigen::MatrixXf& X)
{
    int i, j, nrow, ncol;
   
    nrow = X.rows();
    ncol = X.cols();

    Serial.print("nrow: "); Serial.println(nrow);
    Serial.print("ncol: "); Serial.println(ncol);       
    Serial.println();
   
    for (i=0; i<nrow; i++)
    {
        for (j=0; j<ncol; j++)
        {
            Serial.print(X(i,j), 6);   // print 6 decimal places
            Serial.print(", ");
        }
        Serial.println();
    }
    Serial.println();
}

Linear discriminant pattern matching seems to work well with one example of data.
More data from octave and r examples of lda could help test. I also got something like this to compile for the arduino duo but do not have one to test this on.

Code: Select all

//Josh W
//lda example reference http://people.revoledu.com/kardi/tutorial/LDA/Numerical%20Example.html
//reference http://eigen.tuxfamily.org/dox/TutorialMatrixArithmetic.html

#include <iostream>
#include <math.h>
#include <Eigen/Dense>
#include <Eigen/LU>
using Eigen::MatrixXd;
using namespace std;
using namespace Eigen;
int main()
{
cout << "Hello Pattern matching Linear Discriminent Analisis!" << endl;
cout << "" << endl;
cout << "x data" << endl;

//data matrix x row col
MatrixXd x(4,2);
//cur
x(0,0) = 2.95;//g0
x(1,0) = 2.53;
x(2,0) = 3.57;
x(3,0) = 3.16;

//dia
x(0,1) = 6.63;//g0
x(1,1) = 7.79;
x(2,1) = 5.65;
x(3,1) = 5.47;

std::cout << x << std::endl;
cout << "End of x data" << endl;
cout << "" << endl;

cout << "x1 data" << endl;

MatrixXd x1(3,2);

x1(0,0) = 2.58;//g1
x1(1,0) = 2.16;
x1(2,0) = 3.27;

x1(0,1) = 4.46;//g1
x1(1,1) = 6.22;
x1(2,1) = 3.52;

std::cout << x1 << std::endl;
cout << "End of x1 data" << endl;
cout << "" << endl;

//group adv
cout << "x data adverage ui" << endl;

MatrixXd ui(1,2);//group/feature

ui(0,0)=(x(0,0) + x(1,0) + x(2,0) + x(3,0))/4.0;
ui(0,1)=(x(0,1) + x(1,1) + x(2,1) + x(3,1))/4.0;
std::cout << ui << std::endl;
cout << "" << endl;

cout << "transpose ui to uit" << endl;
//transpose ui to uit
MatrixXd uit(1,2);//group/feature
uit=ui.transpose();
std::cout << uit << std::endl;
cout << "" << endl;

cout << "x1 data adverage ui1" << endl;

MatrixXd ui1(1,2);//group/feature

ui1(0,0)=(x1(0,0) + x1(1,0) + x1(2,0))/3.0;
ui1(0,1)=(x1(0,1) + x1(1,1) + x1(2,1))/3.0;
std::cout << ui1 << std::endl;
cout << "" << endl;

//transpose ui to uit
std::cout << "transpose ui1 to ui1t" << std::endl;
MatrixXd ui1t(1,2);//group/feature
ui1t=ui1.transpose();
std::cout << ui1t << std::endl;
cout << "" << endl;


cout << "x & x1 data adverage u" << endl;
MatrixXd u(1,2);//all group/feature
u(0,0)=(x(0,0) + x(1,0) + x(2,0) + x(3,0) + x1(0,0) + x1(1,0) + x1(2,0))/7.0;

u(0,1)=(x(0,1) + x(1,1) + x(2,1) + x(3,1) + x1(0,1) + x1(1,1) + x1(2,1))/7.0;

std::cout << u << std::endl;
cout << "" << endl;


cout << "mean corrected data xig - u" << endl;
MatrixXd ximinu(4,2);
//cur
ximinu(0,0) = x(0,0) - u(0,0);//f0
ximinu(1,0) = x(1,0) - u(0,0);
ximinu(2,0) = x(2,0) - u(0,0);
ximinu(3,0) = x(3,0) - u(0,0);
//dia
ximinu(0,1) = x(0,1) - u(0,1);//f1
ximinu(1,1) = x(1,1) - u(0,1);
ximinu(2,1) = x(2,1) - u(0,1);
ximinu(3,1) = x(3,1) - u(0,1);
std::cout << ximinu << std::endl;
cout << "" << endl;

cout << "mean corrected data xi1 - u" << endl;


MatrixXd ximinu1(3,2);
//cur
ximinu1(0,0) = x1(0,0) - u(0,0);
ximinu1(1,0) = x1(1,0) - u(0,0);
ximinu1(2,0) = x1(2,0) - u(0,0);
//dia
ximinu1(0,1) = x1(0,1) - u(0,1);//g1
ximinu1(1,1) = x1(1,1) - u(0,1);
ximinu1(2,1) = x1(2,1) - u(0,1);

std::cout << ximinu1 << std::endl;

cout << " " << endl;

cout << "Transpose matricies" << endl;
cout << "xi - u T" << endl;

MatrixXd ximinut(4,2);
ximinut= ximinu.transpose();
std::cout << ximinut<< std::endl;
cout << " " << endl;

cout << "xi1 - u T" << endl;
MatrixXd ximinu1t(3,2);
ximinu1t= ximinu1.transpose();
std::cout << ximinu1t << std::endl;
cout << " " << endl;

cout << "Covariance matrix of group ci" << endl;
MatrixXd ci(2,2);
ci = ( ximinut * ximinu ) /4.0;
std::cout << ci << std::endl;
cout << "" << endl;

cout << "Covariance matrix of group ci1" << endl;
MatrixXd ci1(2,2);
ci1 = ( ximinu1t * ximinu1 ) /3.0;
std::cout << ci1 << std::endl;
cout << "" << endl;

cout << "Pooled within group Covariance matrix c" << endl;
MatrixXd c(2,2);
c(0,0) = 4.0/7.0 * ci(0,0) + 3.0/7.0 * ci1(0,0);
c(1,0) = 4.0/7.0 * ci(1,0) + 3.0/7.0 * ci1(1,0);
c(0,1) = 4.0/7.0 * ci(0,1) + 3.0/7.0 * ci1(0,1);
c(1,1) = 4.0/7.0 * ci(1,1) + 3.0/7.0 * ci1(1,1);
std::cout << c << std::endl;
cout << "" << endl;

cout << "inverse of Pooled within group Covariance matrix cinverse" << endl;
MatrixXd cinverse(2,2);
 cinverse=c.inverse();
std::cout << cinverse << std::endl;
cout << "" << endl;

cout << "Probability of a group" << endl;
cout << "x = 4/7 x1 = 3/7 p(4/7,3/7)" << endl;
Vector2d p(4.0/7.0,3.0/7.0);
std::cout << p << std::endl;
cout << "" << endl;

//discriminent function
//MatrixXd fi(2,2);
//double xk = 1;
//formula for calculatin likelyhood of data in a group...
//fi = uig  * cinverse xkt - 1/2uig cinverse uitg + ln probability
//fi  = ui  * cinverse * x.transpose() - 1/2 * ui * cinverse;// * uit;// +.3;
//fi1 = ui1 * cinverse * x1.transpose() - 1/2 * ui1 * cinverse ui1.transpose + ln(3/7);
//std::cout << fi << std::endl;
MatrixXd xk(1,2);//new data
xk(0,0) = 2.81;//f1
xk(0,1) = 5.46;

MatrixXd xkt(1,2);//new data
xkt=xk.transpose();
//ui  * cinverse * xkt
//1.0/2.0 * ui * cinverse * uit
cout << "ln(p1) =" << endl;

MatrixXd lnp1(1,1);//p1 4/7
lnp1(0,0) = 0.0;
lnp1(0,0)=log(4.0/7.0);

MatrixXd lnp2(1,1);//p1 3/7
lnp2(0,0) = 0.0;
lnp2(0,0)=log(4.0/7.0);

std::cout << lnp1 << std::endl;
cout << "" << endl;
cout << "The LDA of two features of data f1 f2" << endl;

//std::cout << ui   * cinverse * xkt  -1.0/2.0 * ui  * cinverse * uit + lnp1  << std::endl;
//std::cout << ui1  * cinverse * xkt -1.0/2.0 * ui1 * cinverse * ui1t + lnp2 << std::endl;
MatrixXd f1(1,1);//ui   * cinverse * xkt  -1.0/2.0 * ui  * cinverse * uit + lnp1
MatrixXd f2(1,1);//ui1  * cinverse * xkt -1.0/2.0 * ui1 * cinverse * ui1t + lnp2

f1 = ui   * cinverse * xkt  -1.0/2.0 * ui  * cinverse * uit + lnp1;
f2 = ui1  * cinverse * xkt -1.0/2.0 * ui1 * cinverse * ui1t + lnp2;
std::cout << f1  << std::endl;
std::cout << f2  << std::endl;

cout << "The larger of the discriminent functions results is what group the data is in" << endl;
if (f1(0,0)>f2(0,0)) cout << "the data is in group 1" << endl;
if (f1(0,0)<f2(0,0)) cout << "the data is in group 2" << endl;

cout << "" << endl;


cout << "End of program!" << endl;

    return 0;
}