Mahalanobis distance with the matrix library of MQ and Beer. – Statistics – December 18

First of all what is it?

Second some documents

Wikipedia page

We need:

• covariance matrix
• Matrix inversion
• matrix multiplication
• vector average

that much Matrix and vector libraries mql5 actually meets all our requirements.

great. We will build a structure that can be prepared once and reused as long as the sample set does not change.

What do you mean by sample set?

A set of observations with attributes.

To simplify, let’s say we have 10 candles (chart candles) and we have an OHLC on them. So there are 10 samples and 4 attributes or 4 features.

Here is an example usage:

double open(),high(),low(),close();
ArrayResize(open,10,0);
ArrayResize(high,10,0);
ArrayResize(low,10,0);
ArrayResize(close,10,0);
for(int i=0;i<10;i++)
   open(i)=iOpen(_Symbol,_Period,i+1);
   high(i)=iHigh(_Symbol,_Period,i+1);
   low(i)=iLow(_Symbol,_Period,i+1);
   close(i)=iClose(_Symbol,_Period,i+1);
   

mahalanober M;
M.setup(4,10);

  M.fill_feature(0,open);
  M.fill_feature(1,high);
  M.fill_feature(2,low);
  M.fill_feature(3,close);

  
    double md=M.distanceOfSampleToDistribution(2);
    Print("Mahalabonis Distance of bar 2 to the distribution "+DoubleToString(md,4));
  
    md=M.distanceOfSampleToSample(5,0);
    Print("Mahalabonis Distance of bar(0) to bar(5) in the distribution "+DoubleToString(md,4));

And here’s the structure

struct mahalanober{
       
       private:
vector features();
  bool filled();
vector feature_means;
matrix covariance_matrix_inverse;
   int total_features,total_samples;
       public:
       mahalanober(void)reset();
      ~mahalanober(void)reset();
  void reset()
       total_features=0;
       total_samples=0;
       ArrayFree(features);
       ArrayFree(filled);
       feature_means.Init(0);
       covariance_matrix_inverse.Init(0,0);
       
  void setup(int _total_features,
             int _total_samples)
       total_features=_total_features;
       total_samples=_total_samples;
       ArrayResize(features,total_features,0);
       ArrayResize(filled,total_features,0);
       ArrayFill(filled,0,total_features,false);
       feature_means.Init(total_features);
       for(int i=0;i<ArraySize(features);i++)
          features(i).Init(total_samples);
          
       
  bool fill_feature(int which_feature_ix,
                    double &values_across_samples())
       if(which_feature_ix<ArraySize(features))
       if(ArraySize(values_across_samples)==total_samples)
       for(int i=0;i<total_samples;i++)
          features(which_feature_ix)(i)=values_across_samples(i);
          
       feature_means(which_feature_ix)=features(which_feature_ix).Mean();
       filled(which_feature_ix)=true;
       
         if(all_filled())
           calculate_inverse_covariance_matrix();
           
       return(true);
       else
       Print("MHLNB::fill_feature::Amount of values does not match total samples");
       
       else
       Print("MHLNB::fill_feature::Feature("+IntegerToString(which_feature_ix)+") does not exist");
       
       return(false);
       
double distanceOfSampleToDistribution(int which_sample)
       if(all_filled())
       if(which_sample<total_samples)
       
         matrix term0;
         term0.Init(total_features,1);
         for(int i=0;i<total_features;i++)
            term0(i)(0)=features(i)(which_sample)-feature_means(i);
             
         
         matrix term3=term0;
         matrix term1;
         
           term1=term0.Transpose();
           
           matrix term2=term1.MatMul(covariance_matrix_inverse); 
           
           matrix last_term=term2.MatMul(term3);  
           
           
           return(MathSqrt(last_term(0)(0)));      
         else
         Print("MLHNB::distanceOfSampleToDistribution()::Sample ("+IntegerToString(which_sample)+") does not exist returning 0.0");
         
       else
       list_unfilled("distanceOfSampleToDistribution()");
       
       return(0.0);
       
double distanceOfSampleToSample(int sample_a,int sample_b){
       if(all_filled())
       if(sample_a<total_samples)
       if(sample_b<total_samples)
       
         matrix term0;
         term0.Init(total_features,1);
         for(int i=0;i<total_features;i++)
            term0(i)(0)=features(i)(sample_a)-features(i)(sample_b);
             
         
         matrix term3=term0;
         matrix term1;
         
           term1=term0.Transpose();
           
           matrix term2=term1.MatMul(covariance_matrix_inverse); 
           
           matrix last_term=term2.MatMul(term3);  
           
           
           return(MathSqrt(last_term(0)(0)));    
           else
           Print("MLHNB::distanceOfSampleToSample()::Sample ("+IntegerToString(sample_b)+") does not exist returning 0.0");
           
         else
         Print("MLHNB::distanceOfSampleToSample()::Sample ("+IntegerToString(sample_a)+") does not exist returning 0.0");
         
       else
       list_unfilled("distanceOfSampleToSample()");
       
       return(0.0);
       }
       private:
  void calculate_inverse_covariance_matrix()  
       
       matrix samples_by_features;
       samples_by_features.Init(total_samples,total_features);
       
       
         for(int f=0;f<total_features;f++)
         
           for(int s=0;s<total_samples;s++)
              samples_by_features(s)(f)=features(f)(s);
               
           
       
       matrix covariance_matrix=samples_by_features.Cov(false);
       
       covariance_matrix_inverse=covariance_matrix.Inv();
       
  bool all_filled()
       if(total_features>0)
       for(int i=0;i<total_features;i++)
          if(!filled(i))
            return(false);
            
          
       return(true);
       
       return(false);
       
  void list_unfilled(string fx)
       for(int i=0;i<total_features;i++)
          if(!filled(i))
            Print("MLHNB::"+fx+"::Feature("+IntegerToString(i)+") is not filled!");
            
          
       
};

Please let me know if you find any mistakes.

Cheers