Added kernel of RBF.

Author: Kalvar

FCM/KRFuzzyCMeans.h

@@ -11,9 +11,11 @@
 typedef enum KRFuzzyCMeansDistanceFormula
 {
     // Distance by Cosine Similarity
-    KRFuzzyCMeansDistanceFormulaByCosine    = 0,
+    KRFuzzyCMeansDistanceFormulaCosine    = 0,
     // Distance by Euclidean Distance
-    KRFuzzyCMeansDistanceFormulaByEuclidean = 1
+    KRFuzzyCMeansDistanceFormulaEuclidean,
+    // Distance by RBF
+    KRFuzzyCMeansDistanceFormulaRBF
 }KRFuzzyCMeansDistanceFormula;
 
 /*
@@ -49,6 +51,8 @@ typedef void(^KRFuzzyCMeansPerIteration)(NSInteger times, NSArray *clusters, NSA
 @property (nonatomic, assign) NSInteger m;
 //訓練完是否自動儲存
 @property (nonatomic, assign) BOOL doneThenSave;
+//使用 RBF 時，能自訂 Sigma 標準差
+@property (nonatomic, assign) float sigma;
 
 @property (nonatomic, assign) KRFuzzyCMeansDistanceFormula distanceFormula;
 

FCM/KRFuzzyCMeans.m

@@ -23,7 +23,7 @@ @interface KRFuzzyCMeans()
 @implementation KRFuzzyCMeans(fixDistance)
 
 // Euclidean distance which multi-dimensional formula, 距離越小越近
--(float)_distanceEuclideanX1:(NSArray *)_x1 x2:(NSArray *)_x2
+-(float)_euclideanX1:(NSArray *)_x1 x2:(NSArray *)_x2
 {
     NSInteger _index = 0;
     float _sum       = 0.0f;
@@ -32,13 +32,12 @@ -(float)_distanceEuclideanX1:(NSArray *)_x1 x2:(NSArray *)_x2
         _sum        += powf([_x floatValue] - [[_x2 objectAtIndex:_index] floatValue], 2);
         ++_index;
     }
-    //return _sum;
     // 累加完距離後直接開根號
     return (_index > 0) ? sqrtf(_sum) : _sum;
 }
 
 // Cosine Similarity method that multi-dimensional, 同歸屬度越大越近
--(float)_distanceCosineSimilarityX1:(NSArray *)_x1 x2:(NSArray *)_x2
+-(float)_cosineSimilarityX1:(NSArray *)_x1 x2:(NSArray *)_x2
 {
     float _sumA  = 0.0f;
     float _sumB  = 0.0f;
@@ -58,17 +57,35 @@ -(float)_distanceCosineSimilarityX1:(NSArray *)_x1 x2:(NSArray *)_x2
     return ( _ab > 0.0f ) ? ( _sumAB / sqrtf( _ab ) ) : 0.0f;
 }
 
+-(double)_rbf:(NSArray *)_x1 x2:(NSArray *)_x2
+{
+    double _sum      = 0.0f;
+    NSInteger _index = 0;
+    for( NSNumber *_value in _x1 )
+    {
+        // Formula : s = s + ( v1[i] - v2[i] )^2
+        double _v  = [_value doubleValue] - [[_x2 objectAtIndex:_index] doubleValue];
+        _sum      += ( _v * _v );
+        ++_index;
+    }
+    // Formula : exp^( -s / ( 2.0f * sigma * sigma ) )
+    return pow(M_E, ((-_sum) / ( 2.0f * self.sigma * self.sigma )));
+}
+
 // 距離概念是越小越近，歸屬度概念是越大越近 ( 或取其差值，使歸屬度同距離越小越近 )
 -(float)_distanceX1:(NSArray *)_x1 x2:(NSArray *)_x2
 {
     float _distance = 0.0f;
     switch (self.distanceFormula)
     {
-        case KRFuzzyCMeansDistanceFormulaByCosine:
-            _distance = 1.0f - [self _distanceCosineSimilarityX1:_x1 x2:_x2];
+        case KRFuzzyCMeansDistanceFormulaCosine:
+            _distance = 1.0f - [self _cosineSimilarityX1:_x1 x2:_x2];
             break;
-        case KRFuzzyCMeansDistanceFormulaByEuclidean:
-            _distance = [self _distanceEuclideanX1:_x1 x2:_x2];
+        case KRFuzzyCMeansDistanceFormulaEuclidean:
+            _distance = [self _euclideanX1:_x1 x2:_x2];
+            break;
+        case KRFuzzyCMeansDistanceFormulaRBF:
+            _distance = [self _rbf:_x1 x2:_x2];
             break;
         default:
             break;
@@ -342,8 +359,10 @@ -(instancetype)init
         _lastCenters        = nil;
         _currentIteration   = 0;
 
-        _distanceFormula    = KRFuzzyCMeansDistanceFormulaByEuclidean;
+        _distanceFormula    = KRFuzzyCMeansDistanceFormulaEuclidean;
         _trainedSaves       = [KRFuzzyCMeansSaves sharedInstance];
+        
+        _sigma              = 2.0f;
     }
     return self;
 }

KRFuzzyCMeans.podspec

@@ -1,6 +1,6 @@
 Pod::Spec.new do |s|
   s.name         = "KRFuzzyCMeans"
-  s.version      = "1.3"
+  s.version      = "1.4"
   s.summary      = "Fuzzy C-Means is clustering algorithm combined fuzzy theory on Machine Learning."
   s.description  = <<-DESC
                    KRFuzzyCMeans has implemented Fuzzy C-Means (FCM) the fuzzy (ファジー理論) clustering / classification algorithm (クラスタリング分類) in Machine Learning (マシンラーニング). It could be used in data mining (データマイニング) and image compression (画像圧縮).

KRFuzzyCMeans/ViewController.m

@@ -22,7 +22,7 @@ - (void)viewDidLoad
     _krFcm.doneThenSave     = YES;
     _krFcm.m                = 3;
     _krFcm.convergenceError = 0.001f;
-    _krFcm.distanceFormula  = KRFuzzyCMeansDistanceFormulaByEuclidean; //KRFuzzyCMeansDistanceFormulaByCosine
+    _krFcm.distanceFormula  = KRFuzzyCMeansDistanceFormulaRBF; //KRFuzzyCMeansDistanceFormulaEuclidean; //KRFuzzyCMeansDistanceFormulaByCosine
     [_krFcm addCenters:@[@5.0f, @5.0f]];     //The center 1, cluster 1 start in here
     [_krFcm addCenters:@[@10.0f, @10.0f]];   //The center 2, cluster 2 start in here
     [_krFcm addCenters:@[@12.0f, @14.0f]];   //The center 3, cluster 3 start in here

LICENSE

@@ -1,4 +1,4 @@
-Copyright (c) 2014 - 2015 Kuo-Ming Lin (Kalvar Lin) (http://kalvar-kaki.blogspot.tw/)
+Copyright (c) 2014 - 2016 Kuo-Ming Lin (Kalvar Lin) (http://kalvar-kaki.blogspot.tw/)
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

README.md

@@ -7,7 +7,7 @@ KRFuzzyCMeans has implemented Fuzzy C-Means (FCM) the fuzzy (ファジー理論)
 
 ```ruby
 platform :ios, '7.0'
-pod "KRFuzzyCMeans", "~> 1.3"
+pod "KRFuzzyCMeans", "~> 1.4"
 ```
 
 ## How to use
@@ -17,13 +17,21 @@ pod "KRFuzzyCMeans", "~> 1.3"
 #import "KRFuzzyCMeans.h"
 ```
 
+##### Distance Methods
+
+``` objective-c
+KRFuzzyCMeansDistanceFormulaEuclidean
+KRFuzzyCMeansDistanceFormulaCosine
+KRFuzzyCMeansDistanceFormulaRBF
+```
+
 #### Training
 ``` objective-c
 KRFuzzyCMeans *_krFcm   = [KRFuzzyCMeans sharedFCM];
 _krFcm.doneThenSave     = YES;
 _krFcm.m                = 3;
 _krFcm.convergenceError = 0.001f;
-_krFcm.distanceFormula  = KRFuzzyCMeansDistanceFormulaByEuclidean; //KRFuzzyCMeansDistanceFormulaByCosine
+_krFcm.distanceFormula  = KRFuzzyCMeansDistanceFormulaEuclidean; //KRFuzzyCMeansDistanceFormulaCosine
 [_krFcm addCenters:@[@5.0f, @5.0f]];     //The center 1, cluster 1 start in here
 [_krFcm addCenters:@[@10.0f, @10.0f]];   //The center 2, cluster 2 start in here
 [_krFcm addCenters:@[@12.0f, @14.0f]];   //The center 3, cluster 3 start in here
@@ -66,7 +74,7 @@ _krFcm.distanceFormula  = KRFuzzyCMeansDistanceFormulaByEuclidean; //KRFuzzyCMea
 
 ## Version
 
-V1.3
+V1.4
 
 ## License