SVM.py

import matplotlib.pyplot as plt
from matplotlib import style
import numpy as np
style.use('ggplot')

data_dict = {-1:np.array([[1,7],[2,8],[3,8],]),
              1:np.array([[5,1],[6,-1],[7,3],])}


class Support_Vector_Machine:
    def __init__(self, visualization = True):
        self.visualization = visualization
        self.colors = {1:'r', -1:'b'}
        if self.visualization:
            self.fig = plt.figure()
            self.ax = self.fig.add_subplot(1,1,1)

    def fit(self, data):
        self.data = data
        opt_dict = {}

        transforms = [[1,1],[-1,1],[-1,-1],[1,-1]]

        all_data = []
        for yi in self.data:
            for featureset in self.data[yi]:
                for feature in featureset:
                    all_data.append(feature)

        self.max_feature_value = max(all_data)
        self.min_feature_value = min(all_data)
        all_data = None

        step_sizes = [self.max_feature_value * 0.1, self.max_feature_value * 0.01, self.max_feature_value * 0.001]

        b_range_multiple = 5
        b_multiple = 5
        latest_optimum = self.max_feature_value*10

        for step in step_sizes:
            w = np.array([latest_optimum, latest_optimum])
            optimized = False
            while not optimized:
                for b in np.arange(-1*(self.max_feature_value*b_range_multiple), self.max_feature_value*b_range_multiple, step*b_multiple):
                    for transformation in transforms:
                        w_t = w*transformation
                        found_option = True

                        for i in self.data:
                            for xi in self.data[i]:
                                yi = i
                                if not yi*(np.dot(w_t,xi)+b) >= 1:
                                    found_option = False

                        if found_option:
                            opt_dict[np.linalg.norm(w_t)] = [w_t,b]

                if w[0] < 0:
                    optimized = True
                    print('Optimized a step')
                else:
                    w = w - step

            norms = sorted([n for n in opt_dict])
            opt_choice = opt_dict[norms[0]]
            self.w = opt_choice[0]
            self.b = opt_choice[1]
            latest_optimum = opt_choice[0][0] + step*2

    def predict(self, features):
        classification = np.sign(np.dot(np.array(features), self.w) + self.b)

        if classification != 0 and self.visualization:
            self.ax.scatter(features[0], features[1], s = 200, marker = '*', c = self.colors[classification])
        else:
            print('Featureset ',features, ' is on the decision boundary')
            
        return classification

    def visualize(self):
        [[self.ax.scatter(x[0],x[1],s=100,color=self.colors[i]) for x in data_dict[i]] for i in data_dict]

        def hyperplane(x, w, b, v):
            return (-w[0]*x-b+v) / w[1]

        datarange = (self.min_feature_value*0.9,self.max_feature_value*1.1)
        hyp_x_min = datarange[0]
        hyp_x_max = datarange[1]

        psv1 = hyperplane(hyp_x_min, self.w, self.b, 1)
        psv2 = hyperplane(hyp_x_max, self.w, self.b, 1)
        self.ax.plot([hyp_x_min,hyp_x_max],[psv1,psv2], 'k')

        nsv1 = hyperplane(hyp_x_min, self.w, self.b, -1)
        nsv2 = hyperplane(hyp_x_max, self.w, self.b, -1)
        self.ax.plot([hyp_x_min,hyp_x_max],[nsv1,nsv2], 'k')

        db1 = hyperplane(hyp_x_min, self.w, self.b, 0)
        db2 = hyperplane(hyp_x_max, self.w, self.b, 0)
        self.ax.plot([hyp_x_min,hyp_x_max],[db1,db2], 'g--')

        plt.show()

def main():
    svm = Support_Vector_Machine()
    svm.fit(data = data_dict)

    predict_us = [[0,10],[1,3],[3,4],[3,5],[5,5],[5,6],[6,-5],[5,8]]

    for p in predict_us:
        svm.predict(p)

    svm.visualize()

if __name__ == '__main__':
    main()