Question

我正在关注《学习表单数据》这本书，该书具有以下练习：

创建线性可分离的输入数据集。
在生成的数据集上实现单层感知器。

要创建数据集，它表示先选择一个二维平面，然后在该平面中选择一条随机线。平面一侧的点归为正，另一侧的点归为负。我能够在https://datasciencelab.wordpress.com/2014/01/10/machine-learning-classics-the-perceptron/

的帮助下进行跟踪

import numpy as np
import random
import os, subprocess

class Perceptron:
def __init__(self, N):
    # Random linearly separated data
    xA,yA,xB,yB = [random.uniform(-1, 1) for i in range(4)]
    self.V = np.array([xB*yA-xA*yB, yB-yA, xA-xB])
    self.X = self.generate_points(N)

def generate_points(self, N):
    X = []
    for i in range(N):
        x1,x2 = [random.uniform(-1, 1) for i in range(2)]
        x = np.array([1,x1,x2])
        s = int(np.sign(self.V.T.dot(x)))
        X.append((x, s))
    return X

def plot(self, mispts=None, vec=None, save=False):
    fig = plt.figure(figsize=(5,5))
    plt.xlim(-1,1)
    plt.ylim(-1,1)
    V = self.V
    a, b = -V[1]/V[2], -V[0]/V[2]
    l = np.linspace(-1,1)
    plt.plot(l, a*l+b, 'k-')
    cols = {1: 'r', -1: 'b'}
    for x,s in self.X:
        plt.plot(x[1], x[2], cols[s]+'o')
    if mispts:
        for x,s in mispts:
            plt.plot(x[1], x[2], cols[s]+'.')
    if vec != None:
        aa, bb = -vec[1]/vec[2], -vec[0]/vec[2]
        plt.plot(l, aa*l+bb, 'g-', lw=2)
    if save:
        if not mispts:
            plt.title('N = %s' % (str(len(self.X))))
        else:
            plt.title('N = %s with %s test points' \
                      % (str(len(self.X)),str(len(mispts))))
        plt.savefig('p_N%s' % (str(len(self.X))), \
                    dpi=200, bbox_inches='tight')

def classification_error(self, vec, pts=None):
    # Error defined as fraction of misclassified points
    if not pts:
        pts = self.X
    M = len(pts)
    n_mispts = 0
    for x,s in pts:
        if int(np.sign(vec.T.dot(x))) != s:
            n_mispts += 1
    error = n_mispts / float(M)
    return error

def choose_miscl_point(self, vec):
    # Choose a random point among the misclassified
    pts = self.X
    mispts = []
    for x,s in pts:
        if int(np.sign(vec.T.dot(x))) != s:
            mispts.append((x, s))
    return mispts[random.randrange(0,len(mispts))]

def pla(self, save=False):
    # Initialize the weigths to zeros
    w = np.zeros(3)
    X, N = self.X, len(self.X)
    it = 0
    # Iterate until all points are correctly classified
    while self.classification_error(w) != 0:
        it += 1
        # Pick random misclassified point
        x, s = self.choose_miscl_point(w)
        # Update weights
        w += s*x
        if save:
            self.plot(vec=w)
            plt.title('N = %s, Iteration %s\n' \
                      % (str(N),str(it)))
            plt.savefig('p_N%s_it%s' % (str(N),str(it)), \
                        dpi=200, bbox_inches='tight')
    self.w = w

def check_error(self, M, vec):
    check_pts = self.generate_points(M)
    return self.classification_error(vec, pts=check_pts)

逻辑和代码的图像如下： 2 D linearly separable data

我想类似地创建N维线性可分离的数据集。例如一组10维的点。指向9维超平面一侧的点将被分类为正，而另一侧的点将被分类为负。

我不知道如何进行。任何帮助表示赞赏。

为单层感知器创建线性可分离的N维数据集

0 个答案: