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机器学习算法-支持向量机SVM

news 来源：原创 2025/5/3 17:30:12

支持向量机-python实现

由于本菜鸟目前还没有学习到软间隔和核函数的处理，so，先分享的硬间隔不带核函数，也就是不涉及非线性可分转化成线性可分的逻辑，后续如果学的懂，就在本篇文章的代码中继续拓展核函数等。

先来看看支持向量机的概念和解决的问题

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咱们来举个例子

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上代码了

# 用于函数求导的
import sympy as sp
import numpy as np# 硬间隔不带核函数支持向量机
class SVM:# learn_rate：学习率# lambda_rate: 转移率# descend_times: 梯度下降次数# w：超平面所有纬度的斜率（是个向量）# b：常数# train_x: 测试输入数据# train_y：测试输出数据# labels: 属性类别def __init__(self, learn_rate=0.01, lambda_rate=0.01, descend_times=1000):self.learn_rate = learn_rateself.lambda_rate = lambda_rateself.descend_times = descend_timesself.w = Noneself.b = Noneself.train_x = []self.train_y = []self.labels = []# 类别映射def type_mapping(self, Y):return np.array([(1 if item == Y[0] or item == 1 else -1) for item in Y])# 对于最后一个an变量,可用a0-an-1化简def getParamsA(self, symbols, Y, size, i):if i < size - 1:return symbols[i]else:res = 0.0for index in range(size - 1):res += (symbols[index] * Y[index])return -1.0 * Y[i] * res# 拉格朗日乘数法求解def lagrange_mutiply(self, X, Y):Y, size = self.type_mapping(Y), len(X)params_symbol = np.array([None] * size)for i in range(size):params_symbol[i] = sp.symbols('a' + str(i))L = 0.0for i in range(size):for j in range(size):L += (self.getParamsA(params_symbol, Y, size, i)* self.getParamsA(params_symbol, Y, size, j)* Y[i] * Y[j]* np.dot(X[i], X[j]))L = sp.simplify(0.5 * L - sum(params_symbol[:size - 1]) - self.getParamsA(params_symbol, Y, size, size - 1))res_symbol, res_var = [], []for i in range(size - 1):res_symbol.append(sp.diff(L, params_symbol[i]))res_var.append(params_symbol[i])diff_solve = sp.solve(res_symbol, res_var)res_last_value = 0.0for i in range(size - 1):res_last_value += (diff_solve[params_symbol[i]] * Y[i])diff_solve[params_symbol[size - 1]] = -1 * Y[size - 1] * res_last_value# 向量中不包含负数w, b = np.zeros(len(X[0])), 0if len([item for item in list(diff_solve.values()) if item < 0]) == 0:for k_i, key in enumerate(params_symbol):w += (diff_solve[key] * Y[k_i] * X[k_i])b = np.dot(w, X[0]) - Y[0]else:  # 向量中包含负数,采取随机梯度下降算法求解w和bfor t in range(self.descend_times):for idx, x_i in enumerate(X):condition = Y[idx] * (np.dot(x_i, w) - b) >= 1if condition:w -= self.learn_rate * (2 * self.lambda_rate * w)else:w -= self.learn_rate * (2 * self.lambda_rate * w - np.dot(x_i, Y[idx]))b -= self.learn_rate * Y[idx]return w, b# 数据处理def fit(self, X, Y, Labels):X, Y = np.array(X), np.array(Y)self.train_x, self.train_y, self.labels = X, Y, Labelsself.w, self.b = self.lagrange_mutiply(X, Y)# 分类判断def predict(self, X):t = 1 if np.dot(self.w, np.array(X)) - self.b > 0 else -1y_ = list(self.type_mapping(self.train_y)).index(t)return self.train_y[y_]m = SVM()
m.fit([[3, 3, 4], [4, 3, 5], [1, 1, 1]], ["正例", "正例", "反例"], ["图像宽度","图像高度","图像大小"])
print(m.predict([1, 2, 2]))