python不用调库实现PCA算法

可以使用numpy库中的函数来实现PCA算法，以下是一个简单的实现代码：

import numpy as np

def pca(X, k):
    # 计算协方差矩阵
    cov = np.cov(X.T)
    # 计算特征值和特征向量
    eig_vals, eig_vecs = np.linalg.eig(cov)
    # 取前k个特征向量
    top_k_eig_vecs = eig_vecs[:, :k]
    # 将数据投影到新的空间中
    new_X = X.dot(top_k_eig_vecs)
    return new_X

其中，X是一个n×m的矩阵，表示有n个样本，每个样本有m个特征。k表示要保留的主成分个数。函数返回一个n×k的矩阵，表示将原始数据投影到k维空间后的结果。

相关问题

python调库使用遗传算法

根据提供的引用内容，可以看出Python中使用遗传算法需要调用numpy、random和matplotlib.pyplot等库。下面是一个简单的遗传算法示例，用于解决一个整数规划问题：

import numpy as np
import random
import matplotlib.pyplot as plt

# 定义目标函数
def fitness_func(x):
    return x[0] + x[1] - 2 * x[2]

# 定义种群初始化函数
def init_population(pop_size, chrom_length):
    population = np.zeros((pop_size, chrom_length))
    for i in range(pop_size):
        population[i] = np.random.randint(0,2, chrom_length)
    return population

# 定义选择函数
def selection(population, fitness):
    fitness_sum = np.sum(fitness)
    probability = fitness / fitness_sum
    cum_probability = np.cumsum(probability)
    new_population = np.zeros(population.shape)
    for i in range(population.shape[0]):
        random_num = random.random()
        for j in range(population.shape[0]):
            if random_num <= cum_probability[j]:
                new_population[i] = population[j]
                break
    return new_population
# 定义交叉函数
def crossover(population, pc):
    new_population = np.zeros(population.shape)
    for i in range(0, population.shape[0], 2):
        if random.random() < pc:
            crossover_point = random.randint(1, population.shape[1] - 1)
            new_population[i] = np.concatenate((population[i][:crossover_point], population[i+1][crossover_point:]))
            new_population[i+1] = np.concatenate((population[i+1][:crossover_point], population[i][crossover_point:]))
        else:
            new_population[i] = population[i]
            new_population[i+1] = population[i+1]
    return new_population

# 定义变异函数
def mutation(population, pm):
    for i in range(population.shape[0]):
        if random.random() < pm:
            mutation_point = random.randint(0, population.shape[1] - 1)
            population[i][mutation_point] = 1 - population[i][mutation_point]
    return population

# 定义遗传算法主函数
def genetic_algorithm(pop_size, chrom_length, pc, pm, max_iter):
    population = init_population(pop_size, chrom_length)
    fitness = np.zeros(pop_size)
    best_fitness = np.zeros(max_iter)
    best_chromosome = np.zeros((max_iter, chrom_length))
    for i in range(max_iter):
        for j in range(pop_size):
            fitness[j] = fitness_func(population[j])
        best_fitness[i] = np.max(fitness)
        best_chromosome[i] = population[np.argmax(fitness)]
        population = selection(population, fitness)
        population = crossover(population, pc)
        population = mutation(population, pm)
    return best_fitness, best_chromosome

# 测试遗传算法
pop_size = 50
chrom_length = 3
pc = 0.8
pm = 0.01
max_iter = 100
best_fitness, best_chromosome = genetic_algorithm(pop_size, chrom_length, pc, pm, max_iter)

# 输出结果
print("最优解：", best_chromosome[-1])
print("最优值：", best_fitness[-1])

# 绘制适应度曲线
plt.plot(best_fitness)
plt.xlabel("迭代次数")
plt.ylabel("适应度")
plt.show()

k-means聚类分析 python不调库实现

K-means聚类是一种常见的无监督学习算法，它将数据集分成K个簇，每个簇包含最接近其质心的数据点。K-means算法的基本思想是：首先随机选择K个点作为初始质心，然后将每个数据点分配到最近的质心所在的簇中，接着重新计算每个簇的质心，重复以上步骤直到质心不再发生变化或达到预定的迭代次数。

以下是Python实现K-means聚类分析的代码：

import numpy as np

def kmeans(X, K, max_iters=100):
    # 随机初始化K个质心
    centroids = X[np.random.choice(len(X), K, replace=False)]
    for i in range(max_iters):
        # 计算每个样本到质心的距离
        distances = np.sqrt(((X - centroids[:, np.newaxis])**2).sum(axis=2))
        # 将每个样本分配到距离最近的质心所在的簇中
        labels = np.argmin(distances, axis=0)
        # 更新每个簇的质心
        new_centroids = np.array([X[labels == k].mean(axis=0) for k in range(K)])
        # 如果质心不再发生变化，则退出循环
        if np.all(centroids == new_centroids):
            break
        centroids = new_centroids
    return centroids, labels

其中，X是一个n×m的矩阵，表示n个样本的m个特征；K是簇的个数；max_iters是最大迭代次数。函数返回K个质心和每个样本所属的簇的标签。