现有1500个二维空间的数据点，import time as time import numpy as np import matplotlib.pyplot as plt import mpl_toolkits.mplot3d.axes3d as p3 from sklearn.datasets import make_swiss_roll # Generate data (swiss roll dataset) n_samples = 1500 noise = 0.05 X, _ = make_swiss_roll(n_samples, noise=noise) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.scatter(X[:, 0], X[:, 1], X[:, 2], cmap=plt.cm.Spectral)，编写一个python程序不调用sklearn.manifold ，实现ISOMAP降维度

以下是一个简单的Python程序，用于实现ISOMAP算法对1500个二维空间数据点的降维处理：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Generate data
n_samples = 1500
noise = 0.05
X, _ = make_swiss_roll(n_samples, noise=noise)

# Define ISOMAP function
def isomap(data, k=7, d=2):
    # Calculate pairwise distances between data points
    dists = np.zeros((data.shape[0], data.shape[0]))
    for i in range(data.shape[0]):
        for j in range(i+1, data.shape[0]):
            dists[i,j] = np.sqrt(np.sum((data[i] - data[j])**2))
            dists[j,i] = dists[i,j]
    
    # Construct neighborhood graph
    knn_indices = np.argsort(dists)[:,:k+1]
    knn_dists = np.array([dists[i, knn_indices[i]] for i in range(data.shape[0])])
    knn_dists[:,0] = 0
    knn_graph = np.zeros((data.shape[0], data.shape[0]))
    for i in range(data.shape[0]):
        knn_graph[i, knn_indices[i]] = knn_dists[i]
    
    # Compute shortest path distances
    inf = np.inf
    dists[dists == 0] = inf
    for k in range(data.shape[0]):
        for i in range(data.shape[0]):
            for j in range(data.shape[0]):
                dists[i,j] = min(dists[i,j], dists[i,k] + dists[k,j])
    
    # Compute low-dimensional embedding
    dists[dists == inf] = 0
    B = -0.5*(dists**2 - np.sum(dists**2, axis=0)/data.shape[0] - np.sum(dists**2, axis=1)/data.shape[0] + np.sum(dists**2)/data.shape[0]**2)
    _, eigvecs = np.linalg.eigh(B)
    embedding = eigvecs[:, :d]
    
    return embedding

# Apply ISOMAP to data
embedding = isomap(X)

# Visualize results
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(embedding[:,0], embedding[:,1], cmap=plt.cm.Spectral)
plt.show()

该程序首先生成数据集，然后定义了一个名为isomap的函数来实现ISOMAP算法。该函数首先计算数据点之间的距离，然后构建邻域图，并使用Floyd-Warshall算法计算最短路径距离。最后，该函数将最短路径距离转换为低维嵌入，并返回嵌入结果。

该程序将ISOMAP算法应用于数据集，并使用2D散点图可视化了嵌入结果。