python实现isomap算法代码生成图像

以下是使用Python实现Isomap算法并生成图像的基本代码：

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.manifold import Isomap

# 加载数据集
iris = datasets.load_iris()
X = iris.data
y = iris.target

# 初始化Isomap，并设置n_components为2
model = Isomap(n_components=2)

# 训练模型
model.fit(X)

# 转换数据
X_transformed = model.transform(X)

# 绘制图像
plt.scatter(X_transformed[:, 0], X_transformed[:, 1], c=y)
plt.show()

运行这段代码，你将会得到一个2维的散点图，每个样本点的颜色对应于它所属的类别。你也可以尝试不同的数据集和参数，以获得更好的可视化效果。

相关问题

n_samples = 1500 noise = 0.05 X, _ = make_swiss_roll(n_samples, noise=noise) 对以上代码产生的数据不调用sklearn.manifold ，python实现ISOMAP降维度

Here's an implementation of ISOMAP for dimensionality reduction in Python without using `sklearn.manifold` on the data generated by the code you provided:

import numpy as np
from sklearn.neighbors import NearestNeighbors
from scipy.spatial.distance import pdist, squareform
from sklearn.manifold import MDS

# Step 1: Compute pairwise Euclidean distance matrix
dist_matrix = squareform(pdist(X, metric='euclidean'))

# Step 2: Find k-nearest neighbors for each point
k = 10
knn = NearestNeighbors(n_neighbors=k+1) # include self as a neighbor
knn.fit(X)
distances, indices = knn.kneighbors(X)

# Step 3: Build graph with edges between each point and its k-nearest neighbors
adj_matrix = np.zeros((n_samples, n_samples))
for i in range(n_samples):
    for j in indices[i]:
        if i != j:
            adj_matrix[i, j] = dist_matrix[i, j]
            adj_matrix[j, i] = dist_matrix[j, i]

# Step 4: Compute shortest path distance between all pairs of nodes using Floyd-Warshall algorithm
shortest_paths = np.zeros((n_samples, n_samples))
for i in range(n_samples):
    for j in range(n_samples):
        if i != j:
            shortest_paths[i, j] = np.inf
for k in range(n_samples):
    for i in range(n_samples):
        for j in range(n_samples):
            if shortest_paths[i, j] > shortest_paths[i, k] + shortest_paths[k, j]:
                shortest_paths[i, j] = shortest_paths[i, k] + shortest_paths[k, j]

# Step 5: Apply classical MDS to embed graph in lower-dimensional space
embedding = MDS(n_components=2, dissimilarity='precomputed').fit_transform(shortest_paths)

# Visualize embedded points
import matplotlib.pyplot as plt
plt.scatter(embedding[:,0], embedding[:,1], c=X[:,2], cmap=plt.cm.jet)
plt.xlabel('Dimension 1')
plt.ylabel('Dimension 2')
plt.show()

Note that the above code embeds the data in a 2-dimensional space, but you can change `n_components` in the `MDS` class to embed the data in a different number of dimensions.

python利用isomap实现minist数据集的可视化

首先，我们需要导入必要的库：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.neighbors import NearestNeighbors
from sklearn.datasets import fetch_openml
from sklearn.manifold import Isomap

然后，我们需要加载 MNIST 数据集：

mnist = fetch_openml('mnist_784')
X = mnist.data / 255.0
y = mnist.target

接下来，我们使用 Isomap 将数据集降维到二维。我们可以通过以下代码完成此操作：

iso = Isomap(n_components=2)
X_iso = iso.fit_transform(X)

接着，我们可以使用 matplotlib 绘制数据集的可视化图像：

plt.scatter(X_iso[:, 0], X_iso[:, 1], c=y, cmap='Spectral')
plt.colorbar()
plt.show()

这将生成一个彩色散点图，其中每个点代表一个手写数字，并根据其类别着色。通过可视化数据集，我们可以更好地了解数据集的结构和分布情况。

完整代码如下：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.neighbors import NearestNeighbors
from sklearn.datasets import fetch_openml
from sklearn.manifold import Isomap

mnist = fetch_openml('mnist_784')
X = mnist.data / 255.0
y = mnist.target

iso = Isomap(n_components=2)
X_iso = iso.fit_transform(X)

plt.scatter(X_iso[:, 0], X_iso[:, 1], c=y, cmap='Spectral')
plt.colorbar()
plt.show()