isomap_approx = scipy.sparse.csgraph.shortest_path(isomap_approx, directed=False) isomap_true = scipy.sparse.csgraph.shortest_path(isomap_true, directed=False) isomap_measured = scipy.sparse.csgraph.shortest_path(isomap_measured, directed=False)转matlab

在 MATLAB 中，你可以使用 `graphallshortestpaths` 函数来实现类似的功能。下面是将上述代码转换为 MATLAB 语法的方式：

isomap_approx = graphallshortestpaths(sparse(isomap_approx));
isomap_true = graphallshortestpaths(sparse(isomap_true));
isomap_measured = graphallshortestpaths(sparse(isomap_measured));

在 MATLAB 中，`graphallshortestpaths` 函数用于计算图中所有节点之间的最短路径。在这里，我们使用 `sparse` 函数将稀疏矩阵 `isomap_approx`、`isomap_true` 和 `isomap_measured` 转换为稀疏图，然后将其作为参数传递给 `graphallshortestpaths` 函数。结果会覆盖原始变量 `isomap_approx`、`isomap_true` 和 `isomap_measured`。请确保你已经加载了 MATLAB 中的 Graph Theory Toolbox，以便使用 `graphallshortestpaths` 函数。

相关问题

转成matlab: mds = manifold.MDS(n_components=2, max_iter=20000, eps=1e-9, dissimilarity="precomputed", n_jobs=1) pos_1 = mds.fit(isomap_approx).embedding_ pos_2 = mds.fit(isomap_true).embedding_ pos_3 = mds.fit(isomap_measured).embedding_

在 MATLAB 中，你可以使用 Multidimensional Scaling (MDS) 的 `mdscale` 函数来实现类似的功能。下面是将上述代码转换为 MATLAB 语法的方式：

options = statset('MaxIter', 20000, 'TolFun', 1e-9);
pos_1 = mdscale(isomap_approx, 2, 'Options', options);
pos_2 = mdscale(isomap_true, 2, 'Options', options);
pos_3 = mdscale(isomap_measured, 2, 'Options', options);

在 MATLAB 中，`mdscale` 函数用于执行多维缩放分析。第一个参数是距离矩阵，这里使用了 `isomap_approx`、`isomap_true` 和 `isomap_measured`。第二个参数 `2` 表示要将数据缩放到二维空间。`Options` 参数允许你设置最大迭代次数和收敛容差等选项，这里使用了 `statset` 函数创建了一个选项结构体 `options`。最后，结果保存在 `pos_1`、`pos_2` 和 `pos_3` 变量中，它们是包含了每个样本的二维坐标的矩阵。

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 ，实现ISOMAP降维度

To implement ISOMAP for dimensionality reduction without using `sklearn.manifold` on the data generated by the above code, you can follow these steps:

1. Compute the pairwise Euclidean distance matrix between all data points in `X`.
2. For each point `x_i` in `X`, find its k-nearest neighbors based on the computed pairwise distance matrix. Here, `k` is a hyperparameter that determines the number of neighbors to consider. You can use `sklearn.neighbors` to find the nearest neighbors.
3. Build a graph where each point `x_i` is a node and edges are added between each point and its k-nearest neighbors. The edge weight can be set as the Euclidean distance between the two points.
4. Compute the shortest path distance between all pairs of nodes in the graph using Dijkstra's algorithm or Floyd-Warshall algorithm.
5. Apply classical multidimensional scaling (MDS) to embed the graph in a lower-dimensional space. MDS aims to preserve the pairwise distances between all points in the graph, so that the embedded points are as close as possible to the original points in terms of their pairwise relationships. You can use `sklearn.manifold.MDS` to perform MDS.

Here's some sample code that implements the above steps:

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
from scipy.sparse.csgraph import dijkstra
shortest_paths = dijkstra(adj_matrix)

# 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
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.