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
时间: 2024-02-24 12:58:13 浏览: 23
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.