Isomap

Isomap is one of the simplest algorithms, and it's based on the idea of reducing the dimensionality while trying to preserve the geodesic distances measured on the original manifold where the input data lies. The algorithm works in three steps. The first operation is a k-nearest neighbors clustering and the construction of the following graph. The vertices will be the samples, while the edges represent the connections among nearest neighbors, and their weight is proportional to the distance to the corresponding neighbor. 

The second step adopts the Dijkstra algorithm to compute the shortest pairwise distances on the graph of all couples of samples. In the following graph, there's a portion of a graph, where some shortest distances ...

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