Uniform manifold approximation and projection (UMAP) is a nonlinear dimensionality reduction technique.
The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance.
What's new in UMAP?
- UMAP introduces the baseline defined by the nearest neighbor, which unifies data, and make graph connected.
- UMAP use eigenvectors of normalized Laplacian as initialization.
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Graph Construction
The first phase of UMAP can be thought of as the construction of a weighted k-neighbour graph.
For each x_i we will define \rho_i and \sigma_i. Let
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and set \sigma_i to be the value such that
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Graph Layout
In practice UMAP uses a force directed graph layout algorithm in low dimensional space.
UMAP步骤
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UMAP与t-SNE的区别
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临近点的个数
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min-dist 越大，即曲线对应的纵坐标越大，距离相近的点，投影到横坐标上的距离就远，相似点的分布越稀疏。
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Hyper-parameters
- n, the number of neighbors to consider when approximating the local metric;
- d, the target embedding dimension;
- min-dist, the desired separation between close points in the embedding space;
- n-epochs, the number of training epochs to use when optimizing the low dimensional representation.