Uniform Manifold Approximation and Projection

最后发布时间:2023-07-24 00:05:35 浏览量:

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.

参考