1 month, 4 weeks ago
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Proposes a novel nonlinear dimensionality reduction technique called InPCA. InPCA preserves global and local structure better than other techniques like t-SNE and diffusion manifolds because it preserves a special sort of distance that the authors call "intensive". Other methods like t-SNE have many tunable parameters and are designed to cluster the data rather than retain global structure. The authors show that InPCA reveals inherent low dimensional structure in the high dimensional output of some the Ising model, an MNIST convnet, and the λCDM model (as a function of its parameters). Another advantage of InPCA is that its computation is deterministic, rather than being the solution to some stochastic optimization like t-SNE.