
Clustering with tSNE, provably
tdistributed Stochastic Neighborhood Embedding (tSNE), a clustering an...
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The Geometry of Nodal Sets and Outlier Detection
Let (M,g) be a compact manifold and let Δϕ_k = λ_k ϕ_k be the sequence ...
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Stochastic Neighbor Embedding separates wellseparated clusters
Stochastic Neighbor Embedding and its variants are widely used dimension...
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On the Diffusion Geometry of Graph Laplacians and Applications
We study directed, weighted graphs G=(V,E) and consider the (not necessa...
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Spectral Echolocation via the Wave Embedding
Spectral embedding uses eigenfunctions of the discrete Laplacian on a we...
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Efficient Algorithms for tdistributed Stochastic Neighborhood Embedding
tdistributed Stochastic Neighborhood Embedding (tSNE) is a method for ...
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Randomized Near Neighbor Graphs, Giant Components, and Applications in Data Science
If we pick n random points uniformly in [0,1]^d and connect each point t...
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On the Dual Geometry of Laplacian Eigenfunctions
We discuss the geometry of Laplacian eigenfunctions Δϕ = λϕ on compact ...
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Numerical Integration on Graphs: where to sample and how to weigh
Let G=(V,E,w) be a finite, connected graph with weighted edges. We are i...
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Recovering Trees with Convex Clustering
Convex clustering refers, for given {x_1, ..., x_n}⊂^p, to the minimizat...
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A forgotten Theorem of Schoenberg on onesided integral averages
Let f:R→R be a function for which we want to take local averages. Assumi...
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Heavytailed kernels reveal a finer cluster structure in tSNE visualisations
Tdistributed stochastic neighbour embedding (tSNE) is a widely used da...
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On the Wasserstein Distance between Classical Sequences and the Lebesgue Measure
We discuss the classical problem of measuring the regularity of distribu...
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The Spectral Underpinning of word2vec
word2vec due to Mikolov et al. (2013) is a word embedding method that is...
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Randomly Aggregated Least Squares for Support Recovery
We study the problem of exact support recovery: given an (unknown) vecto...
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NonConvex Planar Harmonic Maps
We formulate a novel characterization of a family of invertible maps bet...
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Spectral Clustering Revisited: Information Hidden in the Fiedler Vector
We are interested in the clustering problem on graphs: it is known that ...
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Regularized Potentials of Schrödinger Operators and a Local Landscape Function
We study localization properties of lowlying eigenfunctions (Δ +V...
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Stefan Steinerberger
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