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Found 11 papers, 4 papers with code
Sketching the Heat Kernel: Using Gaussian Processes to Embed Data
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data.
CA-PCA: Manifold Dimension Estimation, Adapted for Curvature
The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension.
May the force be with you
Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more).
How can classical multidimensional scaling go wrong?
While $D_l$ is not metric, when given as input to cMDS instead of $D$, it empirically results in solutions whose distance to $D$ does not increase when we increase the dimension and the classification accuracy degrades less than the cMDS solution.
Spectral Methods for Ranking with Scarce Data
In this paper we modify a popular and well studied method, RankCentrality for rank aggregation to account for few comparisons and that incorporates additional feature information.
Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embedding
Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data.
Project and Forget: Solving Large-Scale Metric Constrained Problems
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms.
Project and Forget: Solving Large Scale Metric Constrained Problems
Given a set of distances amongst points, determining what metric representation is most “consistent” with the input distances or the metric that captures the relevant geometric features of the data is a key step in many machine learning algorithms.
Unsupervised Metric Learning in Presence of Missing Data
Here, we present a new algorithm MR-MISSING that extends these previous algorithms and can be used to compute low dimensional representation on data sets with missing entries.
If it ain't broke, don't fix it: Sparse metric repair
The distances between the data points are far from satisfying a metric.
Towards Understanding the Invertibility of Convolutional Neural Networks
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible.
