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Spectral analysis of neighborhood graphs is one of the most widely usedtechniques for exploratory data analysis, with applications ranging frommachine learning to social sciences. In such applications, it is typical tofirst encode relationships between the data samples using an appropriatesimilarity function. Popular neighborhood construction techniques such ask-nearest neighbor (k-NN) graphs are known to be very sensitive to the choiceof parameters, and more importantly susceptible to noise and varying densities.In this paper, we propose the use of quantile analysis to obtain local scaleestimates for neighborhood graph construction. To this end, we build anauto-encoding neural network approach for inferring conditional quantiles of asimilarity function, which are subsequently used to obtain robust estimates ofthe local scales. In addition to being highly resilient to noise or outlyingdata, the proposed approach does not require extensive parameter tuning unlikeseveral existing methods. Using applications in spectral clustering andsingle-example label propagation, we show that the proposed neighborhood graphsoutperform existing locally scaled graph construction approaches.

Robust Local Scaling using Conditional Quantiles of Graph Similarities