Unsupervised Learning -- (an incomplete) list of interesting papers

Clustering

• Gonzalez. Clustering to minimize the maximum intercluster distance.
• Arthur and Vassilvitskii. Kmeans++: the advantages of careful seeding.
• Telgarsky and Vattani. Hartigan’s Method: k-means Clustering without Voronoi.
• Balcan and Blum. Clustering with Interactive Feedback.
• Meila. Comparing Clusterings - An Axiomatic View.
• Bachem, Lucic, Hassani, Krause. Fast and Provably Good Seedings for k-Means.
• Kanungo, Mount, Netanyahu, Piatko, Silverman, and Wu. A local search approximation algorithm for k-means clustering.
• Hartigan. Clustering algorithms.
• Lin and Vitter. Approximation algorithms for geometric median problems.
• Dasgupta. A cost function for similarity-based hierarchical clustering.
• Dasgupta and Long. Performance guarantees for hierarchical clustering.
• Ackerman and Dasgupta. Incremental clustering: the case for extra clusters.
• Jain, Meka and Dhillon. Simultaneous Unsupervised Learning of Disparate Clusterings.
• Jardine and Sibson. Mathematical taxonomy.
• Kleinberg. An impossibility theorem for clustering.
• Balcan, Blum, and Vempala. A discriminative framework for clustering via similarity functions.
• Drineas, Kannan, Frieze, Vempala, and Vinay. Clustering large graphs via the singular value decomposition.
• Bshouty and Long. Finding Planted Partitions in Nearly Linear Time using Arrested Spectral Clustering.
• Chaudhuri, Chung, Tsiatas. Spectral Clustering of Graphs with General Degrees in the Extended Planted Partition Model.
• Sriperumbudur and Steinwart. Consistency and rates for clustering with DBSCAN.

Dimensionality Reduction

• Fakcharoenphol, Rao and Talwar. A tight bound on approximating arbitrary metrics by tree metrics.
• Brinkman and Charikar. On the Impossibility of Dimension Reduction in L1.
• Dasgupta and Gupta. An elementary proof of a theorem of Johnson and Lindenstrauss.
• Larsen and Nelson. Optimality of the Johnson-Lindenstrauss lemma.
• Verma. A note on random projections for preserving paths on a manifold.
• Verma. Distance preserving embeddings for general n-dimensional manifolds.
• Schoenberg. Metric spaces and positive definite functions.
• Kruskal and Wish. Multidimensional scaling.
• Matousek. Lectures on discrete geometry, Chapter 15: Embedding finite metric spaces into normed spaces.
• Tenenbaum, de Silva, and Langford. A global geometric framework for nonlinear dimensionality reduction.
• Roweis and Saul. Nonlinear dimensionality reduction by locally linear embedding.
• Cayton. Algorithms for manifold learning. (survey)
• Verma. Mathematical advances in manifold learning. (survey)
• Clarkson. Tighter bounds for random projections of manifolds.
• Indyk and Naor. Nearest neighbor preserving embeddings.
• Snoeck, Bergam, and Verma. Compressibility barriers to neighborhood-preserving data visualizations.
• van der Maaten and Hinton. Visualizing High-Dimensional Data Using t-SNE.
• Arora, Hu, Kothari. An Analysis of the t-SNE Algorithm for Data Visualization.
• Tony Cai and Ma. Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data.
• Im, Verma and Branson. Stochastic neighbor embedding under f-divergences.
• Arias-Castro. Some theory for ordinal embedding.
• Nickel and Kiela. Poincare Embeddings for Learning Hierarchical Representations.
• De Sa, Gu, Re and Sala. Representation Tradeoffs for Hyperbolic Embeddings.

Density Estimation

• Dasgupta and Schulman. A two-round variant of EM for Gaussian mixtures.
• Dasgupta. Learning mixtures of Gaussians.
• Dasgupta and Kpotufe. Optimal rates for k-NN density and mode estimation.
• Blei, Ng, Jordan. Latent Dirichlet Allocation.
• Anandkumar, Ge, Hsu, Kakade, Telgarsky. Tensor decompositions for learning latent variable models.
• Arora, Ge, Halpern, Mimno, Moitra, Sontag, Wu, Zhu. A Practical Algorithm for Topic Modeling with Provable Guarantees.
• Arora, Ge, Liang, Ma, Zhang. Generalization and Equilibrium in Generative Adversarial Nets.
• Arora, Risteski, Zhang. Do GANs learn the distribution? Some theory and empirics.

Structure discovery

• Diaconis, Goel, Holmes. Horseshoes in multidimensional scaling and local kernel methods.
• Freund, Dasgupta, Kabra, Verma. Learning the structure of manifolds using random projections.
• Fefferman, Mitter, Narayanan. Testing the Manifold Hypothesis.
• Chazal and Michel. An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists.

Misc. Topics

• Dasgupta and Sinha. Randomized partition trees for nearest neighbor search.
• Chaudhuri and Dasgupta. Rates of convergence for the cluster tree.
• Dasgupta and Freund. Random projection trees and low dimensional manifolds.
• Dasgupta, Hsu, Verma. A concentration theorem for projections.
• Clarkson. Nearest-neighbor searching and metric space dimensions.
• Niyogi, Smale, Weinberger. Finding the Homology of Submanifolds with High Confidence from Random Samples.
• Niyogi, Smale, Weinberger. A Topological View of Unsupervised Learning and Clustering.
• Gionis, Indyk, Motwani. Similarity search in high dimensions via hashing.
• Indyk and Motwani. Approximate nearest neighbors: towards removing the curse of dimensionality.
• Donoho. Compressed Sensing.
• Vishwanath, Fukumizu, Kuriki, and Sriperumbudur. On the limits of topological data analysis for statistical inference.