Randomized algorithms
Efficient algorithms for inverting evolution
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Unsupervised learning by probabilistic latent semantic analysis
Machine Learning
Text classification in a hierarchical mixture model for small training sets
Proceedings of the tenth international conference on Information and knowledge management
The Cluster-Abstraction Model: Unsupervised Learning of Topic Hierarchies from Text Data
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Latent Class Models for Collaborative Filtering
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
A Two-Round Variant of EM for Gaussian Mixtures
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Nearly tight bounds on the learnability of evolution
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Nearly tight bounds on the learnability of evolution
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The Journal of Machine Learning Research
Using mixture models for collaborative filtering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On the use of linear programming for unsupervised text classification
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Fitting tree metrics: Hierarchical clustering and Phylogeny
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On Learning Mixtures of Heavy-Tailed Distributions
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Bayesian hierarchical clustering
ICML '05 Proceedings of the 22nd international conference on Machine learning
Application of mixture models to detect differentially expressed genes
IDEAL'05 Proceedings of the 6th international conference on Intelligent Data Engineering and Automated Learning
ACM SIGACT News
Unsupervised Text Learning Based on Context Mixture Model with Dirichlet Prior
Advanced Web and NetworkTechnologies, and Applications
Statistical modeling of large distribution sets
Proceedings of the Fourth SIGMOD PhD Workshop on Innovative Database Research
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Mixture models form one of the most widely used classes of generative models for describing structured and clustered data. In this paper we develop a new approach for the analysis of hierarchical mixture models. More specifically, using a text clustering problem as a motivation, we describe a natural generative process that creates a hierarchical mixture model for the data. In this process, an adversary starts with an arbitrary base distribution and then builds a topic hierarchy via some evolutionary process, where he controls the parameters of the process. We prove that under our assumptions, given a subset of topics that represent generalizations of one another (such as baseball → sports → base), for any document which was produced via some topic in this hierarchy, we can efficiently determine the most specialized topic in this subset, it still belongs to. The quality of the classification is independent of the total number of topics in the hierarchy and our algorithm does not need to know the total number of topics in advance. Our approach also yields an algorithm for clustering and unsupervised topical tree reconstruction. We validate our model by showing that properties predicted by our theoretical results carry over to real data. We then apply our clustering algorithm to two different datasets: (i) "20 newsgroups"[19] and (ii) a snapshot of abstracts of arXiv {2} (15 categories, ~240,000 abstracts). In both cases our algorithm performs extremely well.