The k-means clustering algorithm has a long history and a proven practical performance, however it does not scale to clustering millions of data points into thousands of clusters in high dimensional spaces. The main computational bottleneck is the need to recompute the nearest centroid for every data point at every iteration, a prohibitive cost when the number of clusters is large. In this paper we show how to reduce the cost of the k-means algorithm by large factors by adapting ranked retrieval techniques. Using a combination of heuristics, on two real life data sets the wall clock time per iteration is reduced from 445 minutes to less than 4, and from 705 minutes to 1.4, while the clustering quality remains within 0.5% of the k-means quality.The key insight is to invert the process of point-to-centroid assignment by creating an inverted index over all the points and then using the current centroids as queries to this index to decide on cluster membership. In other words, rather than each iteration consisting of "points picking centroids", each iteration now consists of "centroids picking points". This is much more efficient, but comes at the cost of leaving some points unassigned to any centroid. We show experimentally that the number of such points is low and thus they can be separately assigned once the final centroids are decided. To speed up the computation we sparsify the centroids by pruning low weight features. Finally, to further reduce the running time and the number of unassigned points, we propose a variant of the WAND algorithm that uses the results of the intermediate results of nearest neighbor computations to improve performance.

Recommender systems based on latent factor models have been effectively used for understanding user interests and predicting future actions. Such models work by projecting the users and items into a smaller dimensional space, thereby clustering similar users and items together and subsequently compute similarity between unknown user-item pairs. When user-item interactions are sparse (sparsity problem) or when new items continuously appear (cold start problem), these models perform poorly. In this paper, we exploit the combination of taxonomies and latent factor models to mitigate these issues and improve recommendation accuracy. We observe that taxonomies provide structure similar to that of a latent factor model: namely, it imposes human-labeled categories (clusters) over items. This leads to our proposed taxonomy-aware latent factor model (TF) which combines taxonomies and latent factors using additive models. We develop efficient algorithms to train the TF models, which scales to large number of users/items and develop scalable inference/recommendation algorithms by exploiting the structure of the taxonomy. In addition, we extend the TF model to account for the temporal dynamics of user interests using highorder Markov chains. To deal with large-scale data, we develop a parallel multi-core implementation of our TF model. We empirically evaluate the TF model for the task of predicting user purchases using a real-world shopping dataset spanning more than a million users and products. Our experiments demonstrate the benefits of using our TF models over existing approaches, in terms of both prediction accuracy and running time.We resolve the aforementioned challenges by using a taxonomy over items which is available for many consumer products, e.g., PriceGrabber shopping taxonomy [3], music taxonomy [16], movie taxonomy (genre, director and so on). A fragment of the Yahoo! shopping taxonomy (that we use in our paper) is shown in Figure 1. Since taxonomies are designed by humans, they capture knowledge about the domain at hand, independent of the training data [13] and hence provide scope for improving prediction. As such, taxonomies can provide lineage for items in terms of categories and their ancestors in the taxonomy, thus they help to ameliorate the sparsity issues that are common with online shopping data. Also, taxonomies can help in dealing with the cold start problem because even though the set of individual products/items is highly dynamic,

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Machine-generated documents such as email or dynamic web pages are single instantiations of a pre-defined structural template. As such, they can be viewed as a hierarchy of template and document specific content. This hierarchical template representation has several important advantages for document clustering and classification. First, templates capture common topics among the documents, while filtering out the potentially noisy variabilities such as personal information. Second, template representations scale far better than document representations since a single template captures numerous documents. Finally, since templates group together structurally similar documents, they can propagate properties between all the documents that match the template. In this paper, we use these advantages for document classification by formulating an efficient and effective hierarchical label propagation and discovery algorithm. The labels are propagated first over a template graph (constructed based on either term-based or topic-based similarities), and then to the matching documents. We evaluate the performance of the proposed algorithm using a large donated email corpus and show that the resulting template graph is significantly more compact than the corresponding document graph and the hierarchical label propagation is both efficient and effective in increasing the coverage of the baseline document classification algorithm. We demonstrate that the template label propagation achieves more than 91% precision and 93% recall, while increasing the label coverage by more than 11%.

Unsupervised template induction over email data is a central component in applications such as information extraction, document classification, and auto-reply. The benefits of automatically generating such templates are known for structured data, e.g. machine generated HTML emails. However much less work has been done in performing the same task over unstructured email data.We propose a technique for inducing high quality templates from plain text emails at scale based on the suffix array data structure. We evaluate this method against an industry-standard approach for finding similar content based on shingling, running both algorithms over two corpora: a synthetically created email corpus for a high level of experimental control, as well as user-generated emails from the well-known Enron email corpus. Our experimental results show that the proposed method is more robust to variations in cluster quality than the baseline and templates contain more text from the emails, which would benefit extraction tasks by identifying transient parts of the emails.Our study indicates templates induced using suffix arrays contain approximately half as much noise (measured as entropy) as templates induced using shingling. Furthermore, the suffix array approach is substantially more scalable, proving to be an order of magnitude faster than shingling even for modestly-sized training clusters.Public corpus analysis shows that email clusters contain on average 4 segments of common phrases, where each of the segments contains on average 9 words, thus showing that templatization could help users reduce the email writing effort by an average of 35 words per email in an assistance or auto-reply related task.