A Simple Derivation of the Heap's Law from the Generalized Zipf's Law
I reproduce a rather simple formal derivation of the Heaps' law from the generalized Zipf's law, which I previously published in Russian.
cs.IR↗
arXiv subjects
Leonid Boytsov
Publications and source records attributed to Leonid Boytsov.
Permutation Search Methods are Efficient, Yet Faster Search is Possible
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The underpinning assumption is that, for both metric and non-metric spaces, the distance between permutations is a good proxy for the distance between original points. Thus, it should be possible to efficiently retrieve most true nearest neighbors by examining only a tiny subset of data points whose permutations are similar to the permutation of a query. We further test this assumption by carrying out an extensive experimental evaluation where permutation methods are pitted against state-of-the art benchmarks (the multi-probe LSH, the VP-tree, and proximity-graph based retrieval) on a variety of realistically large data set from the image and textual domain. The focus is on the high-accuracy retrieval methods for generic spaces. Additionally, we assume that both data and indices are stored in main memory. We find permutation methods to be reasonably efficient and describe a setup where these methods are most useful. To ease reproducibility, we make our software and data sets publicly available.
cs.LG↗
Off the Beaten Path: Let's Replace Term-Based Retrieval with k-NN Search
Retrieval pipelines commonly rely on a term-based search to obtain candidate records, which are subsequently re-ranked. Some candidates are missed by this approach, e.g., due to a vocabulary mismatch. We address this issue by replacing the term-based search with a generic k-NN retrieval algorithm, where a similarity function can take into account subtle term associations. While an exact brute-force k-NN search using this similarity function is slow, we demonstrate that an approximate algorithm can be nearly two orders of magnitude faster at the expense of only a small loss in accuracy. A retrieval pipeline using an approximate k-NN search can be more effective and efficient than the term-based pipeline. This opens up new possibilities for designing effective retrieval pipelines. Our software (including data-generating code) and derivative data based on the Stack Overflow collection is available online.
cs.IR↗