Scalable Techniques for Similarity Search

Document similarity is similar to the nearest neighbour problem and has applications in various domains. In order to determine the similarity / dissimilarity of the documents first they need to be converted into sets containing shingles. Each document is converted into k-shingles, k being the length of each shingle. The similarity is calculated using Jaccard distance between sets and output into a characteristic matrix, the complexity to parse this matrix is significantly high especially when the sets are large. In this project we explore various approaches such as Min hashing, LSH & Bloom Filter to decrease the matrix size and to improve the time complexity. Min hashing creates a signature matrix which significantly smaller compared to a characteristic matrix. In this project we will look into Min-Hashing implementation, pros and cons. Also we will explore Locality Sensitive Hashing, Bloom Filters and their advantages

FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search

We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees. We evaluate FLASH on several real, high-dimensional datasets from different domains, including text, malicious URL, click-through prediction, social networks, etc. Our experiments shed new light on the difficulties associated with datasets having several million dimensions. Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH. FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force ($n^2D$), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results

When Hashing Met Matching: Efficient Spatio-Temporal Search for Ridesharing

Carpooling, or sharing a ride with other passengers, holds immense potential for urban transportation. Ridesharing platforms enable such sharing of rides using real-time data. Finding ride matches in real-time at urban scale is a difficult combinatorial optimization task and mostly heuristic approaches are applied. In this work, we mathematically model the problem as that of finding near-neighbors and devise a novel efficient spatio-temporal search algorithm based on the theory of locality sensitive hashing for Maximum Inner Product Search (MIPS). The proposed algorithm can find $k$ near-optimal potential matches for every ride from a pool of $n$ rides in time $O(n^{1 + \rho} (k + \log n) \log k)$ and space $O(n^{1 + \rho} \log k)$ for a small $\rho < 1$. Our algorithm can be extended in several useful and interesting ways increasing its practical appeal. Experiments with large NY yellow taxi trip datasets show that our algorithm consistently outperforms state-of-the-art heuristic methods thereby proving its practical applicability

Hybrid LSH: Faster Near Neighbors Reporting in High-dimensional Space

We study the $r$-near neighbors reporting problem ($r$-NN), i.e., reporting \emph{all} points in a high-dimensional point set $S$ that lie within a radius $r$ of a given query point $q$. Our approach builds upon on the locality-sensitive hashing (LSH) framework due to its appealing asymptotic sublinear query time for near neighbor search problems in high-dimensional space. A bottleneck of the traditional LSH scheme for solving $r$-NN is that its performance is sensitive to data and query-dependent parameters. On datasets whose data distributions have diverse local density patterns, LSH with inappropriate tuning parameters can sometimes be outperformed by a simple linear search. In this paper, we introduce a hybrid search strategy between LSH-based search and linear search for $r$-NN in high-dimensional space. By integrating an auxiliary data structure into LSH hash tables, we can efficiently estimate the computational cost of LSH-based search for a given query regardless of the data distribution. This means that we are able to choose the appropriate search strategy between LSH-based search and linear search to achieve better performance. Moreover, the integrated data structure is time efficient and fits well with many recent state-of-the-art LSH-based approaches. Our experiments on real-world datasets show that the hybrid search approach outperforms (or is comparable to) both LSH-based search and linear search for a wide range of search radii and data distributions in high-dimensional space.Comment: Accepted as a short paper in EDBT 201