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Titlebook: Similarity Search and Applications; 14th International C Nora Reyes,Richard Connor,Jian-Jia Chen Conference proceedings 2021 Springer Natur

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The Effect of Random Projection on Local Intrinsic Dimensionality of which are established by the classical Johnson-Lindenstrauss existence lemma. In this theoretical paper, we analyze the effect of random projection on a natural measure of the local intrinsic dimensionality (LID) of smooth distance distributions in the Euclidean setting. The main contribution of
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A Triangle Inequality for Cosine Similaritych with many standard search structures (such as the VP-tree, Cover-tree, and M-tree); show that this bound is tight and discuss fast approximations for it. We hope that this spurs new research on accelerating exact similarity search for cosine similarity, and possible other similarity measures beyond the existing work for distance metrics.
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On Generalizing Permutation-Based Representations for Approximate Searchermits us to produce longer permutations than traditional ones for the same number of object-pivot distance calculations. The advantage is that the use of inverted files built on permutation prefixes leads to greater efficiency in the search phase when longer permutations are used.
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Optimizing Fair Approximate Nearest Neighbor Searches Using Threaded B+-Trees. that uses cost models to further balance the trade-off between I/O cost and processing time. Finally, we experimentally show that . returns fair results with a very low I/O cost and processing time when compared with the state-of-the-art LSH techniques.
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Local Intrinsic Dimensionality and Graphs: Towards LID-aware Graph Embedding Algorithmswn how NC-LID can be utilized to design LID-elastic graph embedding algorithms based on random walks by proposing two LID-elastic variants of Node2Vec. Our experimental evaluation on real-world graphs demonstrates that NC-LID can point to weak parts of Node2Vec embeddings that can be improved by the proposed LID-elastic extensions.
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Organizing Similarity Spaces Using Metric Hullsof the tree, we provide an implementation of an approximate .NN search operation. Finally, we utilized the Profimedia dataset to evaluate various building and ranking strategies of MH-tree and compared the results with M-tree.
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Relationships Between Local Intrinsic Dimensionality and Tail Entropy entropy variants, all with the potential for serving as the basis for new estimators of LID, or as substitutes for LID-based characterization and feature representations in classification and other learning contexts.
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