By Gregory Shakhnarovich, Trevor Darrell, Piotr Indyk
Regression and category tools according to similarity of the enter to kept examples haven't been generic in functions related to very huge units of high-dimensional info. contemporary advances in computational geometry and desktop studying, even though, may possibly alleviate the issues in utilizing those tools on huge information units. This quantity provides theoretical and useful discussions of nearest-neighbor (NN) tools in computing device studying and examines laptop imaginative and prescient as an software area during which the good thing about those complicated equipment is frequently dramatic. It brings jointly contributions from researchers in thought of computation, laptop studying, and laptop imaginative and prescient with the ambitions of bridging the gaps among disciplines and featuring cutting-edge tools for rising applications.
The individuals specialize in the significance of designing algorithms for NN seek, and for the comparable class, regression, and retrieval projects, that stay effective whilst the variety of issues or the dimensionality of the information grows very huge. The e-book starts with theoretical chapters on computational geometry after which explores how one can make the NN process workable in desktop studying functions the place the dimensionality of the knowledge and the scale of the information units make the naïve equipment for NN seek prohibitively dear. the ultimate chapters describe profitable functions of an NN set of rules, locality-sensitive hashing (LSH), to imaginative and prescient projects.
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Extra resources for Nearest-Neighbor Methods in Learning and Vision
Example text
To motivate such approaches, we return to some basic considerations regarding nearest-neighbor search. Bounds Using the Nearest in a Subset. The task of nearest-neighbor searching can be viewed as having two parts: finding the nearest neighbor, and proving that all other sites are not the nearest neighbor. Moreover, any nearest-neighbor algorithm, at any given time while processing a query, has computed the distance from the query point q to some subset P of the sites. So the algorithm needs to use the distance evaluations from q to P to prove that some sites cannot be the answer to the query.
They do this by way of a series of packings implicitly constructed in the course of building a minimum spanning tree. 1 only “slightly,” to take at each step the point whose minimum distance is smallest, instead of largest, then the minimum spanning tree results by connecting each newly added point to its nearest neighbor in the current set. 1. 1 41 Constant Dimension and Nearest-Neighbors Search Basic Properties, Spread Some basic properties of metric spaces Z = (S, D) with bounded Assouad dimension, that is, constant doubling dimension, are useful in nearest neighbor searching.
1, there is an (r/γ)-cover of B(s, 2r) of size O((2r/(r/γ))d) = O((2γ)d ). Therefore any site s with r < D(s, s ) ≤ 2r has some site in the (r/γ)-cover that is closer to s than D(s, s ) by a factor of at least r/(r/γ) = γ, and the number of sites s with r < D(s, s ) ≤ 2r that have s (γ)-near is O((2γ)d). 42 Nearest-Neighbor Searching and Metric Space Dimensions If p is the closest point in S to s, at distance r , then consideration of r = 2r , 4r , 8r , . , shows that at most log Δ(S) values of r need be considered, each contributing at most O((2γ)d) sites with s (γ)-near in S.