Introduces Boltzmann margin to prove near-exponential convergence rates for kNN classification.
Survey of Nearest Neighbor Techniques
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abstract
The nearest neighbor (NN) technique is very simple, highly efficient and effective in the field of pattern recognition, text categorization, object recognition etc. Its simplicity is its main advantage, but the disadvantages can't be ignored even. The memory requirement and computation complexity also matter. Many techniques are developed to overcome these limitations. NN techniques are broadly classified into structure less and structure based techniques. In this paper, we present the survey of such techniques. Weighted kNN, Model based kNN, Condensed NN, Reduced NN, Generalized NN are structure less techniques whereas k-d tree, ball tree, Principal Axis Tree, Nearest Feature Line, Tunable NN, Orthogonal Search Tree are structure based algorithms developed on the basis of kNN. The structure less method overcome memory limitation and structure based techniques reduce the computational complexity.
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Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.
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Near-Exponential Convergence Rates for kNN Classification based on Boltzmann Margin
Introduces Boltzmann margin to prove near-exponential convergence rates for kNN classification.
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Parallel Sparse and Data-Sparse Factorization-based Linear Solvers
Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.