Main Implementation of kd-Tree in MATLAB
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A kd-tree is a multidimensional data structure that efficiently supports operations like range searches and nearest neighbor searches, particularly demonstrating superior performance in high-dimensional spaces. In MATLAB implementations, constructing a kd-tree typically requires four essential subfunctions: a tree construction function, a search function, a splitting function, and a dimension selection function. Each subfunction serves specific purposes - the tree builder recursively partitions data space using hyperplanes, the search function traverses the tree using distance metrics for nearest neighbor queries, the splitting function determines optimal cut points based on variance or median values, and the dimension selector chooses split axes using cyclical or variance-maximization approaches. Mastery of these functions' implementation is crucial, involving key algorithms like quickselect for median finding and backtracking for optimized nearest neighbor searches.
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