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In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional is that which concerns exactly k orthogonal axes or a space of any number of dimensions. [1] k-d trees are a useful data structure for several applications, such as:
Bounding interval hierarchies (BIH) exhibit many of the properties of both bounding volume hierarchies (BVH) and kd-trees. Whereas the construction and storage of BIH is comparable to that of BVH, the traversal of BIH resemble that of kd-trees. Furthermore, BIH are also binary trees just like kd-trees (and in fact their superset, BSP trees ...
scikit-learn (formerly scikits.learn and also known as sklearn) is a free and open-source machine learning library for the Python programming language. [3] It features various classification, regression and clustering algorithms including support-vector machines, random forests, gradient boosting, k-means and DBSCAN, and is designed to interoperate with the Python numerical and scientific ...
This approach effectively converts the data structure from an augmented binary tree to an augmented kd-tree, thus significantly complicating the balancing algorithms for insertions and deletions. A simpler solution is to use nested interval trees. First, create a tree using the ranges for the y-coordinate.
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster.
The corresponding implicit k-d trees are complete implicit k-d trees. A complete splitting function is for example the grid median splitting-function. It creates fairly balanced implicit k-d trees by using k-dimensional integer hyperrectangles hyprec[2][k] belonging to each node of the implicit k-d tree. The hyperrectangles define which ...
A contribution to scikit-learn provides an implementation of the HDBSCAN* algorithm. pyclustering library includes a Python and C++ implementation of DBSCAN for Euclidean distance only as well as OPTICS algorithm. SPMF includes an implementation of the DBSCAN algorithm with k-d tree support for Euclidean distance only.
A decision tree or a classification tree is a tree in which each internal (non-leaf) node is labeled with an input feature. The arcs coming from a node labeled with an input feature are labeled with each of the possible values of the target feature or the arc leads to a subordinate decision node on a different input feature.