Showing papers on "Interval tree published in 2022"
11 Sep 2022
TL;DR: In this paper , a matrix representation of the hierarchical structure of the decision tree is proposed to travel the binary decision tree by maximum inner product search, without the recursive traversal of tree-based methods.
Abstract: We will show how to implement binary decision tree traversal in the language of matrix computation. Our main contribution is to propose some equivalent algorithms of binary tree traversal based on a novel matrix representation of the hierarchical structure of the decision tree. Our key idea is to travel the binary decision tree by maximum inner product search. We not only implement decision tree methods without the recursive traverse but also delve into the partitioning nature of tree-based methods.
TL;DR: The developed method of building algorithmic tree models allows one to work with training samples of a large amount of different types of information (discrete data) and provides high speed and economy of hardware resources in the process of generating the final classification scheme, as well as to build classification trees with predetermined accuracy.
Abstract: Context. The work is dedicated to the identification of a simple and effective mechanism by which it is possible to build algorithmic classification trees (algorithmic tree models) on the basis of fixed initial information in the form of a discrete data training sample. The constructed algorithmic classification tree will unmistakably classify (recognize) the entire training sample on which the model is built, have a minimum structure (structural complexity) and consist of components – autonomous classification and recognition algorithms as the vertices of the structure (attributes of the tree).
Objective. The aim of this work is to create a simple, effective and universal method of constructing classification (recognition) models based on the concept of algorithmic trees for arrays of real hydrographic data, where the obtained schemes of classification systems (classification tree structure) are characterized by a tree structure (construction) and autonomous classification algorithms (sets of generalized features) as their structural elements (construction blocks).
Method. The general scheme of synthesizing classification trees in a form of algorithmic trees on the basis of a procedure of approximation of an array of discrete data by a set of elementary classifiers, which for the set initial training sample builds a tree-like structure, i.e. a model of the algorithmic tree, is suggested. Moreover, the constructed scheme consists of a set of autonomous classification and recognition algorithms evaluated at each step/stage of constructing the classification tree for this initial sample. A method for constructing an algorithmic classification tree has been developed, the main idea of which is to approximate step-by-step the initial sample of an arbitrary volume and structure by a set of elementary classification algorithms. The method of algorithmic tree in the formation of the current algorithmic tree vertex, node, generalized feature provides selection of the most effective, highquality elementary classifiers from the initial set and completion of only those paths in the tree structure where the largest number of errors (failures) occurs. The structural complexity of the algorithmic tree design is estimated based on the number of transitions, vertices and tiers of the model structure, which allows one to improve the quality of its subsequent analysis, provide an effective decomposition mechanism, and build algorithmic tree structures under fixed constraint sets. The method of the algorithmic tree synthesis allows one to build different types of tree-like recognition models with different initial sets of elementary classifiers with predetermined accuracy for a wide class of problems of the artificial intelligence theory.
Results. The developed method of building algorithmic tree models allows one to work with training samples of a large amount of different types of information (discrete data) and provides high speed and economy of hardware resources in the process of generating the final classification scheme, as well as to build classification trees with predetermined accuracy.
Conclusions. An approach to the synthesis of new recognition algorithms (schemes) based on a library (set) of already known algorithms (methods) and schemes has been developed. That is, an effective scheme for recognizing discrete objects based on stepby-step evaluation and selection of classification algorithms (generalized features) at each step of the scheme synthesis is presented. Based on the suggested concept of algorithmic classification trees, a model of the structure of the algorithm tree was built, which provided classification of flood situations for the Uzh river basin.