Tree-structured Algorithm Research Articles

THE ALGORITHM TREE METHOD IN SOLVING THE TASK OF CLASSIFYING HYDROGRAPHIC DATA

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.

Error Estimates for a Tree Structure Algorithm Solving Finite Horizon Control Problems

In the dynamic programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this approach suffers from the “curse of dimensionality” and this limitation has reduced its use in real world applications. Here, we analyze a dynamic programming algorithm based on a tree structure to mitigate the “curse of dimensionality”. The tree is built by the discrete time dynamics avoiding the use of a fixed space grid which is the bottleneck for highdimensional problems, this also drops the projection on the grid in the approximation of the value function. In this work, we present first order error estimates for the the approximation of the value function based on the tree-structure algorithm. The estimate turns out to have the same order of convergence of the numerical method used for the approximation of the dynamics. Furthermore, we analyze a pruning technique for the tree to reduce the complexity and minimize the computational effort. Finally, we present some numerical tests to show the theoretical results.

Method of algorithmic classification trees based on constraints

The general problem of constructing algorithmic recognition (classification) trees based on a limited method in the theory of artificial intelligence is considered. The object of this research is the concept of an algorithmic classification tree based on a bounded method. The subject of the research is actual methods, algorithms and schemes (limited method) for constructing algorithmic classification trees. A limited method for constructing algorithmic classification trees is proposed, which for a given initial training sample of any size builds a tree structure (algorithm tree model), which consists of a set of autonomous classification algorithms and recognition evaluated at each stage of constructing algorithm trees based on this initial sample. That is, a limited method for constructing an algorithmic classification tree is proposed, the main idea of which is a step-by-step approximation of the initial sample of an arbitrary volume and structure by a set of independent classification and recognition algorithms. This method, when forming the current vertex of the algorithmic tree, ensures that the most efficient (high-quality) autonomous classification algorithms are selected from the initial set and only those paths in the tree structure where the greatest number of classification errors occur are completed. The limited method of constructing an algorithmic classification tree makes it possible to build different types of tree-like recognition models with predefined accuracy for a wide class of problems in the theory of artificial intelligence. The limited method of the algorithmic classification tree developed and presented in this paper received a software implementation and was investigated and compared with the methods of logical classification trees, methods of the algorithmic classification tree (first and second types) when solving the problem of recognizing real geological data. Figs.: 2. Tabl.: 1. Refs.: 34 titles.

Sediment transport modeling in non-deposition with clean bed condition using different tree-based algorithms.

To reduce the problem of sedimentation in open channels, calculating flow velocity is critical. Undesirable operating costs arise due to sedimentation problems. To overcome these problems, the development of machine learning based models may provide reliable results. Recently, numerous studies have been conducted to model sediment transport in non-deposition condition however, the main deficiency of the existing studies is utilization of a limited range of data in model development. To tackle this drawback, six data sets with wide ranges of pipe size, volumetric sediment concentration, channel bed slope, sediment size and flow depth are used for the model development in this study. Moreover, two tree-based algorithms, namely M5 rule tree (M5RT) and M5 regression tree (M5RGT) are implemented, and results are compared to the traditional regression equations available in the literature. The results show that machine learning approaches outperform traditional regression models. The tree-based algorithms, M5RT and M5RGT, provided satisfactory results in contrast to their regression-based alternatives with RMSE = 1.184 and RMSE = 1.071, respectively. In order to recommend a practical solution, the tree structure algorithms are supplied to compute sediment transport in an open channel flow.

A HJB-POD approach for the control of nonlinear PDEs on a tree structure

The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the Hamilton-Jacobi-Bellman equation, with the same dimension of the original problem. Recently, a new numerical method to compute the value function on a tree structure has been introduced. The method allows to work without a structured grid and avoids any interpolation.Here, we aim at testing the algorithm for nonlinear two dimensional PDEs. We apply model order reduction to decrease the computational complexity since the tree structure algorithm requires to solve many PDEs. Furthermore, we prove an error estimate which guarantees the convergence of the proposed method. Finally, we show efficiency of the method through numerical tests.

High-order approximation of the finite horizon control problem via a tree structure algorithm

Abstract Solving optimal control problems via Dynamic Programming is a difficult task that suffers for the ”curse of dimensionality”. This limitation has reduced its practical impact in real world applications since the construction of numerical methods for nonlinear PDEs in very high dimension is practically unfeasible. Recently, we proposed a new numerical method to compute the value function avoiding the construction of a space grid and the need for interpolation techniques. The method is based on a tree structure that mimics the continuous dynamics and allows to solve optimal control problems in high-dimension. This property is particularly useful to attack control problems with PDE constraints. We present a new high-order approximation scheme based on the tree structure and show some numerical results.

An Efficient DP Algorithm on a Tree-Structure for Finite Horizon Optimal Control Problems

The classical dynamic programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton--Jacobi--Bellman equation. The DP scheme for the numerical approximation of viscosity solutions of Bellman equations is typically based on a time discretization which is projected on a fixed state-space grid. The time discretization can be done by a one-step scheme for the dynamics and the projection on the grid typically uses a local interpolation. Clearly the use of a grid is a limitation with respect to possible applications in high-dimensional problems due to the curse of dimensionality. Here, we present a new approach for finite horizon optimal control problems where the value function is computed using a DP algorithm with a tree structure algorithm constructed by the time discrete dynamics. In this way there is no need to build a fixed space triangulation and to project on it. The tree will guarantee a perfect matching with the discrete dynamics and drop off the cost of the space interpolation allowing for the solution of very high-dimensional problems. Numerical tests will show the effectiveness of the proposed method.

Implementation of Tree Structure and Recursive Algorithm for Balinese Traditional Snack Recipe on Android Based Application

Due to the difficulty of obtaining information about the dough of Balinese traditional snack(jajanan tradisional Bali), causing Hindu community in Bali, do not know the importance of the role of traditional snack in Yadnya ceremony. Rapid technological developments that pushed for an alternative in order that information is easily obtained by making an application. Implementation of tree structure in the process of preparing an Android-based information allow users to know the material linkages with other materials. Other support such as recursive algorithm which is used to ease in calculation of the amount of materials displayed on the Application. therefore expected with this application, Hindu community in Bali will be easier to understand and find out information about the dough of Balinese traditional snack.

Frequent Pattern Mining Algorithms Analysis

Frequent pattern mining is the most researched field in data mining. This paper provides comparative study of fundamental algorithms and performance analysis with respect to both execution time and memory usage. It also provides brief overview of current trends in frequent pattern mining and it applications. There are two categories of frequent pattern mining the algorithm, namely Apriori algorithm and Tree structure algorithm. The Apriori based algorithm uses generate and test strategy approach to find frequent pattern by constructing candidate items and checking their counts and frequency from transactional databases. The Tree structure algorithm uses a text only approach. There is no need to generate candidate item sets. Many tree based structures have been proposed to represent the data for efficient pattern discovery including FP-Tree, CAT-Tree, CAN-Tree, CP-Tree, and etc. Most of the tree based structure allows efficient mining with single scan over the database. In this paper, we describe the formatting guidelines for IJCA Journal Submission. General Terms Your general terms must be any term which can be used for general classification of the submitted material such as Pattern Recognition, Security, Algorithms et. al.

A Recent Review on Itemset Tree Mining: MEIT Technique

rule mining forms the core of data mining and it is termed as one of the well-researched techniques of data mining. It aims to extract interesting correlations, frequent patterns, associations or casual structures among sets of items in the transaction databases or other data repositories. Hence, Association rule mining is imperative to mine patterns and then generate rules from these obtained patterns. This paper provides the preliminaries of basic concepts about Itemset mining and survey the list of existing tree structure algorithms. These algorithms include various tasks such as fast query processing, optimizing memory space and reducing tree construction time. For mining maximal frequent pattern various algorithms used which optimization the search space for pruning. Keywordsrule mining, Itemset mining, Itemset tree, MEIT, maximal frequent pattern

A Conversation with Richard A. Olshen

Richard Olshen was born in Portland, Oregon, on May 17, 1942. Richard spent his early years in Chevy Chase, Maryland, but has lived most of his life in California. He received an A.B. in Statistics at the University of California, Berkeley, in 1963, and a Ph.D. in Statistics from Yale University in 1966, writing his dissertation under the direction of Jimmie Savage and Frank Anscombe. He served as Research Staff Statistician and Lecturer at Yale in 1966–1967. Richard accepted a faculty appointment at Stanford University in 1967, and has held tenured faculty positions at the University of Michigan (1972–1975), the University of California, San Diego (1975–1989), and Stanford University (since 1989). At Stanford, he is Professor of Health Research and Policy (Biostatistics), Chief of the Division of Biostatistics (since 1998) and Professor (by courtesy) of Electrical Engineering and of Statistics. At various times, he has had visiting faculty positions at Columbia, Harvard, MIT, Stanford and the Hebrew University. Richard’s research interests are in statistics and mathematics and their applications to medicine and biology. Much of his work has concerned binary tree-structured algorithms for classification, regression, survival analysis and clustering. Those for classification and survival analysis have been used with success in computer-aided diagnosis and prognosis, especially in cardiology, oncology and toxicology. He coauthored the 1984 book Classification and Regression Trees (with Leo Brieman, Jerome Friedman and Charles Stone) which gives motivation, algorithms, various examples and mathematical theory for what have come to be known as CART algorithms. The approaches to tree-structured clustering have been applied to problems in digital radiography (with Stanford EE Professor Robert Gray) and to HIV genetics, the latter work including studies on single nucleotide polymorphisms, which has helped to shed light on the presence of hypertension in certain subpopulations of women. Richard also has a long-standing interest in the analyses of longitudinal data. This includes a detailed study of the pharmacokinetics of intracavitary chemotherapy with systemic rescue (with Stephen Howell and John Rice). Related efforts have focused on “mature walking,” concomitants of high cholesterol, and aspects of glomerular filtration in patients with nephrotic disorders (with Bryan Myers). With the late David Sutherland, Edmund Biden and Marilynn Wyatt, he coauthored the monograph The Development of Mature Walking. Richard’s other stochastic-statistical interests include exchangeability, conditional significance levels of particular test statistics, CART-like estimators in regression and successive standardization of rectangular arrays of numbers. Richard is an elected Fellow of the IMS, the AAAS, the ASA and the IEEE. He is a former Guggenheim Fellow and has been a Research Scholar in Cancer of the American Cancer Society.

The construction of a hospital disease tracking and control system with a disease infection probability model.

With relatively short latency and rapid propagation, viral diseases could be transmitted through the air to medical personnel or the public during the incubation period. To reduce the possibilities of spread, this research creates an infection probability model based on the settling velocity and concentration distribution of infectious droplets. Then, radio frequency identification (RFID) technology is employed to track the travel history (time, date and place) of the infected patients. A tree structure algorithm and an infection probability model are applied to trace the transmission routes, discover the correlations between carriers and suspected cases, and finally calculate the infection probability on the basis of time interval. In case of an epidemic outbreak or once an infected case is confirmed, the disease tracking and control system could be initiated by accessing RFID logs to plot the carriers’ time of onset and to trace possible routes of transmission via tree diagrams. The disease tracking and control system developed in this research can assist hospitals in assessing the risk of infection among medical personnel, as well as in prompt implementation of infection prevention and control measures, in order to reduce hospital acquired infections and provide a safe health care setting.

Improved visibility calculations with tree trunk obstruction modeling from aerial LiDAR

Viewshed and line-of-sight are spatial analysis functions used in applications ranging from urban design to archaeology to hydrology. Vegetation data, a difficult variable to effectively emulate in computer models, is typically omitted from visibility calculations or unrealistically simulated. In visibility analyzes performed on a small scale, where calculation distances are a few hundred meters or less, ineffective incorporation of vegetation can lead to significant modeling error. Using an aerial LiDAR (light detection and ranging) data set of a lodgepole pine (Pinus contorta) dominant ecosystem in Idaho, USA, tree obstruction metrics were derived and integrated into a short-range visibility model. A total of 15 visibility plots were set at a micro-scale level, with visibility modeled to a maximum of 50 m from an observation point. Digital photographs of a 1 m2 target set at 5 m increments along three sightline paths for each visibility plot were used to establish control visibility values. Trunk obstructions, derived from mean vegetation height LiDAR data and processed through a series of tree structure algorithms, were factored into visibility calculations and compared to reference data. Results indicate the model calculated using trunk obstructions with LiDAR demonstrated a mean error of 8.8% underestimation of target visibility, while alternative methods using mean vegetation height and bare-earth models have an underestimation of 65.7% and overestimation of 31.1%, respectively.

Evolving Tic-Tac-Toe Playing Algorithms Using Co-Evolution, Interactive Fitness and Genetic Programming

 Abstract—This paper presents a novel use of Genetic Programming, Co-Evolution and Interactive Fitness to evolve algorithms for the game of Tic-Tac-Toe. The selected tree-structured algorithms are evaluated based on a fitness-less double-game strategy and then compete against a human player. This paper will outline the evolution process which leads to producing the best Tic-Tac-Toe playing algorithm. The evolved algorithms have proven effective for playing against human opponents.

An improved beamlet tree-structured algorithm and its application in pavement crack detection

In order to overcome the high computational complexity of beamlet tree-structure algorithm, the paper proposes an improved algorithm and applies it to pavement crack detection, thereby; solving the problem of pavement crack detection which has the disadvantages of poor noise immunity and inaccurate test results. First, the pavement crack image is rectified by multiplicative factors to eliminate the influence of non-uniform background illumination. Then, the image is transferred to the binary image by Otsu’s threshold segmentation algorithm. At last, based on discrete Beamlet transform and integrating multi-scale tree structure of beamlet itself, extract pavement crack from the binary image by using the beamlet tree-structured algorithm, which change a “bottom to top” strategy to look for the optimal value of objective function into a “top to bottom” searching process. Therefore, the proposed method reduces calculation complexity and time. Experimental results show that the proposed method can quickly extract crack from the complex pavement background and noises. Moreover, it keeps the continuity of the crack as well. Key words: Beamlet transform, tree-structured algorithm, Otsu algorithm, crack detection.

Tree-structured algorithm for long weak motif discovery

Motifs in DNA sequences often appear in degenerate form, so there has been an increased interest in computational algorithms for weak motif discovery. Probabilistic algorithms are unable to detect weak motifs while exact methods have been able to detect only short weak motifs. This article proposes an exact tree-based motif detection (TreeMotif) algorithm capable of discovering longer and weaker motifs than by the existing methods. TreeMotif converts the graphical representation of motifs into a tree-structured representation in which a tree that branches with nodes from every sequence represents motif instances. The method of tree construction is novel to motif discovery based on graphical representation. TreeMotif is more efficient and scalable in handling longer and weaker motifs than the existing algorithms in terms of accuracy and execution time. The performances of TreeMotif were demonstrated on synthetic data as well as on real biological data. https://sites.google.com/site/shqssw/treemotif sunh0013@e.ntu.edu.sg Supplementary data are available at Bioinformatics online.

Identification, prediction and detection of the process fault in a cement rotary kiln by locally linear neuro-fuzzy technique

In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input–output model is identified for the plant. To identify the various operation points in the kiln, locally linear neuro-fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. Then, using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 min prediction horizon. The other two models are presented for the two faulty situations in the kiln with 7 min prediction horizon. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used in this study.

Adaptive partitioning schemes for bipartite ranking

Recursive partitioning methods are among the most popular techniques in machine learning. The purpose of this paper is to investigate how to adapt this methodology to the bipartite ranking problem. Following in the footsteps of the TreeRank approach developed in Clémençon and Vayatis (Proceedings of the 2008 Conference on Algorithmic Learning Theory, 2008 and IEEE Trans. Inf. Theory 55(9):4316–4336, 2009), we present tree-structured algorithms designed for learning to rank instances based on classification data. The main contributions of the present work are the following: the practical implementation of the TreeRank algorithm, well-founded solutions to the crucial issues related to the splitting rule and the choice of the “right” size for the ranking tree. From the angle embraced in this paper, splitting is viewed as a cost-sensitive classification task with data-dependent cost. Hence, up to straightforward modifications, any classification algorithm may serve as a splitting rule. Also, we propose to implement a cost-complexity pruning method after the growing stage in order to produce a “right-sized” ranking sub-tree with large AUC. In particular, performance bounds are established for pruning schemes inspired by recent work on nonparametric model selection. Eventually, we propose indicators for variable importance and variable dependence, plus various simulation studies illustrating the potential of our method.

Identification, Prediction and Detection of the Process Fault in a Cement Rotary Kiln by Locally Linear Neuro-Fuzzy Technique

Abstract In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input–output model is identified for the plant. To identify the various operation points in the kiln, locally linear neuro-fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. Then, using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 min prediction horizon. The other two models are presented for the two faulty situations in the kiln with 7 min prediction horizon. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used in this study.

Identification of Nonlinear Predictor and Simulator Models of a Cement Rotary Kiln by Locally Linear Neuro-Fuzzy Technique

One of the most important parts of a cement factory is the cement rotary kiln which plays a key role in quality and quantity of produced cement. In this part, the physical exertion and bilateral movement of air and materials, together with chemical reactions take place. Thus, this system has immensely complex and nonlinear dynamic equations. These equations have not worked out yet. Only in exceptional case; however, a large number of the involved parameters were crossed out and an approximation model was presented instead. This issue caused many problems for designing a cement rotary kiln controller. In this paper, we presented nonlinear predictor and simulator models for a real cement rotary kiln by using nonlinear identification technique on the Locally Linear Neuro-Fuzzy (LLNF) model. For the first time, a simulator model as well as a predictor one with a precise fifteen minute prediction horizon for a cement rotary kiln is presented. These models are trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. At the end, the characteristics of these models are expressed. Furthermore, we presented the pros and cons of these models. The data collected from White Saveh Cement Company is used for modeling.