Number Of Tree Nodes Research Articles

An Innovative Tree Gradient Boosting Method Based Image Object detection from a Uniform Background Scene

Object detection is a wide area problem domain in the field of computer and machine vision. Complex background adds challenge and error margin as well to the problem significantly lot algorithms for object detection are hard to comply with occlusion and pixel bending moment affect. In this paper a highly robust algorithm ORBTRIAN for a less resolution image has been proposed and implemented using ORB detection with gradient boosting machine learning algorithm. The work has been compared with Adaboost and Surf based technology. The analysis shows 3.8% increase in performance of earlier model. The feature points extracted from ORB method are further processed to reduce the processing further. Only those points are selected which are triangularly farthest from centroid of it and only 1 point of feature selected. Thus the result is around 28%, much faster than earlier computation. The tree based GB has been implemented in this algorithm. With more number of feature points more classes need to be recognized and hence the computations performed is required an unreasonable amount of effort and time. So some nearby classes are assigned at same level using our algorithm to reduce the number of tree nodes. Overall performance of the proposed algorithm shows a significant increase in efficiency in computation time.

Pricing Variance, Gamma and Corridor Swaps Using Multinomial Trees

This article introduces a new methodology to approximate the prices of variance, gamma and corridor swaps in a stochastic volatility framework applicable to any given tree structure. The efficiency of this tree method is based on the decomposing the payoff structure into nested conditional expectations which may be calculated using a single pass through the tree. The total number of calculations is commensurable with the number of tree nodes, making it substantially faster than Monte Carlo simulations. We exemplify the methodology using two different tree structures that approximate several types of stochastic volatility models. Furthermore, this methodology is general enough to be applied to any given tree structure. Extensive numerical tests show that the methodology introduced is fast, efficient and accurate. The method was applied to volatility instruments quoted on the CBOE.

Efficiently Updating the Discovered Sequential Patterns for Sequence Modification

Mining sequential patterns (SPs) is a popular data mining task, which consists in finding interesting, unexpected, and useful patterns in sequence databases. It has several applications in many domains. However, most sequential pattern mining algorithms assume that databases are static, i.e. that they do not change over time. But in real-word applications, sequences are often modified. Thus, it is an important issue to design algorithms for updating SPs in a dynamic database environment. Although some algorithms have been proposed to maintain SPs in dynamic databases, these algorithms may have poor performance, especially when databases contain long sequences or a large number of sequences. This paper addresses this issue by proposing a novel dynamic mining approach named PreFUSP-TREE-MOD to address the problem of maintaining and updating discovered SPs when sequences in a database are modified. The proposed approach adopts the previously proposed pre-large concept using two support thresholds, to avoid scanning the database when possible, for updating the set of discovered patterns. Due to the pruning properties of the pre-large concept, the PreFUSP-TREE-MOD maintenance algorithm can effectively reduce the cost of database scans to maintain and update the built FUSP-tree for sequence modification. When the number of modified sequences is less than the safety bound of the pre-large concept, the proposed maintenance algorithm outperforms traditional SPM algorithms in batch mode, and the state-of-the-art maintenance algorithm in terms of execution time and number of tree nodes.

An UBMFFP Tree for Mining Multiple Fuzzy Frequent Itemsets

Frequent itemsets are useful for discovering interesting associations hidden in large databases. Many mining algorithms use data with binary attributes to represent the occurrence of items and find frequent itemsets. However, many real-world applications provide a richer source of transactions with quantitative values. The fuzzy frequent pattern tree algorithm was thus proposed for extracting fuzzy frequent itemsets from the quantitative transactions. In this paper, a tree structure called the upper-bound multiple fuzzy frequent-pattern (UBMFFP)-tree is designed for improving the pruning effect in the mining process. A two-phase fuzzy mining approach based on the tree structure is also proposed to obtain the complete fuzzy frequent itemsets from a quantitative database. The proposed fuzzy mining approach recursively and efficiently finds the upper-bound fuzzy counts of itemsets with the aid of the tree structure. It prunes unpromising itemsets in the first phase, and then finds the actual fuzzy frequent itemsets in the second phase. Experimental results indicate that the proposed UBMFFP-tree algorithm has good performance in terms of execution time and number of tree nodes.

A CMFFP-tree algorithm to mine complete multiple fuzzy frequent itemsets

In the past, many algorithms were proposed to adopt fuzzy-set theory for discovering fuzzy association rules from quantitative databases. The fuzzy frequent pattern (FFP)-tree and the compressed fuzzy frequent pattern (CFFP)-tree algorithms were respectively proposed to mine the incomplete fuzzy frequent itemsets from the tree-based structures. In the past, multiple fuzzy frequent pattern (MFFP)-tree algorithm was proposed to keep more linguistic terms for mining fuzzy frequent itemsets. Since the MFFP-tree algorithm inherits the property of the FFP-tree algorithm, numerous tree nodes are thus required to build the MFFP-tree structure for mining the desired multiple fuzzy frequent itemsets. In this paper, the compressed multiple fuzzy frequent pattern (CMFFP)-tree algorithm is designed to keep not only the linguistic term with maximum membership value but also the other frequent linguistic terms for mining the completely fuzzy frequent itemsets. In the designed CMFFP-tree algorithm, the multiple frequent linguistic terms are sorted in descending order of their occurrence frequencies to build the CMFFP-tree structure. The construction process is the same as the CFFP-tree algorithm except more information are kept for later mining process to discover the completely fuzzy frequent itemsets. Each node in the CMFFP-tree uses the additional array to keep the membership values of its prefix path by intersection operation. A CMFFP-mine algorithm is also designed to efficiently mine the multiple fuzzy frequent itemsets from the developed CMFFP-tree structure. Experiments are then conducted to show the performance of the proposed CMFFP-tree algorithm in terms of execution time and the number of tree nodes, compared to those of the MFFP-tree and CFFP-tree algorithms.

Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data

In this paper, a multi-objective uniform-diversity genetic programming (MUGP) algorithm deployed for robust Pareto modeling and prediction of complex nonlinear processes using some input-output data table. The uncertainties included in measured data are considered to obtain more robust models. The considered benchmarks are an explosive cutting and forming processes, in which the nonlinear behavior between the input and output of processes are detected using MUGP. For both case studies, a multi-objective modeling and prediction procedure firstly performed using deterministic data. Secondly, the same identification procedure carried out using probabilistic uncertainty in the experimental input-output data. The objective functions considered are namely, training error, prediction error and number of tree nodes (complexity of models) in the deterministic approach. Accordingly, the mean and standard deviation of training error and prediction error are considered in robust Pareto modeling and prediction of such processes. In this way, Pareto front of such modeling and prediction is first obtained for both explosive cutting and forming processes with deterministic data. Such Pareto front is then obtained using experimental input-output-data having probabilistic uncertainty in input parameters through a Monte Carlo simulation (MCS) approach. In addition, it has been shown that for both cases, the trade-off models obtained from deterministic data have significant biases when tested on data with probabilistic uncertainty. Finally, the obtained results of such multi-objective robust model identification show promising results in terms of compensating uncertainty in the experimental input-output-data.

Efficiently Maintaining the Fast Updated Sequential Pattern Trees With Sequence Deletion

Among the discovered knowledge, sequential-pattern mining is used to discover the frequent subsequences from a sequence database. Most research handles the static database in batch mode to discover the desired sequential patterns. In the past, the fast updated (FUP) and Fast UPdated 2 (FUP2) concepts were adopted to, respectively, maintain and update the discovered sequential patterns with sequence insertion and sequence deletion based on the designed FUP sequential pattern (FUSP)-tree structure. Based on the FUP or FUP2 concepts, original customer sequences are required to be rescanned if it is necessary to maintain and update the unpromising (small) sequences from the original database. In the past, pre-large concept was designed to keep the prelarge itemsets as the buffer to avoid the database rescan each time whether transaction insertion or deletion in the dynamic databases. In this paper, the prelarge concept is adopted to handle the discovered sequential patterns with sequence deletion. An FUSP tree is first built to keep only the frequent 1-sequences from the original database. The prelarge 1-sequences are also kept in a set for later maintenance approach. When some sequences are deleted from the original database, the proposed algorithm is then performed to divide the kept frequent 1-sequences and prelarge 1-sequences from the original database and the mined 1-sequences from the deleted customer sequences into three parts with nine cases. Each case is then processed by the designed algorithm to maintain and update the built FUSP tree. When the number of deleted customer sequences is smaller than the safety bound of the prelarge concept, the original customer sequences are unnecessary to be rescanned, but the sequential patterns can still be actually maintained and updated. Experiments are conducted to show the performance of the proposed algorithm in terms of execution time and the number of tree nodes.

A new mining approach for uncertain databases using CUFP trees

In the past, many algorithms have been proposed to mine frequent itemsets from transactional databases, in which the presence or absence of items in transactions was certainly known. In some applications, items may also be uncertain in transactions with their existential probabilities ranging from 0 to 1 in the uncertain dataset. Apparently, the processing in uncertain datasets is quite different from those in certain datasets. The UF-tree algorithm was proposed to construct the UF-tree structure from an uncertain dataset and mine frequent itemsets from the tree. In the UF-tree construction process, however, only the same items with the same existential probabilities in transactions were merged together in the tree, thus causing many redundant nodes in the tree. In this paper, a new tree structure called the compressed uncertain frequent-pattern tree (CUFP tree) is designed to efficiently keep the related information in the mining process. In the CUFP tree, the same items will be merged in a branch of the tree even when the existential probabilities in transactions are not the same. A mining algorithm called the CUFP-mine algorithm is then proposed based on the tree structure to find uncertain frequent patterns. Experimental results show that the proposed approach has a better performance than UF-tree algorithm both in the execution time and in the number of tree nodes.

Enumeration of General t-ary Trees and Universal Types

We consider t-ary trees characterized by their numbers of nodes and their total path length. When t=2 these are called binary trees, and in such trees a parent node may have up to t child nodes. We give asymptotic expansions for the total number of trees with nodes and path length p, when n and p are large. We consider several different ranges of n and p. For n→∞ and p=O(n^{3/2}) we recover the Airy distribution for the path length in trees with many nodes, and also obtain higher order asymptotic results. For p→∞ and an appropriate range of n we obtain a limiting Gaussian distribution for the number of nodes in trees with large path lengths. The mean and variance are expressed in terms of the maximal root of the Airy function. Singular perturbation methods, such as asymptotic matching and WKB type expansions, are used throughout, and they are combined with more standard methods of analytic combinatorics, such as generating functions, singularity analysis, saddle point method, etc. The results are applicable to problems in information theory, that involve data compression schemes which parse long sequence into shorter phrases. Numerical studies show the accuracy of the various asymptotic approximations. Key Words: Trees; Universal Types; Asymptotics; Path Length; Singular Perturbations

An Efficient Tree-based Fuzzy Data Mining Approach

In the past, many algorithms were proposed for mining association rules, most of which were based on items with binary values. In this paper, a novel tree structure called the compressed fuzzy frequent pattern tree (CFFP tree) is designed to store the related information in the fuzzy mining process. A mining algorithm called the CFFP-growth mining algorithm is then proposed based on the tree structure to mine the fuzzy frequent itemsets. Each node in the tree has to keep the membership value of the contained item as well as the membership values of its super-itemsets in the path. The database scans can thus be greatly reduced with the help of the additional information. Experimental results also compare the performance of the proposed approach both in the execution time and the number of tree nodes at two different numbers of regions, respectively.

Stochastic lot-sizing with backlogging: computational complexity analysis

For a multi-stage stochastic programming problem, one approach is to explore a scenario tree based formulation for the problem and solve the formulation efficiently. There has been significant research progress on how to generate scenario trees in the literature. However, there is limited work on analyzing the computational complexity of the scenario-tree based formulation that considers the number of tree nodes as the input size. In this paper, we use stochastic lot-sizing problems as examples to study the computational complexity issues for the scenario-tree based formulations. We develop production path properties and a general dynamic programming framework based on these properties. The dynamic programming framework allows us to show that the optimal value function is piecewise linear and continuous, which enables us to develop polynomial time algorithms for several different problems, including those with backlogging and varying capacities under certain conditions. As special cases, we develop polynomial time algorithms that run in $${\mathcal{O}(n^2)}$$ and $${\mathcal{O}(n^2T\,{\rm log}\,n)}$$ times, respectively for stochastic uncapacitated and constant capacitated lot-sizing problems with backlogging, regardless of the scenario tree structure.

Feature‐selection ability of the decision‐tree algorithm and the impact of feature‐selection/extraction on decision‐tree results based on hyperspectral data

The decision‐tree (DT) algorithm is a very popular and efficient data‐mining technique. It is non‐parametric and computationally fast. Besides forming interpretable classification rules, it can select features on its own. In this article, the feature‐selection ability of DT and the impacts of feature‐selection/extraction on DT with different training sample sizes were studied by using AVIRIS hyperspcetral data. DT was compared with three other feature‐selection methods; the results indicated that DT was an unstable feature selector, and the number of features selected by DT was strongly related to the sample size. Trees derived with and without feature‐selection/extraction were compared. It was demonstrated that the impacts of feature selection on DT were shown mainly as a significant increase in the number of tree nodes (14.13–23.81%) and moderate increase in tree accuracy (3.5–4.8%). Feature extraction, like Non‐parametric Weighted Feature Extraction (NWFE) and Decision Boundary Feature Extraction (DBFE), could enhance tree accuracy more obviously (4.78–6.15%) and meanwhile a decrease in the number of tree nodes (6.89–16.81%). When the training sample size was small, feature‐selection/extraction could increase the accuracy more dramatically (6.90–15.66%) without increasing tree nodes.

Collection-aware optimum sequencing of operations and closed-form solutions for the distribution of a divisible load on arbitrary processor trees

The problem of optimally distributing a divisible load to the nodes of an arbitrary processor tree is tackled in this paper. The rigorous mathematical foundation presented allows the derivation of the sequence of operations that is necessary to obtain the minimum processing time, along with closed-form expressions that yield the solution in time O(NP), where P is the number of tree nodes and N their maximum degree. The main contributions of this work are: (1) both load distribution and result collection overheads are considered, thus providing better resource utilization, and (2) arbitrary processor trees are examined in contrast with previous approaches that examined either complete homogeneous trees, or single level trees. Additionally, approximate algorithms for solving the problem of specifying the optimum subset of active processors for a given load, are presented and evaluated.