Search

Connect6 is an intuitive and fair game with no first-hand advantage. Because of the large search tree, the search depth is often lower, to sacrifice strength of chess to improve search efficiency. In this case, this paper proposes an optimization algorithm for pruning Connect6 search tree based on the principal variation search and transposition tables algorithms. The optimization algorithm obtained PV node through searching, narrowed the pruning interval, and stored the key value of the situation into the transposition table through searching, and then directly returned the evaluation value when the same chess game was searched again, which greatly improved the search efficiency. Through a large number of repeated experiments, the effectiveness of the algorithm can be proved.

Minimax Algorithm, is a solution to reduce the burden on hardware in chess engine. However, a more in-depth method is needed to further increase the search algorithm. One of those solutions is called Alpha-Beta Pruning algorithm. The idea is to eliminate the unnecessary nodes in the search tree.

Tree-based methods are a non-parametric modelling strategy that can be used in combination with generalized linear models or Cox proportional hazards models, mostly at an exploratory stage. Their popularity is mainly due to the simplicity of the technique along with the ease in which the resulting model can be interpreted. Variable selection bias from variables with many possible splits or missing values has been identified as one of the problems associated with tree-based methods. A number of unbiased recursive partitioning algorithms have been proposed that avoid this bias by using p -values in the splitting procedure of the algorithm. The final tree is obtained using direct stopping rules (pre-pruning strategy) or by growing a large tree first and pruning it afterwards (post-pruning). Some of the drawbacks of pre-pruned trees based on p -values in the presence of interaction effects and a large number of explanatory variables are discussed, and a simple alternative post-pruning solution is presented that allows the identification of such interactions. The proposed method includes a novel pruning algorithm that uses a false discovery rate (FDR) controlling procedure for the determination of splits corresponding to significant tests. The new approach is demonstrated with simulated and real-life examples.

Entropy-based pruning has a limit in selecting a fine distribution of phrase pairs to be pruned in a threshold.Changing the distribution through other divergence metrics improves pruning efficiency in our preliminary empirical analysis.Derived problematic factors are fixed divergence distribution and missing impact of word-coupling strength.We propose a fine pruning method using two parameters to control the factors and analyze their effects to divergence change.It improves pruning efficiency compared with Entropy-based pruning in practical translations of English, Spanish, and French. A widely used automatic translation approach, phrase-based statistical machine translation, learns a probabilistic translation model composed of phrases from a large parallel corpus with a large language model. The translation model is often enormous because of many combinations of source and target phrases, which leads to the restriction of applications to limited computing environments. Entropy-based pruning resolves this issue by reducing the model size while retaining the translation quality. To safely reduce the size, this method detects redundant components by evaluating a relative entropy of models before and after pruning the components. In the literature, this method is effective, but we have observed that it can be improved more by adjusting the divergence distribution determined by the relative entropy. In the results of preliminary experiments, we derive two factors responsible for limiting pruning efficiency of entropy-based pruning. The first factor is proportion of pairs composing translation models with respect to their translation probability and its estimate. The second factor is the exponential increase of the divergence for pairs with low translation probability and estimate. To control the factors, we propose a divergence-based fine pruning using a divergence metric to adapt the curvature change of the boundary conditions for pruning and Laplace smoothing. In practical translation tasks for English-Spanish and English-French language pairs, this method shows statistically significant improvement on the efficiency up to 50% and average 12% more pruning compared to entropy-based pruning to show the same translation quality.

Learning from imbalanced data is attracting an increasing interest by the machine learning community. This is mainly due to the high number of real applications that are affected by this situation. The adaptation of the standard decision trees to deal with imbalanced data represents one of the important number of approaches that have been developed to address this problem. This adaptation has been proposed under three different perspectives: splitting criterion, assignment rule and pruning. In this paper, we focus our attention to the pruning of decision trees. We propose an adaptation of the standard pruning algorithm MCCP to address the skewed-data problem. Our contribution affects two levels: adaption of the metric used in selecting nodes to be firstly pruned and change of the evaluation measure used in selecting the best decision-tree through the pruning set. Our goal is to show that, contrary to the popular belief in the literature enquiring into the uselessness of decision tree pruning, an adaptive pruning technique for imbalanced situations is more efficient and more accurate towards the minority class. A total of twelve binary class data-sets having different imbalance ratio are used to test the performance of the proposed method. Experimental results show that the proposed post-pruning approach can increase the performance of imbalanced decision trees in terms of evaluation measures that are recent and appropriate for the context of imbalanced classification.

Branch-and-bound approaches are promising in pruning fruitless search space during the resource constrained scheduling. However, such approaches only compare the estimated upper and lower bounds of an incomplete schedule to the length of the best feasible schedule at that iteration, which does not fully exploit the potential of the pruning during the search. Aiming to improve the performance of resource constrained scheduling, this paper proposes a parallel structure-aware pruning approach that can traverse the search space significantly faster than state-of-the-art branch-and-bound techniques. This paper makes three major contributions: i) it proposes an efficient pruning technique using the structural scheduling information of the obtained best feasible schedules; ii) it investigates how to perform parallel search to enable efficient multi-directional search and generation of effective fences by tuning the operation enumeration order; and iii) it presents a framework that supports the sharing of minimum upper-bound and fence information among different search tasks to enable efficient parallel structure-aware pruning. The experimental results demonstrate that our parallel pruning approach can drastically reduce the overall resource constrained scheduling time under a wide variety of resource constraints.

The continuous non-revisiting genetic algorithm (cNrGA) uses the entire search history and parameter-less adaptive mutation to significantly enhance search performance. Storing the entire search history is natural and costs little when the number of fitness evaluations is small or moderate. However, if the number of evaluations required is substantial, some memory management is desirable. In this paper, we propose two pruning mechanisms to keep the memory used constant. They are least recently used pruning and random pruning. The basic idea is to prune a unit of memory when the memory threshold is reached and some new search information is required to be stored, thus keeping the overall memory used constant. Meanwhile, both pruning strategies naturally form parameter-less adaptive mutation operators. A study is carried out to evaluate the impact on performance caused by loss of search history information. Experimental results show that (1) both strategies can maintain the performance of cNrGA, up to the empirical limit when 90 % of the search history is not recorded, (2) cNrGA and its variants with constant memory outperform the real-coded genetic algorithm and the standard particle swarm optimization. By pre-extracting all the current prune-able history information and storing them into a list, namely, to-prune-list, the overhead of both pruning strategies becomes small. This suggests that cNrGA can be extended to use in situations when the number of fitness evaluations is much larger than before with no significant effect on statistical performance. This widens the applicability of cNrGA to include more practical problems that require larger number of fitness evaluations before converging to the global optima.

Although ordering-based pruning algorithms possess relatively high efficiency, there remains room for further improvement. To this end, this paper describes the combination of a dynamic programming technique with the ensemble-pruning problem. We incorporate dynamic programming into the classical ordering-based ensemble-pruning algorithm with complementariness measure (ComEP), and, with the help of two auxiliary tables, propose a reasonably efficient dynamic form, which we refer to as ComDPEP. To examine the performance of the proposed algorithm, we conduct a series of simulations on four benchmark classification datasets. The experimental results demonstrate the significantly higher efficiency of ComDPEP over the classic ComEP algorithm. The proposed ComDPEP algorithm also outperforms two other state-of-the-art ordering-based ensemble-pruning algorithms, which use uncertainty weighted accuracy and reduce-error pruning, respectively, as their measures. It is noteworthy that, the effectiveness of ComDPEP is just the same with that of the classical ComEP algorithm.

intention of MapReduce Sets for Pruning Decomposition expressions analysis has to suggest criteria how Pruning Decomposition expressions in Pruning Decomposition data can be defined in a meaningful way and how they should be compared. Similitude based MapReduce Sets for Pruning Decomposition Expression Analysis and MapReduce Sets for Assignment is expected to adhere to fundamental principles of the scientific Pruning Decomposition process that are expressiveness of Pruning Decomposition models and reproducibility of their Pruning Decomposition inference. Pruning Decomposition expressions are assumed to be elements of a Pruning Decomposition expression space or Conjecture class and Pruning Decomposition data provide "information" which of these Pruning Decomposition expressions should be used to interpret the Pruning Decomposition data. An inference Pruning Decomposition algorithm constructs the mapping between Pruning Decomposition data and Pruning Decomposition expressions, in particular by a Pruning Decomposition cost minimization process. Fluctuations in the Pruning Decomposition data often limit the Pruning Decomposition precision, which we can achieve to uniquely identify a single Pruning Decomposition expression as interpretation of the Pruning Decomposition data. We advocate an information theoretic perspective on Pruning Decomposition expression analysis to resolve this dilemma where the tradeoff between Pruning Decomposition informativeness of statistical inference Pruning Decomposition and their Pruning Decomposition stability is mirrored in the information-theoretic Pruning Decomposition optimum of high Pruning Decomposition information rate and zero communication expression error. The inference Pruning Decomposition algorithm is considered as an outlier object Pruning Decomposition path, which naturally limits the resolution of the Pruning Decomposition expression space given the uncertainty of the Pruning Decomposition data. KeywordsPruning Decomposition expressions, kernel function.

Data mining is a knowledge discovery process that analyzes data and generate useful pattern from it. Classification is the technique that uses pre-classified examples to classify the required results. Decision tree is used to model classification process. Using feature values of instances, Decision trees classify those instances. Each node in a decision tree represents a feature in an instance to be classified. In this research work ID3, C4.5 and C5.0 Compare with each other. Among all these classifiers C5.0 gives more accurate and efficient result. This research work used C5.0 as the base classifier so proposed system will classify the result set with high accuracy and low memory usage. The classification process generates fewer rules compare to other techniques so the proposed system has low memory usage. Error rate is low so accuracy in result set is high and pruned tree is generated so the system generates fast results as compare with other technique. In this research work proposed system use C5.0 classifier that Performs feature selection and reduced error pruning techniques which are described in this paper. Feature selection technique assumes that the data contains many redundant features. so remove that features which provides no useful information in any context. Select relevant features which are useful in model construction. Crossvalidation method gives more reliable estimate of predictive. Over fitting problem of the decision tree is solved by using reduced error pruning technique. With the proposed system achieve 1 to 3% of accuracy, reduced error rate and decision tree is construed within less time.

In many applications, top-k query is an important operation to return a set of interesting points in a potentially huge data space. The existing algorithms, either maintaining too many candidates, or requiring assistant structures built on the specific attribute subset, or returning results with probabilistic guarantee, cannot process top-k query on massive data efficiently. This paper proposes a sorted-list-based TKAP algorithm, which utilizes some data structures of low space overhead, to efficiently compute top-k results on massive data. In round-robin retrieval on sorted lists, TKAP performs adaptive pruning operation and maintains the required candidates until the stop condition is satisfied. The adaptive pruning operation can be adjusted by the information obtained in round-robin retrieval to achieve a better pruning effect. The adaptive pruning rule is developed in this paper, along with its theoretical analysis. The extensive experimental results, conducted on synthetic and real-life data sets, show the significant advantage of TKAP over the existing algorithms.

We address the problem of index pruning without compromising the quality of ad-hoc similarity search among sets and ranked lists. We discuss three different ways to prune the index structure and, by linking the index structure with the concept of Locality Sensitive Hashing (LSH), we introduce two solutions to query processing over the pruned index. Through a probabilistic analysis we ensure that a user-defined recall goal is still guaranteed. We are able to formulate an optimization problem that can determine the optimal pruning factor for all three pruning methods. The experimental evaluations over real-world data validate that the optimal pruning factor indeed ensures the recall goal without any significant effect on the quality of similarity search on a much smaller index.

Ensemble learning is a method of combining learners to obtain more reliable and accurate predictions in supervised and unsupervised learning. However, the ensemble sizes are sometimes unnecessarily large which leads to additional memory usage, computational overhead and decreased effectiveness. To overcome such side effects, pruning algorithms have been developed; since this is a combinatorial problem, finding the exact subset of ensembles is computationally infeasible. Different types of heuristic algorithms have developed to obtain an approximate solution but they lack a theoretical guarantee. Error Correcting Output Code (ECOC) is one of the well-known ensemble techniques for multiclass classification which combines the outputs of binary base learners to predict the classes for multiclass data. In this paper, we propose a novel approach for pruning the ECOC matrix by utilizing accuracy and diversity information simultaneously. All existing pruning methods need the size of the ensemble as a parameter, so the performance of the pruning methods depends on the size of the ensemble. Our unparametrized pruning method is novel as being independent of the size of ensemble. Experimental results show that our pruning method is mostly better than other existing approaches.

As is well known, the Greedy Ensemble Pruning (GEP) algorithm, also called the Directed Hill Climbing Ensemble Pruning (DHCEP) algorithm, possesses relatively good performance and high speed. However, because the algorithm only explores a relatively small subspace within the whole solution space, it often produces suboptimal solutions of the ensemble pruning problem. Aiming to address this drawback, in this work, we propose a novel Randomized GEP (RandomGEP) algorithm, also called the Randomized DHCEP (RandomDHCEP) algorithm, that effectively enlarges the search space of the classical DHCEP while maintaining the same level of time complexity with the help of a randomization technique. The randomization of the classical DHCEP algorithm achieves a good tradeoff between the effectiveness and efficiency of ensemble pruning. Besides, the RandomDHCEP algorithm naturally inherits the two intrinsic advantages that a randomized algorithm usually possesses. First, in most cases, its running time or space requirements are smaller than well-behaved deterministic ensemble pruning algorithms. Second, it is easy to comprehend and implement. Experimental results on three benchmark classification datasets verify the practicality and effectiveness of the RandomGEP algorithm.

Ensemble pruning is substantial for the successful application of an ensemble system. A novel method for Ensemble Pruning via BackTracking algorithm (EnPBT) was proposed by us in our previous work. Backtracking algorithm can systematically search for the solutions of a problem in a depth-first and jumping manner, suitable for solving all those large-scale combinatorial problems. The validity of EnPBT algorithm has been verified in our previous work. However, the relatively slow pruning speed might be a drawback of EnPBT. Aiming at this problem, an efficient and novel ensemble pruning algorithm is proposed in this paper, i.e. One-Path and Two-Trips (OPTT) ensemble pruning algorithm. It is very fast in pruning speed, while its classification performance has no significant difference with EnPBT, as demonstrated in the experimental results of this work. In short, OPTT achieves a proper trade-off between pruning effectiveness and efficiency.

Ensemble methods have been successfully used as a classification scheme. The reduction of the complexity of this popular learning paradigm motivated the appearance of ensemble pruning algorithms. This paper presents a new ensemble pruning method which highly reduces the complexity of ensemble methods and performs better than complete bagging in terms of classification accuracy. More importantly, it is a very fast algorithm. It consists in ordering all base classifiers with respect to a new criterion which exploits an unsupervised ensemble margin. This method highlights the major influence of low margin instances on the performance of the pruning task and, more generally, the potential of low margin instances for the design of better ensembles. Comparison to both the naive approach of randomly pruning base classifiers and another ordering-based pruning algorithm is carried out in an extensive empirical analysis.

Ensemble pruning is crucial for the consideration of both efficiency and predictive accuracy of an ensemble system. This paper proposes a new Competitive technique for Ensemble Pruning based on Cross-Validation (CEPCV). The data to be learnt by neural computing models are mostly drifting with time and environment, therefore a dynamic ensemble pruning method is indispensable for practical applications, while the proposed CEPCV method is just the kind of dynamic ensemble pruning method, which can realize on-line ensemble pruning and take full advantage of potentially valuable information. The algorithm naturally inherits the predominance of cross-validation technique, which implies that those networks regarded as winners in selective competitions and chosen into the pruned ensemble have the ''strongest'' generalization capability. It is essentially based on the strategy of ''divide and rule, collect the wisdom'', and might alleviate the local minima problem of many conventional ensemble pruning approaches only at the cost of a little greater computational cost, which is acceptable to most applications of ensemble learning. The comparative experiments among the four ensemble pruning algorithms, including: CEPCV and the state-of-the-art Directed Hill Climbing Ensemble Pruning (DHCEP) algorithm and two baseline methods, i.e. BSM, which chooses the Best Single Model in the initial ensemble based on their performances on the pruning set, and ALL, which reserves all network members of the initial ensemble, on ten benchmark classification tasks, demonstrate the effectiveness and validity of CEPCV.

Background: We study an important problem of similarity grouping processing on stream data that inherently contain uncertainty. Method: In this paper SBSP - [Stage by Stage Pruning] a novel pruning method is proposed for fast, accurate clustering and classifying the data where the two stages were grouped into a single framework MYFRAME. Findings : The proposed approach group the data-by-data level pruning using Manhattan distance in first stage. In the second stage, the data is grouped by object level pruning in hyperspace. Improvements: Currently, this approach is applied in real time applications such as object detection, video retrieval, people detection and tracking, earth quake monitoring etc.

The minimax algorithm, also called the negamax algorithm, remains today the most widely used search technique for two-player perfect-information games. However, minimaxing has been shown to be susceptible to game tree pathology, a paradoxical situation in which the accuracy of the search can decrease as the height of the tree increases. Althöfer’s alternative minimax algorithm has been proven to be invulnerable to pathology. However, it has not been clear whether alpha-beta pruning, a crucial component of practical game programs, could be applied in the context of Alhöfer’s algorithm. In this brief paper, we show how alpha-beta pruning can be adapted to Althöfer’s algorithm.

The efficiency of three forward-pruning techniques, i.e., futility pruning, null-move pruning, and LMR, is analyzed in shogi, a Japanese chess variant. It is shown that the techniques with the α – β pruning reduce the effective branching factor of shogi endgames to 2.8 without sacrificing much accuracy of the search results. Because the average number of the raw branching factor in shogi is around 80, the pruning techniques reduce the search space more effectively than in chess.

Highlights? Bottom-up pruning is extended to multiple tree context. ? Suitable pruning criteria are proposed. ? Method is tested on a number of UCI datasets. ? Method produces single trees with good performance/compactness. ? Applied to a churn prediction problem, interpretable trees were produced. A generalisation of bottom-up pruning is proposed as a model level combination method for a decision tree ensemble. Bottom up pruning on a single tree involves choosing between a subtree rooted at a node, and a leaf, dependant on a pruning criterion. A natural extension to an ensemble of trees is to allow subtrees from other ensemble trees to be grafted onto a node in addition to the operations of pruning to a leaf and leaving the existing subtree intact. Suitable pruning criteria are proposed and tested for this multi-tree pruning context. Gains in both performance and in particular compactness over individually pruned trees are observed in tests performed on a number of datasets from the UCI database. The method is further illustrated on a churn prediction problem in the telecommunications domain.

Classification is an important data mining task that discovers hidden knowledge from the labeled datasets. Most approaches to pruning assume that all dataset are equally uniform and equally important, so they apply equal pruning to all the datasets. However, in real-world classification problems, all the datasets are not equal and considering equal pruning rate during pruning tends to generate a decision tree with large size and high misclassification rate. We approach the problem by first investigating the properties of each dataset and then deriving data-specific pruning value using expert knowledge which is used to design pruning techniques to prune decision trees close to perfection. An efficient pruning algorithm dubbed EKBP is proposed and is very general as we are free to use any learning algorithm as the base classifier. We have implemented our proposed solution and experimentally verified its effectiveness with forty real world benchmark dataset from UCI machine learning repository. In all these experiments, the proposed approach shows it can dramatically reduce the tree size while enhancing or retaining the level of accuracy.

Association rule mining is one of the most exploited areas in data mining, which includes applications from business to data classification and summarization. Thus, several association rule-based c...

Information retrieval (IR) systems typically compress their indexes in order to increase their efficiency. Static pruning is a form of lossy data compression: it removes from the index, data that is estimated to be the least important to retrieval performance, according to some criterion. Generally, pruning criteria are derived from term weighting functions, which assign weights to terms according to their contribution to a document's contents. Usually, document-term occurrences that are assigned a low weight are ruled out from the index. The main assumption is that those entries contribute little to the document content. We present a novel pruning technique that is based on a probabilistic model of IR. We employ the Probability Ranking Principle as a decision criterion over which posting list entries are to be pruned. The proposed approach requires the estimation of three probabilities, combining them in such a way that we gather all the necessary information to apply the aforementioned criterion. We evaluate our proposed pruning technique on five TREC collections and various retrieval tasks, and show that in almost every situation it outperforms the state of the art in index pruning. The main contribution of this work is proposing a pruning technique that stems directly from the same source as probabilistic retrieval models, and hence is independent of the final model used for retrieval.

We present a high-speed planning method with compact precomputed search trees using a new pruning method and evaluate the effectiveness and the efficiency of our precomputation planning. Its speed is faster than an A* planner in maps in which the obstacle rate is the same as indoor environments. Precomputed search trees are one way of reducing planning time; however, there is a time-memory trade off. Our precomputed search tree (PCS) is built with pruning based on a rule of constant memory, the maximum size pruning method (MSP) which is a preset ratio of pruning. Using MSP, we get a large precomputed search tree which is a reasonable size. Additionally, we apply the node selection strategy (NSS) to MSP. We extend the outer edge of the tree and enhance the path reachability. In maps less than 30% obstacle rates on a map, the runtime of precomputation planning is more than one order of magnitude faster than the planning without precomputed search trees. Our precomputed tree finds an optimal path in maps with 25% obstacle rates. Then our precomputation planning speedily produces the optimal path in indoor environments.

Ensemble pruning deals with the reduction of base classifiers prior to combination in order to improve generalization and prediction efficiency. Existing ensemble pruning algorithms require much pruning time. This paper presents a fast pruning approach: pattern mining based ensemble pruning (PMEP). In this algorithm, the prediction results of all base classifiers are organized as a transaction database, and FP-Tree structure is used to compact the prediction results. Then a greedy pattern mining method is explored to find the ensemble of size k. After obtaining the ensembles of all possible sizes, the one with the best accuracy is outputted. Compared with Bagging, GASEN, and Forward Selection, experimental results show that PMEP achieves the best prediction accuracy and keeps the size of the final ensemble small, more importantly, its pruning time is much less than other ensemble pruning algorithms.

In this study, we proposed a general pruning procedure to reduce the dimension of a large database so that the properties of the extracted subset can be well defined. Since learning functions have been widely applied, we take this group of functions as an example to demonstrate the proposed procedure. Based on the concept of Support Vector Machine (SVM), three major stages of preliminary pruning, fitting function, and refining are proposed to discover a subset that possess the characteristics of some learning function from the given large data set. Three models were used to illustrate and evaluate the proposed pruning procedure and the results have shown to be promising in application.

When learning is based on noisy data, the induced rule sets have a tendency to overfit the training data, and this degrades the performance of the resulting classifier. Consequently, the ability to tolerate noise is a necessity for robust, practical learning methods. Pruning is a common way of handling noisy data. This paper presents a new pruning technique built on the sound foundation of the minimum description length principle. The proposed pruning technique has the advantage that it does not require the set of examples employed for pruning to be distinct from the set used to build the rule set. The new technique is designed to improve the performance of the RULe Extraction System (RULES) family of inductive learning algorithms, but can be used for pruning rule sets created by other learning algorithms. It was tested in RULES-6, the latest algorithm in the family, and showed significant performance improvements.

Decision trees are well-known and established models for classification and regression. In this paper, we focus on the estimation and the minimization of the misclassification rate of decision tree classifiers. We apply Lidstone's Law of Succession for the estimation of the class probabilities and error rates. In our work, we take into account not only the expected values of the error rate, which has been the norm in existing research, but also the corresponding reliability (measured by standard deviations) of the error rate. Based on this estimation, we propose an efficient pruning algorithm, called k-norm pruning, that has a clear theoretical interpretation, is easily implemented, and does not require a validation set. Our experiments show that our proposed pruning algorithm produces accurate trees quickly, and compares very favorably with two other well-known pruning algorithms, CCP of CART and EBP of C4.5.

Support vector machine (SVM), which is analytically solved to reach its optimal structural formula, can be represented as a network architecture resembling artificial neural networks (multilayer perceptrons) that have been pruned to obtain model parsimony or improve generalization. This study presents two methods of pruning the support vector networks, and applies them to a case study of real-time flood stage forecasting. One method prunes the input variables by the cross-correlation method, while the other prunes the support vectors according to the derived relationship among SVM parameters. These pruning methods do not revise the SVM algorithm, and the pruned models therefore still have the optimal architecture. The real-time forecasting performance pertaining to the original and the pruned SVM models are compared, and comparison results indicate that the pruning reduces the network complexity but does not degrade the forecasting ability. Moreover, the deletion of support vectors and the change in their weights during the pruning process are identified, revealing that the support vectors with small weight (and hence less significant) tend to be pruned off, while the support vectors that are more informative to characterize the floods are preserved after the pruning. Finally, this study suggests that the proposed support vector pruning method be a potential data mining technique.

N-gram models are the most widely used language models in large vocabulary continuous speech recognition. Since the size of the model grows rapidly with respect to the model order and available training data, many methods have been proposed for pruning the least relevant -grams from the model. However, correct smoothing of the N-gram probability distributions is important and performance may degrade significantly if pruning conflicts with smoothing. In this paper, we show that some of the commonly used pruning methods do not take into account how removing an -gram should modify the backoff distributions in the state-of-the-art Kneser-Ney smoothing. To solve this problem, we present two new algorithms: one for pruning Kneser-Ney smoothed models, and one for growing them incrementally. Experiments on Finnish and English text corpora show that the proposed pruning algorithm provides considerable improvements over previous pruning algorithms on Kneser-Ney smoothed models and is also better than the baseline entropy pruned Good-Turing smoothed models. The models created by the growing algorithm provide a good starting point for our pruning algorithm, leading to further improvements. The improvements in the Finnish speech recognition over the other Kneser-Ney smoothed models are statistically significant, as well.

A CSP search algorithm, like FC or MAC, explores a search tree during its run. Every node of the search tree can be associated with a CSP created by the refined domains of unassigned variables. If the algorithm detects that the CSP associated with a node is insoluble, the node becomes a dead-end. A strategy of pruning "by analogy" states that the current node of the search tree can be discarded if the CSP associated with it is "more constrained" than a CSP associated with some dead-end node. In this paper we present a method of pruning based on the above strategy. The information about the CSPs associated with dead-end nodes is kept in the structures called responsibility sets and kernels. We term the method that uses these structures for pruning RKP, which is abbreviation of Responsibility set, Kernel, Propagation. We combine the pruning method with algorithms FC and MAC. We call the resulting solvers FC-RKP and MAC-RKP, respectively. Experimental evaluation shows that MAC-RKP outperforms MAC-CBJ on random CSPs and on random graph coloring problems. The RKP-method also has theoretical interest. We show that under certain restrictions FC-RKP simulates FC-CBJ. It follows from the fact that intelligent backtracking implicitly uses the strategy of pruning "by analogy."

The continuous Non-revisiting Genetic Algorithm (cNrGA) uses the entire search history and parameter-less adaptive mutation to significantly enhance search performance. Experimental results show that it has better performance than Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a state of the art evolutionary algorithm. Storing the search history is natural and costs little when fitness evaluations are expensive. However, if the number of evaluations required is substantial, some memory management is desirable. In this paper, we propose two pruning mechanisms to keep the memory used constant. They are Random pruning and Least Recently Used pruning. The idea is to prune a node when a memory threshold is reached and a new node is required to be inserted, thus keeping the overall memory used constant. Experimental results show that both strategies can maintain the performance of cNrGA, up to the limit when 90% of the nodes are not recorded. This suggests that cNrGA can be extended to use in situations when the number of fitness evaluations are much larger than before with no significant effect on statistical performance, which widens the applicability of cNrGA to include more practical problems that require larger number of fitness evaluations before converging to the global optimum.

Cost-sensitive decision trees have a great success in building models for classification tasks in data mining and machine learning. Decision tree pruning technique is regarded as an important component of the optimization of decision tree. However, many previous cost-sensitive decision trees researches focus on minimizing the misclassification rate and removing nodes when the cost of the pruned tree is less than the original one. In this paper, we propose an effective method for building cost-sensitive decision tree and a probabilistic pruning mechanism for the decision tree. There are two major contributions of this paper. Firstly, the cost-sensitive decision tree is built to make predictions to minimize the total cost of test costs and different costs associated with different types of misclassification. Compared with existing models, leaves are labeled by minimizing the total cost instead of the majority class. Secondly, we design a probabilistic pruning mechanism where the pruning probability is related to the change of costs around pruning. The pruning results yield worse performance on the training set, but better performance on the testing set. Therefore, the probabilistic pruning mechanism improves the performance of the cost-sensitive decision tree. Experimental results show the efficiency of the probabilistic pruning mechanism for cost-sensitive decision tree.

Aiming at how to find the possible existence of the threat paths in Connect6, this paper puts forward to a new searching algorithm — Alpha-Beta-TSS. The algorithm couples Alpha-Beta Pruning Search to TSS (Threat Space Search). It has the strong ability of solving and the solution has a high accuracy.

The cost-complexity pruning generates nested subtrees and selects the best one. However, its computational cost is large since it uses holdout sample or cross-validation. On the other hand, the pruning algorithms based on posterior calculations such as BIC (MDL) and MEP are faster, but they sometimes produce too big or small trees to yield poor generalization errors. In this paper, we propose an alternative pruning procedure which combines the ideas of the cost-complexity pruning and posterior calculation. The proposed algorithm uses only training samples, so that its computational cost is almost same as the other posterior-based algorithms, and at the same time yields similar accuracies as the cost-complexity pruning. Moreover it can be used for comparing non-nested trees, which is necessary for the BUMPing procedure. The empirical results show that the proposed algorithm performs similarly as the cost-complexity pruning in standard situations and works better for BUMPing.

In this paper forward-pruning methods, such as multi-cut and null move, are tested at so-called ALL nodes. We improved the principal variation search by four small but essential additions. The new PVS algorithm guarantees that forward pruning is safe at ALL nodes. Experiments show that multi-cut at ALL nodes (MC-A) when combined with other forward-pruning mechanisms give a significant reduction of the number of nodes searched. In comparison, a (more) aggressive version of the null move (variable null-move bound) gives less reduction at expected ALL nodes. Finally, it is demonstrated that the playing strength of the lines of action program MIA is significantly (scoring 21% more winning points than the opponent) increased by MC-A.

Error based pruning can be used to prune a decision tree and it does not require the use of validation data. It is implemented in the widely used C4.5 decision tree software. It uses a parameter, the certainty factor, that affects the size of the pruned tree. Several researchers have compared error based pruning with other approaches, and have shown results that suggest that error based pruning results in larger trees that give no increase in accuracy. They further suggest that as more data is added to the training set, the tree size after applying error based pruning continues to grow even though there is no increase in accuracy. It appears that these results were obtained with the default certainty factor value. Here, we show that varying the certainty factor allows significantly smaller trees to be obtained with minimal or no accuracy loss. Also, the growth of tree size with added data can be halted with an appropriate choice of certainty factor. Methods of determining the certainty factor are discussed for both small and large data sets. Experimental results support the conclusion that error based pruning can be used to produce appropriately sized trees with good accuracy when compared with reduced error pruning.

A non-preference based pruning algorithm is proposed to rank the Pareto-optimal solutions according to the cost and reliability trade-off for solving multi-objective redundancy allocation problem. The proposed method demonstrates on multi-objective redundancy allocation problem with mixing of non-identical component types in each subsystem. The objectives of system design are to maximize system reliability and minimize system cost simultaneously while satisfying system requirement constraints. Non-dominated sorting genetic algorithm-II (NSGA-II) finds an approximation of Paretooptimal solutions. After obtaining the approximation of Pareto-optimal solutions by NSGA-II, K-means clustering is used to cluster the approximation of Pareto-optimal solutions into some trade-off regions. Thereafter, the Paretooptimal solutions are ranked based on the cost and reliability trade-off compare to the centroid solution of each cluster. The results show that the proposed method is able to identify the most-compromised solution.

Decision tree is a divide and conquer classification method used in machine learning. Most pruning methods for decision trees minimize a classification error rate. In uncertain domains, some sub-trees that do not decrease the error rate can be relevant in pointing out some populations of specific interest or to give a representation of a large data file. A new pruning method (called DI pruning) is presented here. It takes into account the complexity of sub-trees and is able to keep sub-trees with leaves yielding to determine relevant decision rules, although they do not increase the classification efficiency. DI pruning allows to assess the quality of the data used for the knowledge discovery task. In practice, this method is implemented in the UnDeT software.

Move pruning is a technique used in game tree search which incorporates heuristic knowledge to reduce the number of moves under consideration from a particular game state. This paper investigates Heuristic Move Pruning on the strategic card game Lords of War. We use heuristics to guide our pruning and experiment with different techniques of applying pruning and their relative effectiveness. We also present a technique of artificially rolling forward a game state in an attempt to more accurately determine which moves are appropriate to prune from the decision tree. We demonstrate that heuristic move pruning is effective in Lords of War, and also that artificially rolling forward the game state can increase the effectiveness of heuristic move pruning.

The efficiency of the αβ-algorithm as a minimax search procedure can be attributed to its effective pruning at the so-called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by also expanding some of the remaining moves. Our results show a strong correlation between the number of promising move alternatives at cut-nodes and a new principal variation emerging. Furthermore, a new forward-pruning method is introduced that uses this additional information to ignore potentially futile subtrees. We also provide experimental results with the new pruning method in the domain of chess.

Trained radial basis function networks are well-suited for use in extracting rules and explanations because they contain a set of locally tuned units. However, for rule extraction to be useful, these networks must first be pruned to eliminate unnecessary weights. The pruning algorithm cannot search the network exhaustively because of the computational effort involved. It is shown that using multiple pruning methods with smart ordering of the pruning candidates, the number of weights in a radial basis function network can be reduced to a small fraction of the original number. The complexity of the pruning algorithm is quadratic (instead of exponential) in the number of network weights. Pruning performance is shown using a variety of benchmark problems from the University of California, Irvine machine learning database.

In the half century since minimax was first suggested as a strategy for adversary game search, various search algorithms have been developed. The standard approach has been to use improvements to the Alpha–Beta ( α – β ) algorithm. Some of the more powerful improvements examine continuations beyond the nominal search depth if they are of special interest, while others terminate the search early. The latter case is referred to as forward pruning. In this paper we discuss some important aspects of forward pruning, especially regarding risk-management, and propose ways of making risk-assessment. Finally, we introduce two new pruning methods based on some of the principles discussed here, and present experimental results from application of the methods in an established chess program.

Classification is an important problem in data mining. Given a database of records, each with a class label, a classifier generates a concise and meaningful description for each class that can be used to classify subsequent records. A number of popular classifiers construct decision trees to generate class models. These classifiers first build a decision tree and then prune subtrees from the decision tree in a subsequent i>pruning phase to improve accuracy and prevent “overfitting”. Generating the decision tree in two distinct phases could result in a substantial amount of wasted effort since an entire subtree constructed in the first phase may later be pruned in the next phase. In this paper, we propose PUBLIC, an improved decision tree classifier that integrates the second “pruning” phase with the initial “building” phase. In PUBLIC, a node is not expanded during the building phase, if it is determined that it will be pruned during the subsequent pruning phase. In order to make this determination for a node, before it is expanded, PUBLIC computes a lower bound on the minimum cost subtree rooted at the node. This estimate is then used by PUBLIC to identify the nodes that are certain to be pruned, and for such nodes, not expend effort on splitting them. Experimental results with real-life as well as synthetic data sets demonstrate the effectiveness of PUBLIC's integrated approach which has the ability to deliver substantial performance improvements.

Neural networks are often employed as tools in classification tasks. The use of large networks increases the likelihood of the task's being learned, although it may also lead to increased complexity. Pruning is an effective way of reducing the complexity of large networks. We present discriminant components pruning (DCP), a method of pruning matrices of summed contributions between layers of a neural network. Attempting to interpret the underlying functions learned by the network can be aided by pruning the network. Generalization performance should be maintained at its optimal level following pruning. We demonstrate DCP's effectiveness at maintaining generalization performance, applicability to a wider range of problems, and the usefulness of such pruning for network interpretation. Possible enhancements are discussed for the identification of the optimal reduced rank and inclusion of nonlinear neural activation functions in the pruning algorithm.

This paper proposes a fast exact algorithm to solve the Pallet Loading Problem (PLP) using depth-first strategy. A new concept called Maximal Breadth Filling Sequence (MBFS) is introduced to bring down the size of the search tree. The algorithm makes use of two pruning rules — lower-bound pruning and state-dominance pruning. Although depth-first search, by itself, requires very little memory, the dominance pruning rule makes effective utilization of the available memory. For large problems, more the memory available, more effective is the dominance pruning. The algorithm has been tested on standard problem sets. It has been found to be quite fast in outputting optimal solutions. Empirical findings are given in detail.

The article presents an algorithm that combines Minimax's alpha-beta pruning with IDA*'s depth-first iteration and forward pruning. We prove that the algorithm, which we call Two - agent IDA* (TIDA*), is correct and is guaranteed to terminate—provided its heuristic is consistent. Minimax search has been applied with other ‘forward’ pruning or selective search techniques, but none of these techniques is guaranteed to compute the correct minimax result. We also prove that TIDA*'s accuracy monotonically increases with search depth, thus avoiding certain pathologies. Empirical results with 3×3, 4×4 and 5×5 Tic-Tac-Tff grids show that TIDA* outperforms MAB, provided both algorithms use the same consistent heuristic. However, results on a more complex search space—the 3D version of Tic-Tac-Tff—show that MAB with a good inconsistent heuristic can outperform TIDA* with a consistent heuristic even though TIDA* searches 1 to 1·5 levels deeper. This result and other empirical results suggest that an algorithm that s...