Splitting Rule Research Articles

A dynamic multicast tree based routing scheme without replication in delay tolerant networks

Delay tolerant networks (DTNs) are a special type of wireless mobile networks which may lack continuous network connectivity. Multicast is an important routing function that supports the distribution of data to a group of users: a service needed for many potential DTN applications. While multicasting in the Internet and in mobile ad hoc networks has been studied extensively, efficient multicasting in DTNs is a considerably different and challenging problem due to the probabilistic nature of contact among nodes. This paper aims to provide a non-replication multicasting scheme in DTNs while keeping the number of forwardings low. The address of each destination is not replicated, but is assigned to a particular node based on its contact rate level and active level. Our scheme is based on a dynamic multicast tree where each leaf node corresponds to a destination. Each tree branch is generated at a contact based on the compare–split rule proposed in this paper. The compare part determines when a new search branch is needed, and the split part decides how the destination set should be partitioned. When only one destination is left in the destination set, we use either wait (no further relay) or focus (with further relay) to reach the final destination. The effectiveness of our approach is verified through extensive simulations. Ratio-based-split performs best in the compare–split step, both in synthetic and real traces. Using the wait scheme can reduce the number of forwardings, while using the focus scheme can reduce the latency.

Uniform distribution of generalized Kakutani’s sequences of partitions

We consider a generalized version of Kakutani’s splitting procedure where an arbitrary starting partition π is given and in each step all intervals of maximal length are split into m parts, according to a splitting rule ρ. We give conditions on π and ρ under which the resulting sequence of partitions is uniformly distributed.

An Independent Set Packet Classification Algorithm Using Priority Sorting

Independent set algorithms, as a kind of packet classification algorithms with space efficiency, has lower execution efficiency for the lack of priority consideration in linear matching process. In addition, new independent sets created frequently as a result of dynamic updates greatly increase its dependence on the consumption of storage space. In order to overcome these above disadvantages, an improved algorithm based on independent sets using priority sorting (ISSP) is proposed and an improvement strategy of split rule is designed for higher storage efficiency in dynamic updates. The simulation results further show that the improved algorithm, compared with IS algorithm, reduces its dependence on storage space in dynamic updates and has higher execution efficiency.

Knowledge discovery in data streams with regression tree methods

AbstractThis paper presents an advanced review of regression tree methods for mining data streams. Batch regression tree methods are known for their simplicity, interpretability, accuracy, and efficiency. They use fast divide‐and‐conquer greedy algorithms that recursively partition the given training data into smaller subsets. The result is a tree‐shaped model with splitting rules in the internal nodes and predictions in the leaves. Most batch regression tree methods take a complete dataset and build a model using that data. Generally, this tree model cannot be modified if new data is acquired later. Their successors, the incremental model and interval trees algorithms, are able to build and retrain a model on a step‐by‐step basis by incorporating new numerical training instances into the model as they become available. Moreover, these algorithms produce even more compact and accurate models than batch regression tree algorithms because they use intervals or functional models with a change detection mechanism, which makes them a more suitable choice for regression analysis of data streams. Finally, this review summarizes the performance results of the reviewed methods and crystallizes 10 requirements for successful implementation of a regression tree algorithm in data stream mining area. © 2011 Wiley Periodicals, Inc.This article is categorized under: Algorithmic Development > Spatial and Temporal Data Mining Technologies > Machine Learning Technologies > Prediction

A Tableau Calculus for Minimal Modal Model Generation

Model generation and minimal model generation is useful for fault analysis, verification of systems and validation of data models. Whereas for classical propositional and first-order logic several model minimization approaches have been developed and studied, for non-classical logic the topic has been much less studied. In this paper we introduce a minimal model generation calculus for multi-modal logic K(m) and extensions of K(m) with the axioms T and B. The calculus provides a method to generate all and only minimal modal Herbrand models, and each model is generated exactly once. A novelty of the calculus is a non-standard complement splitting rule designed for minimal model generation. Experiments show the rule has the added benefit of reducing the search space.

A decision tree-based on-line preventive control strategy for power system transient instability prevention

Maintaining transient stability is a basic requirement for secure power system operations. Preventive control deals with modifying the system operating point to withstand probable contingencies. In this article, a decision tree (DT)-based on-line preventive control strategy is proposed for transient instability prevention of power systems. Given a stability database, a distance-based feature estimation algorithm is first applied to identify the critical generators, which are then used as features to develop a DT. By interpreting the splitting rules of DT, preventive control is realised by formulating the rules in a standard optimal power flow model and solving it. The proposed method is transparent in control mechanism, on-line computation compatible and convenient to deal with multi-contingency. The effectiveness and efficiency of the method has been verified on New England 10-machine 39-bus test system.

Geometric Decision Tree

In this paper, we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy for assessing the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.

A string pattern regression algorithm and its application to pattern discovery in long introns.

We present a new approach to pattern discovery called string pattern regression, where we are given a data set that consists of a string attribute and an objective numerical attribute. The problem is to find the best string pattern that divides the data set in such a way that the distribution of the numerical attribute values of the set for which the pattern matches the string attribute, is most distinct, with respect to some appropriate measure, from the distribution of the numerical attribute values of the set for which the pattern does not match the string attribute. By solving this problem, we are able to discover, at the same time, a subset of the data whose objective numerical attributes are significantly different from rest of the data, as well as the splitting rule in the form of a string pattern that is conserved in the subset. Although the problem can be solved in linear time for the substring pattern class, the problem is NP-hard in the general case (i.e. more complex patterns), and we present an exact but efficient branch-and-bound algorithm which is applicable to various pattern classes. We apply our algorithm to intron sequences of human, mouse, fly, and zebrafish, and show the practicality of our approach and algorithm. We also discuss possible extensions of our algorithm, as well as promising applications, such as microarray gene expression data.

Novel head and neck cancer survival analysis approach: Random survival forests versus cox proportional hazards regression

Electronic patient files generate an enormous amount of medical data. These data can be used for research, such as prognostic modeling. Automatization of statistical prognostication processes allows automatic updating of models when new data is gathered. The increase of power behind an automated prognostic model makes its predictive capability more reliable. Cox proportional hazard regression is most frequently used in prognostication. Automatization of a Cox model is possible, but we expect the updating process to be time-consuming. A possible solution lies in an alternative modeling technique called random survival forests (RSFs). RSF is easily automated and is known to handle the proportionality assumption coherently and automatically. Performance of RSF has not yet been tested on a large head and neck oncological dataset. This study investigates performance of head and neck overall survival of RSF models. Performances are compared to a Cox model as the "gold standard." RSF might be an interesting alternative modeling approach for automatization when performances are similar. RSF models were created in R (Cox also in SPSS). Four RSF splitting rules were used: log-rank, conservation of events, log-rank score, and log-rank approximation. Models were based on historical data of 1371 patients with primary head-and-neck cancer, diagnosed between 1981 and 1998. Models contain 8 covariates: tumor site, T classification, N classification, M classification, age, sex, prior malignancies, and comorbidity. Model performances were determined by Harrell's concordance error rate, in which 33% of the original data served as a validation sample. RSF and Cox models delivered similar error rates. The Cox model performed slightly better (error rate, 0.2826). The log-rank splitting approach gave the best RSF performance (error rate, 0.2873). In accord with Cox and RSF models, high T classification, high N classification, and severe comorbidity are very important covariates in the model, whereas sex, mild comorbidity, and a supraglottic larynx tumor are less important. A discrepancy arose regarding the importance of M1 classification (see Discussion). Both approaches delivered similar error rates. The Cox model gives a clinically understandable output on covariate impact, whereas RSF becomes more of a "black box." RSF complements the Cox model by giving more insight and confidence toward relative importance of model covariates. RSF can be recommended as the approach of choice in automating survival analyses.

Partitioning Sequencing Situations and Games

The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research. This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors.

A Cluster Tree Method For Text Categorization

The decision tree is a flexible and useful classification tool. But on the data with high dimensionality, it meets problems. For most of current decision tree algorithms, when splitting a node of a tree, only the “best” one feature is selected and used. Since more features are ignored, the classification accuracy is not high. To solve the problem, this paper uses a cluster tree for text categorization. Unlike familiar decision trees (e.g. CART, C4.5), clustering results are used as the splitting rule and more features are considered. Obviously, the used clustering algorithm is an very important to the cluster tree. For better performance, a text clustering algorithm is proposed to enhance the cluster tree. Experiments show that the cluster tree solves the high-dimensionality problem and outperforms C4.5 and CART on text data. Sometimes, it may do better than LibSVM, which may be the most powerful tool for text categorization.

A Combined Superposition and Model Evolution Calculus

We present a new calculus for first-order theorem proving with equality, $ \mathcal{ME}+$ Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of these two rather complementary calculi in a single framework. In particular, Model Evolution, as a lifted version of the propositional DPLL procedure, contributes a non-ground splitting rule that effectively permits to split a clause into non variable disjoint subclauses. In the paper we present the calculus in detail. Our main result is its completeness under semantically justified redundancy criteria and simplification rules. We also show how under certain assumptions the model representation computed by a (finite and fair) derivation can be queried in an effective way.

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.

Consistency of random survival forests

We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables—that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan–Meier survival function.

Splitting rules of electronic miniband in Fibonacci superlattices: a gap map approach

The splitting rules of fragmental miniband in Fibonacci superlattices (FSLs) with arbitrary basis and generation orders are presented through a gap map diagram. Based on the gap map, we find the invariant conditions of the band structure splitting in the FSL for arbitrary generation orders. Moreover, the band structure splitting can be divided to form many regions, each having a similar pattern. In each region, the widths of most gap bands except two major gaps will decrease for increasing the generation order. It is interesting that the center and gap width of the major gaps will converge to constant values for increasing the generation order of the FSL. Based on the splitting rules displayed in the gap map, it is convenient to predict the fragmental band structure in the FSL for arbitrary generation orders and bases.

Crystal-field ground state of the noncentrosymmetric superconductorCePt3Si: A combined polarized soft x-ray absorption and polarized neutron study

We determined the crystal-field split Hund's rule ground state of the non-centrosymmetric heavy fermion superconductor CePt3Si with polarization dependent soft X-ray absorption spectroscopy (XAS) and polarized neutron scattering. We are also able to give the sequence of the crystal-field states from the temperature evolution of the linear dichroic signal in the XAS. The quantitative analysis of the XAS temperature dependence together with the neutron transition energies complete the identification of the crystal-field level scheme.

Partitioning sequencing situations and games

The interaction between sequencing situations and cooperative games starting from the paper of Curiel et al. [Curiel, I., Pederzoli, G., Tijs S., 1989. Sequencing games. European Journal of Operational Research 40, 344-351], has become an established line of research within the theory of operation research games. The current paper introduces a new model in this field: partitioning sequencing situations and associated games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. We define cooperative games corresponding to partitioning sequencing situations and show that these games are convex. Moreover, we present a game independent expression for the Shapley value of these games. Finally, it is shown that the partitioning equal gain splitting rule leads to a core allocation which is the average of two specific marginal vectors.

Numerical Simulation of Particle Dispersion in the Wake of a Circular Cylinder

In this article, numerical simulation of the Navier-Stokes equations was performed for the large-scale structures of a two-dimensional temporally developing cylinder flow and the associated dispersion patterns of particles were simulated. The time-dependent Navier-Stokes equations were integrated in time using a mixed explicit-implicit operator splitting rules. The spatial discretization was processed using spectral-element method. Non-reflecting conditions were employed at the outflow boundary. Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases. The simulation results of the flow field agree well with experimental data. Due to the effects of the coherent structures, the particles demonstrate a more organized dispersion process in the space and a periodic dispersion characteristic in the time. Particle dispersion increases with the flow Reynolds number and so does for particle concentration, which is independent of particle size. However, for particles at different Stokes numbers, the dispersion patterns are different. The particles at smaller Stokes number congregate mainly in the vortex core regions and the particles at larger Stokes number disperse much less along the lateral direction with the even distribution. The higher density distribution at the outer boundary of large-scale vortex structure characterizes the dispersion pattern of particles at the Stokes numbers of order of unity. Furthermore, these particles disperse largely along the lateral direction and show the nonuniform distribution of concentration.

A new family of Markov branching trees: the alpha-gamma model

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in size-biased order, and we study their limiting behaviour.

Batch Sequencing and Cooperation

Game theoretic analysis of sequencing situations has been restricted to manufacturing systems which consist of machines that can process only one job at a time. However, in many manufacturing systems, operations are carried out by batch machines which can simultaneously process multiple jobs. This paper aims to extend the game theoretical approach to the cost allocation problems arising from sequencing situations on systems that consist of batch machines. We first consider sequencing situations with a single batch machine and analyze cooperative games arising from these situations. It is shown that these games are convex and an expression for the Shapley value of these games is provided. We also introduce an equal gain splitting rule for these sequencing situations and provide an axiomatic characterization. Second, we analyze various aspects of flow-shop sequencing situations which consist of batch machines only. In particular, we provide two cases in which the cooperative game arising from the flow-shop sequencing situation is equal to the game arising from a sequencing situation that corresponds to one specific machine in the flow-shop.