Partitioning Procedure Research Articles

Model-based recursive partitioning of extended redundancy analysis with an application to nicotine dependence among US adults.

Extended redundancy analysis (ERA) is used to reduce multiple sets of predictors to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioural studies, auxiliary covariates (e.g., gender, ethnicity) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the model parameters vary across subgroups differentiated by covariates. To address this issue, we combine ERA with model-based recursive partitioning in a single framework. This combined method, MOB-ERA, aims to partition observations into heterogeneous subgroups recursively based on a set of covariates while fitting a specified ERA model to data. Upon the completion of the partitioning procedure, one can easily examine the difference in the estimated ERA parameters across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of partitioning covariates, as well as interpreting their interactions. In the analysis of public data concerning nicotine dependence among US adults, the method uncovered heterogeneous subgroups characterized by several sociodemographic covariates, each of which yielded different directional relationships between three predictor sets and nicotine dependence.

Health Monitoring of Large-Scale Civil Structures: An Approach Based on Data Partitioning and Classical Multidimensional Scaling.

A major challenge in structural health monitoring (SHM) is the efficient handling of big data, namely of high-dimensional datasets, when damage detection under environmental variability is being assessed. To address this issue, a novel data-driven approach to early damage detection is proposed here. The approach is based on an efficient partitioning of the dataset, gathering the sensor recordings, and on classical multidimensional scaling (CMDS). The partitioning procedure aims at moving towards a low-dimensional feature space; the CMDS algorithm is instead exploited to set the coordinates in the mentioned low-dimensional space, and define damage indices through norms of the said coordinates. The proposed approach is shown to efficiently and robustly address the challenges linked to high-dimensional datasets and environmental variability. Results related to two large-scale test cases are reported: the ASCE structure, and the Z24 bridge. A high sensitivity to damage and a limited (if any) number of false alarms and false detections are reported, testifying the efficacy of the proposed data-driven approach.

Simultaneous confidence intervals for ranks using the partitioning principle

We consider the problem of constructing simultaneous confidence intervals (CIs) for the ranks of n means based on their estimates together with the (known) standard errors of those estimates. We present a generic method based on the partitioning principle in which the parameter space is partitioned into disjoint subsets and then each one of them is tested at level α. The resulting CIs have then a simultaneous coverage of 1−α. We show that any procedure which produces simultaneous CIs for ranks can be written as a partitioning procedure. We present a first example where we test the partitions using the likelihood ratio (LR) test. Then, in a second example we show that a recently proposed method for simultaneous CIs for ranks using Tukey’s honest significant difference test has an equivalent procedure based on the partitioning principle. By embedding these two methods inside our generic partitioning procedure, we obtain improved variants. We illustrate the performance of these methods through simulations and real data analysis on hotel ratings. While the novel method that uses the LR test and its variant produce shorter CIs when the number of means is small, the Tukey-based method and its variant produce shorter CIs when the number of means is high.

Efficient mortar‐based algorithms for embedding 1D fibers into 3D volumes

AbstractMany composite materials are based on 1D fibers being embedded into 3D solid volumes, e.g. carbon‐fiber reinforced plastics in aerospace engineering or fiber‐reinforced concrete in civil engineering to name only two prominent examples. The present contribution highlights the most important numerical methods and algorithmic building blocks for an efficient analysis of such systems based on cutting‐edge finite element formulations for nonlinear beams and a novel beam‐to‐solid volume coupling approach inspired by classical mortar methods. A particular emphasis is put on the efficient parallel implementation for large‐scale simulations, which includes suitable procedures for domain partitioning and geometry‐based search.

Evaluation of Antimicrobial, Thrombolytic and CNS-Depressant Activities of Three Medicinal Plants Available in Bangladesh

The aim of the present study was to explore antimicrobial, thrombolytic and CNS-depressant activity of three medicinal plants Plumbago zeylanica, Trewia nudiflora and Aphanamixis polystachya available in Bangladesh. At room temperature, the plant parts were subjected to cold extraction with methanol, giving rise to concentrated methanolic extracts (MEF) followed by fractionation applying revised Kupchan partitioning procedure to obtain different soluble fractions namely to hexene fraction (HXF), ethyl acetate fraction (EAF), chloroform fraction (CLF) and aqueous fraction (AQF). To study the antimicrobial activity of these fractions, the disc diffusion method was used, where kenamycin was used as standard. Thrombolytic potential was determined by investigating clot rupture (% clot lysis) for this purpose streptokinase was employed as the positive control whereas water was the negative control. For the evaluation of CNS depressant activity, the open-field method was utilized and diazepam was chosen as the reference standard. Among the three plants, the crude methanolic fraction of P. zeylanica demonstrated good antimicrobial action over the majority of the bacterial strains assayed and the crude methanolic extract exhibited the maximum antimicrobial activity against S. aeruginosa (zone of inhibition was 23.46 ± 2.19 mm). The chloroform fraction of T. nudiflora showed the highest thrombolytic activity (43.45 ± 2.12% clot lysis). It was observed that the four extracts from the plants under investigation had CNS depressant activity. Particularly, the aqueous fraction of P. zeylanica (12.00 ± 0.913); n-hexane fraction of T. nudiflora (09.75±0.854) and A. polystachya (08.50 ± 0.645) demonstrated consistently significant CNS depressant activity, in terms of the number of squares crossed at 120 min; producing a prominent decrease in the measurement of movement.

Cola: an R/Bioconductor package for consensus partitioning through a general framework

Classification of high-throughput genomic data is a powerful method to assign samples to subgroups with specific molecular profiles. Consensus partitioning is the most widely applied approach to reveal subgroups by summarizing a consensus classification from a list of individual classifications generated by repeatedly executing clustering on random subsets of the data. It is able to evaluate the stability of the classification. We implemented a new R/Bioconductor package, cola, that provides a general framework for consensus partitioning. With cola, various parameters and methods can be user-defined and easily integrated into different steps of an analysis, e.g., feature selection, sample classification or defining signatures. cola provides a new method named ATC (ability to correlate to other rows) to extract features and recommends spherical k-means clustering (skmeans) for subgroup classification. We show that ATC and skmeans have better performance than other commonly used methods by a comprehensive benchmark on public datasets. We also benchmark key parameters in the consensus partitioning procedure, which helps users to select optimal parameter values. Moreover, cola provides rich functionalities to apply multiple partitioning methods in parallel and directly compare their results, as well as rich visualizations. cola can automate the complete analysis and generates a comprehensive HTML report.

Distributed Optimization of Visual Sensor Networks for Coverage of a Large-Scale 3-D Scene

Visual coverage is an important task for environment perception. In this article, the coverage of a large-scale 3-D scene represented by a polygon mesh model is considered, and a visual sensor network deployment algorithm is proposed through the combination of space partition, greedy and local search procedures. Comparing with existing approaches, the proposed algorithm can handle large-scale 3-D polygon meshes much faster in a scalable and distributed way, with superior coverage performance. First, we propose a new data structure called “chunk-triangle” in order to accelerate the computing process to identify visible triangles for a given camera. Furthermore, a GPU-based parallel algorithm is presented to shorten the time consumed for occlusion detection. Second, a new fast, scalable and distributed deployment approach is proposed for a camera sensor network to cover large-scale 3-D polygon meshes. The deployment algorithm generates a solution space of individual candidate cameras followed by camera selection. In camera selection, we partition the target scene space into some regions and conduct greedy search, respectively, in each region in order to choose a preliminary set of cameras with high initial coverage quality. Then, a local search strategy is further conducted to improve the coverage performance by compensating for the lost in rough space partition, and thus, results in an optimal deployment configuration of the camera network. Comparative evaluation results demonstrate the advantages of the proposed approach versus existing methods in terms of time cost, scalability, and coverage performance.

Sediment yield from a forested mountain basin in inland Pacific Northwest: Rates, partitioning, and sources

Sediment yield estimates, combined with information regarding sediment sources and partitioning (bedload vs. suspended load), can provide important insights into geomorphic character of the landscape of interest. This study reports such an analysis, conducted in a forested mountain basin in inland Pacific Northwest using reservoir deposits, ground surveys, and repeat LiDAR mapping. Our research generated three key conclusions. First, we estimated mean specific yield of clastic sediment from the study basin during the last century as ~51 Mg km−2 a−1. In the context of a data compilation from mountain basins in northwestern North America, this value was among the highest for inland basins, and among the lowest when compared with coastal basins. Second, a sediment source analysis provided valuable clues regarding the relative importance of various geomorphic processes operating in the system under study. These findings were consistent with our hypothesis that anthropogenic disturbances may be an important factor that conditions sediment yield from the basin. A mix of quantitative and qualitative evidence suggested that the estimated sediment yield value reflects a transient increase associated with past timber harvest, road construction, and large wood removal. Legacies of these disturbances appear to have the opposite effect on contemporary processes, limiting lateral activity of the channel as well as hillslope-channel connectivity. Third, our partitioning procedure revealed that bedload constituted approximately a third of the total clastic load exported from the basin. This finding suggests that, in this and similar fluvial systems, sediment yield recovery following major geomorphic disturbances could be protracted, as a considerable portion of mobilized sediment that moves as bedload is routed and evacuated from the basin for years or decades after rapid flushing of suspended material. Moreover, this finding indicates that the common assumption that bedload constitutes 10–20% of the total load can lead to underestimation in mountain basins.

An efficient GPU-based fractional-step domain decomposition scheme for the reaction–diffusion equation

In the present study, an efficient GPU-based corrected explicit–implicit domain decomposition scheme is proposed to accelerate fractional steps solvers. Implicit time advancement in fractional steps solvers leads to several independent tri-diagonal systems. In the present method, by decomposing the domain and predicting the solution at the interface points, the original tri-diagonal systems are decomposed to several independent systems; this allows partitioning the workloads. After solving the systems, correction is performed to stabilize the solution. The method is implemented using different strategies and memory coalescing, and cache throttling techniques are employed to improve the performance. Numerical experiments are conducted for two- and three-dimensional reaction–diffusion problems to measure the accuracy, stability, and efficiency of the method. The new efficient prediction and correction schemes presented in this study preserve the accuracy and the stability of the solver even for a large number of sub-domains. Therefore, the method provides many independent tri-diagonal systems and creates a large number of threads to keep the GPU occupied. The partitioning procedure is well adapted for GPU-computing; thus, the method effectively accelerates the solution and outperforms the previous methods in terms of computational time.

Partitioning Functional Test Sequences Into Multicycle Functional Broadside Tests

Multicycle tests have several advantages including the ability to support test compaction. By extracting multicycle functional broadside tests from functional test sequences, it is possible to ensure functional operation conditions during the functional capture cycles between the scan operations of a test. The challenge that this article addresses is that the computational effort of extracting $l$ -cycle functional broadside tests from a functional test sequence increases linearly with $l$ . Therefore, the computational effort of a test generation procedure that increases $l$ gradually to match $l$ to the circuit is quadratic in $l$ . This makes it infeasible to consider large values of $l$ that are important for test compaction. To address this challenge the paper develops a partitioning procedure under which test extraction requires the same computational effort for every $l$ . This article also describes a test generation procedure that is linear in $l$ . Experimental results for transition faults in benchmark circuits demonstrate the importance of large values of $l$ for test compaction.

Fast CU partition decision for H.266/VVC based on the improved DAG-SVM classifier model

One of the biggest changes in H.266/Versatile Video Coding (VVC) is introduced quad-tree with nested multi-type tree (QTMT) coding tree architecture, where the multi-type tree (MTT) structure in H.266/VVC includes binary tree (BT) and ternary tree (TT). Compared with H.265/High Efficiency Video Coding (HEVC) which only is divided by quad-tree (QT), the QTMT architecture makes the coding unit (CU) partition procedure more complexity. In this paper, we design a fast CU partition decision algorithm based on the improved Directed Acyclic Graph Support Vector Machine (DAG-SVM) model to reduce the complexity of CU partition. The video sequences are first encoded on the H.266/VVC and Test Model 4.0 (VTM 4.0), and the characteristics of the video sequences are extracted for training through the improved F-score method, where the correlation between a feature and CU partition is high. Then, the offline training is used for the improved DAG-SVM model. Finally, the trained DAG-SVM model is embedded in VTM 4.0 to early forecast the optimal CU partition modes. Simulation results indicate that the proposed method increases the time savings to 54.74% while maintaining the encoding performance. Furthermore, the proposed method exceeds the latest methods of H.266/VVC.

PointHop: An Explainable Machine Learning Method for Point Cloud Classification

An explainable machine learning method for point cloud classification, called the PointHop method, is proposed in this work. The PointHop method consists of two stages: 1) local-to-global attribute building through iterative one-hop information exchange, and 2) classification and ensembles. In the attribute building stage, we address the problem of unordered point cloud data using a space partitioning procedure and developing a robust descriptor that characterizes the relationship between a point and its one-hop neighbor in a PointHop unit. When we put multiple PointHop units in cascade, the attributes of a point will grow by taking its relationship with one-hop neighbor points into account iteratively. Furthermore, to control the rapid dimension growth of the attribute vector associated with a point, we use the Saab transform to reduce the attribute dimension in each PointHop unit. In the classification and ensemble stage, we feed the feature vector obtained from multiple PointHop units to a classifier. We explore ensemble methods to improve the classification performance furthermore. It is shown by experimental results that the PointHop method offers classification performance that is comparable with state-of-the-art methods while demanding much lower training complexity.

What do beta diversity components reveal from presence-absence community data? Let us connect every indicator to an indicandum!

Abstract Extracting meaningful information from community data is among the most challenging tasks of community ecology. Whereas presence-absence data matrices are commonly used in different analytical frameworks, we argue that the conceptual distinction among community patterns (on which inference is made), pairwise pattern components (PPCs, which reflect the unique response of communities for pairs of sites), and measures (which quantify a relevant property of PPCs), liberates our field from the possible misinterpretation of results derived from existing approaches. The novel concept suggested here is the PPC, which can be efficiently used to identify response types of communities, thereby shortening the list of potential explanatory processes. Consequently, the introduction of PPCs supports the analysis of real data sets and links patterns to ecological hypotheses. Based on PPCs, we proposed a new partitioning of beta diversity (SET framework) into intersection (I) of nestedness and beta diversity and the relative complement (RC) of nestedness in beta diversity. We performed an algebraic assessment of three existing partitioning frameworks of beta diversity: the BAS (Baselga, 2010, Global Ecology and Biogeography), POD (Podani and Schmera, 2011 Oikos) and SET (present paper). We found that when a community pattern is anti-nested, which is characterized by the presence of both Replacement and Richness difference PPCs, the BAS framework falsely indicates a 100% share of replacement from beta diversity. In contrast, the POD and SET partitioning procedures detect the presence and the proper size of PPCs for all types of community patterns. In conclusion, we argue that breaking down community patterns into PPCs and then quantifying the importance of these PPCs form a straightforward strategy to extract information from community data under a broad range of circumstances.

Common power laws for cities and spatial fractal structures

City-size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from China, France, Germany, India, Japan, and the United States, we first document that large cities are significantly more spaced out than would be expected by chance alone. We next construct spatial hierarchies for countries by first partitioning geographic space using a given number of their largest cities as cell centers and then continuing this partitioning procedure within each cell recursively. We find that city-size distributions in different parts of these spatial hierarchies exhibit power laws that are, again, far more similar than would be expected by chance alone-suggesting the existence of a spatial fractal structure.

Method for Ordering Procedures of Dividing States by Procedures with Two and Three Results Taking into Account their Cost and Weight of States

A method for streamlining state partitioning procedures with two and three outcomes is considered. A terminology and methods of the questionnaire theory were used, and the sequence of partitioning procedures itself was defined as a heterogeneous questionnaire with questions having two or three answers. This class of questionnaires is special and is defined by the authors as a class of binary-ternary questionnaires. This is the simplest class of heterogeneous questionnaires. An increase in number of answers to a question in practice can give an advantage in parameters of the questionnaires, including in the indicator of its effectiveness – the average implementation cost. It is noted that the use of binary-ternary questionnaires in practice can reduce the average time for identifying events on a questionnaire, which is extremely important in those applications of questionnaires in which there is a time limit for identifying events, for example, in critical application systems. A method for optimizing binary-ternary questionnaires is presented, based on the search for the most preferred questions for each subset of identifiable events. The choice of preferred questions is based on establishing a comparison relationship between them. The article describes all possible types of comparison relations between two questions with two answers, two questions with three answers, and also between a question with two answers and a question with three answers. An example of obtaining a mathematical expression for a function that characterizes the preference of questions over each other, as well as a generalized formula for choosing the most preferred question for any heterogeneous questionnaires is given. An algorithm has been formed for the method of ordering questions, which allows one to construct a binary-ternary questionnaire with the lowest implementation cost in polynomial time. An example of a binary-ternary questionnaire optimization by the presented method is given.

Method for Ordering Procedures of Dividing States by Procedures with Two and Three Results Taking into Account their Cost and Weight of States

A method for streamlining state partitioning procedures with two and three outcomes is considered. A terminology and methods of the questionnaire theory were used, and the sequence of partitioning procedures itself was defined as a heterogeneous questionnaire with questions having two or three answers. This class of questionnaires is special and is defined by the authors as a class of binary-ternary questionnaires. This is the simplest class of heterogeneous questionnaires. An increase in number of answers to a question in practice can give an advantage in parameters of the questionnaires, including in the indicator of its effectiveness – the average implementation cost. It is noted that the use of binary-ternary questionnaires in practice can reduce the average time for identifying events on a questionnaire, which is extremely important in those applications of questionnaires in which there is a time limit for identifying events, for example, in critical application systems. A method for optimizing binary-ternary questionnaires is presented, based on the search for the most preferred questions for each subset of identifiable events. The choice of preferred questions is based on establishing a comparison relationship between them. The article describes all possible types of comparison relations between two questions with two answers, two questions with three answers, and also between a question with two answers and a question with three answers. An example of obtaining a mathematical expression for a function that characterizes the preference of questions over each other, as well as a generalized formula for choosing the most preferred question for any heterogeneous questionnaires is given. An algorithm has been formed for the method of ordering questions, which allows one to construct a binary-ternary questionnaire with the lowest implementation cost in polynomial time. An example of a binary-ternary questionnaire optimization by the presented method is given.

Developing a New Spatial Unit for Macroscopic Safety Evaluation Based on Traffic Density Homogeneity

Macrolevel crash modeling has been extensively applied to investigate the safety effects of demographic, socioeconomic, and land use factors, in order to add safety knowledge into traffic planning and policy-making. In recent years, with the increasing attention to regional traffic management and control, the safety effects of macrolevel traffic flow parameters may also be of interest, in order to provide useful safety knowledge for regional traffic operation. In this paper, a new spatial unit was developed using a recursive half-cut partitioning procedure based on a normalized cut (NC) minimization method and traffic density homogeneity. Two Bayesian lognormal models with different conditional autoregressive (CAR) priors were applied to examine the safety effects of traffic flow characteristics at the NC level. It was found that safety effects of traffic flow exist at such macrolevel, indicating the necessity of considering safety for regional traffic control and management. Furthermore, traffic flow effects were also examined for another two spatial units: Traffic Analysis Zone (TAZ) and Census Tract (CT). It was found that ecological fallacy and atomic fallacy could exist without considering traffic flow parameters at those planning-based levels. In general, safety needs to be considered for regional traffic operation and the effects of traffic flow need to be considered for spatial crash modeling at various spatial levels.

K-MACE and Kernel K-MACE Clustering

Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on nalizing the partitioning results. K-means is one of the popular methods of clustering that requires CNC. Validity index methods use an additional optimization procedure to estimate the CNC for K-means. We propose an alternative validity index approach denoted by k-Minimizing Average Central Error (KMACE). Average Central Error (ACE) is the average error between the unavailable cluster center and the estimated cluster center for each sample data. Kernel K-MACE is kernel K-means that is equipped with the proposed CNC estimator. In addition, kernel K-MACE includes an automatically tuned procedure for choosing the Gaussian kernel parameters. Simulation results for both synthetic and real data show superiority of K-MACE and kernel K-MACE over the conventional clustering methods not only in CNC estimation but also in the partitioning procedure.

A Simple and Efficient Optimized Solid-Liquid Extraction with Low Temperature Partition Procedure for Dissipation and Translocation Study of Pesticide Residues in Rice Grains

Pesticides are used globally to protect food against pest attack. This study evaluates the dissipation of bifenthrin and deltamethrin residues in unhulled rice and the translocation of these insecticide residues in husked rice stored at 25 °C in a biochemical oxygen demand (BOD) incubator for 35 days. For pesticide determination, the simple and efficient solid-liquid extraction methods with low temperature partition (SLE/LTP) followed by gas chromatography with electron capture detection (GC-ECD), for unhulled and husked rice were optimized and validated. These methods produced results of validated parameters consistent with Brazilian legislation, showing good efficiency (recovery rate above 95%) and limit of quantification (LOQ) < 0.090 mg kg−1 for bifenthrin and LOQ < 0.070 mg kg−1 for deltamethrin. There was a 40% dissipation of deltamethrin residues after 15 days of storage of the unhulled rice. For the insecticide bifenthrin, dissipation during the 35 days of storage was not verified. The remaining residues of dissipation in the rice grains were below the maximum residue level (MRL) prescribed by the law. The insecticide residues did not translocate in the husked rice grains destined for final consumption.

Editor Note 1

Editor Note 1