Partition Of Objects Research Articles

Parsimonious consensus hierarchies, partitions and fuzzy partitioning of a set of hierarchies

Methodology is described for fitting a fuzzy partition and a parsimonious consensus hierarchy (ultrametric matrix) to a set of hierarchies of the same set of objects. A model defining a fuzzy partition of a set of hierarchical classifications, with every class of the partition synthesized by a parsimonious consensus hierarchy is described. Each consensus includes an optimal consensus hard partition of objects and all the hierarchical agglomerative aggregations among the clusters of the consensus partition. The performances of the methodology are illustrated by an extended simulation study and applications to real data. A discussion is provided on the new methodology and some interesting future developments are described.

Partitioning intensity inhomogeneity colour images via Saliency-based active contour

Partitioning or segmenting intensity inhomogeneity colour images is a challenging problem in computer vision and image shape analysis. Given an input image, the active contour model (ACM) which is formulated in variational framework is regularly used to partition objects in the image. A selective type of variational ACM approach is better than a global approach for segmenting specific target objects, which is useful for applications such as tumor segmentation or tissue classification in medical imaging. However, the existing selective ACMs yield unsatisfactory outcomes when performing the segmentation for colour (vector-valued) with intensity variations. Therefore, our new approach incorporates both local image fitting and saliency maps into a new variational selective ACM to tackle the problem. The euler-lagrange (EL) equations were presented to solve the proposed model. Thirty combinations of synthetic and medical images were tested. The visual observation and quantitative results show that the proposed model outshines the other existing models by average, with the accuracy of 2.23% more than the compared model and the Dice and Jaccard coefficients which were around 12.78% and 19.53% higher, respectively, than the compared model.

Noise-aware and correlation analysis-based for fuzzy-rough feature selection

Feature selection has gained significant attention, with a focus on removing redundant or irrelevant features to improve subsequent machine learning tasks. The fuzzy rough set is extensively utilized for feature selection because of its ability to manage uncertainty. The fuzzy dependency-based approach represents an effective branch within the domain of fuzzy rough set models. However, it has been revealed that fuzzy dependency function is not robust to noise data while the noise objects often occur. Furthermore, as the size of dataset increases, the computational complexity of evaluating metrics also tends to increase due to potentially unnecessary computational effort. Hence, to address both of these research issues simultaneously, we propose a fuzzy rough correlation-based feature selection algorithm, denoted as FRCB. The introduction of neighborhood radius constraints and granularity conditions aims to interpret and mitigate the impact of noisy data by partitioning objects into a Core-Boundary-Outlier structure. A more robust hybrid fuzzy relation and correlation-based fuzzy rough dependency is proposed by considering the representativeness and attractiveness of the core to other objects within the internal class, as well as the impacts on other objects in external classes. To minimize processing overhead and time complexity, redundant features are identified through correlation analysis, which involves evaluating, ranking, and grouping before proceeding to the next iteration. The experiments were conducted using eleven datasets. The analysis of the noise curves and the raw data curve indicates that the proposed correlation-based fuzzy rough dependency is more robust than other benchmarking methods. Moreover, the results of the classification and running time comparisons indicate that the FRCB algorithm proposed in this study exhibits superior performance compared to the baseline methods.

Defining Clusters by Topology Warping Features, an Interpretable Data Clustering Method

Clustering is the task of dividing a data-set into different groups, called clusters, based on similarity. Despite being extensively studied, many state-of-the-art clustering algorithms lack interpretability. While it is useful to partition objects into clusters, it can be equally useful to understand why each cluster has been created. This motivates the desire for a clustering algorithm which can explain its partition. Our proposed method is a clustering process which seeks to explain which variables of a data-set are responsible for each cluster. We analyze the shape of the data, through the mathematical concept of a topological space. A space which is optimal for clustering is one which contains several disconnected islands, quantified as the number of connected components. Subsets of variables can then be selected and the resulting connected components of the topological space calculated. If this space is promising then the resulting disconnected region is the set of data-points which make up a cluster, and the subset of variables are what define it. We chose the variables to consider by grouping them via their correlation or through complex methods, e.g evolutionary algorithms. Our method provides a simple explanation since we can confidently assert that particular variables are why a data point is in a certain cluster. Alongside test data for comparison with existing algorithms, our methodology was applied to a community-based adolescents lipidomics dataset. Results on this dataset revealed 3 distinct clusters which can be explained by the distinct set of lipids that define them. Further optimization showed the existence of a cluster defined by a single lipid.

Research on Road Network Partitioning Considering the Coupling of Network Connectivity and Traffic Attributes

The urban road network is a large and complex system characterized by significant heterogeneity arising from different spatial structures and traffic demands. To facilitate effective management and control, it is necessary to partition the road network into homogeneous sub-areas. In this regard, we aim to propose a hybrid method for partitioning sub-areas with intra-area homogeneity, inter-area heterogeneity, and similar sizes, called CSDRA. It is specifically designed for bidirectional road networks with segment weights that encompass traffic flow, speed, or roadside facility evaluation. Based on community detection and spectral clustering, this proposed method comprises four main modules: initial partition, partitioning of large sub-areas, reassignment of small sub-areas, and boundary adjustment. In the preliminary partitioning work, we also design a road network reconstruction method which further helps to enhance the intra-area homogeneity and inter-area heterogeneity of partitioning results. Furthermore, to align with the requirement for comparable work units in practical traffic management and control, we control the similarity in the size of sub-areas by enforcing upper and lower bound constraints on the size of the sub-areas. We verify the outperformance of the proposed method by an experiment on the partitioning of an urban road network in Guangzhou, China, where we employ sidewalk barrier-free score data as segment weights. The results demonstrate the effectiveness of both the road network reconstruction method and the CSDRA proposed in this paper, as they significantly improve the partitioning outcomes compared with other methods using different evaluation indicators corresponding to the partitioning objectives. Finally, we investigate the influence of constraint parameters on the evaluation indicator. Our findings indicate that appropriately configuring these constraint parameters can effectively minimize sub-region size variations while having minimal impact on other aspects.

Clustering-based method for big spatial data partitioning

“Internet of Things” (IoT) is considered one of the main focus areas of research in computer systems and networks. Since IoT devices are installed in static geographic places or on board a moving trackable object, the data generated by the device is mainly characterized as spatial data. The spatial data generated by IoT devices scale up in volume, velocity, and veracity so they tend to be considered “Big Data”. “Big Spatial Data” requires the development of special frameworks that use state-of-the-art technologies in data storage, query, and analysis. These frameworks are mainly characterized by the use of a parallel programming model that partitions the spatial data into smaller chunks that can be handled in parallel. The development of an optimal method for spatial data partitioning is essential in implementing such systems.In this paper, we propose, design, and implement a new method for spatial data partitioning based on K-Means clustering, an unsupervised machine learning algorithm. The design is based on a well-defined conceptual, mathematical, and programming model for a general spatial data partitioning method. The main component of the suggested model is an implementation of K-Means clustering suited for spatial data.The new method is designed, implemented, and tested to prove its ability to achieve partitioning objectives and the efficiency of its performance. The results of the tests are benchmarked against one of the most widely adopted approaches in partitioning spatial data and prove the ability of the novel method to surpass it in some of the evaluation criteria.

Cluster quality analysis based on SVD, PCA-based k-means and NMF techniques: an online survey data

With the increase in computerisation in every field, a huge amount of data is collected from everywhere. Therefore, extracting useful information has become a necessary task in the present era. Data mining helps to extract the information and uncover the relationship among the data. Clustering is an unsupervised technique used for partitioning objects into several groups and discover the hidden relationship among the data. There are many techniques used for clustering. In this article, a comparative study and analysis of three famous clustering techniques are done: principal component analysis (PCA), singular value decomposition (SVD) and non-negative matrix factorisation (NMF) for the clustering of a database. The database collected through a set of questionnaire surveys related to day-to-day activities. Then a comparison of their natural clustering ability is being done. Also, the use of normalised mutual information (NMI) and purity as two-cluster quality evaluation measures are explored. Then an attempt is made to show the amount of information from the original data matrix that the approximated data matrix contains. Next, to verify the accuracy of the variance covered by the approximated data matrix, the Frobenius norm is used. At last, the results are compared with the variance covered by using singular values, and a detailed analysis of each data matrix is explained.

Deep Multiview Clustering via Iteratively Self-Supervised Universal and Specific Space Learning.

Multiview clustering seeks to partition objects via leveraging cross-view relations to provide a comprehensive description of the same objects. Most existing methods assume that different views are linear transformable or merely sampling from a common latent space. Such rigid assumptions betray reality, thus leading to unsatisfactory performance. To tackle the issue, we propose to learn both common and specific sampling spaces for each view to fully exploit their collaborative representations. The common space corresponds to the universal self-representation basis for all views, while the specific spaces are the view-specific basis accordingly. An iterative self-supervision scheme is conducted to strengthen the learned affinity matrix. The clustering is modeled by a convex optimization. We first solve its linear formulation by the popular scheme. Then, we employ the deep autoencoder structure to exploit its deep nonlinear formulation. The extensive experimental results on six real-world datasets demonstrate that the proposed model achieves uniform superiority over the benchmark methods.

Analysis of the Mathematical Visualization Process of Female Students in Solving Contextual Problems Based on Cognitive Style

This study aimed to describe the process of mathematical visualization of female students in solving contextual problems in terms of differences in cognitive style. This type of research is qualitative research with a descriptive approach. The research subjects consisted of two 8th grade students with SPFI and SPFD cognitive styles. The results showed that field-independent female subjects explored objects only from one point of view, from the side they produced 3D objects and were divided into 4 parts. SPFI uses an object-partition strategy. SPFI scans objects in both 3D and 2D. SPFI performs object manipulation in the form of rotation. While SPFD explores objects in 2D because it uses a point of view from the side of the object. SPFD identifies the presence of blocks and triangles. SPFD uses an object partitioning strategy. SPFD does not pay attention to the spatial aspect of the scanned object. SPFD performs object manipulation in the form of a triangular object rotation of 1800 clockwise. Therefore, teachers need to pay attention to the strategies carried out by students in terms of gender and cognitive style in solving cognitive problems so that students can perform optimally.

Clustering stock price volatility using intuitionistic fuzzy sets

Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-separability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility.

Partitioning and Reordering for Spike-Based Distributed-Memory Parallel Gauss--Seidel

Gauss--Seidel (GS) is a widely used iterative method for solving sparse linear systems of equations and also known to be effective as a smoother in algebraic multigrid methods. Parallelization of GS is a challenging task since solving the sparse lower triangular system in GS constitutes a sequential bottleneck at each iteration. We propose a distributed-memory parallel GS (dmpGS) by implementing a parallel sparse triangular solver (stSpike) based on the Spike algorithm. stSpike decouples the global triangular system into smaller systems that can be solved concurrently and requires the solution of a much smaller reduced sparse lower triangular system which constitutes a sequential bottleneck. In order to alleviate this bottleneck and to reduce the communication overhead of dmpGS, we propose a partitioning and reordering model consisting of two phases. The first phase is a novel hypergraph partitioning model whose partitioning objective simultaneously encodes minimizing the reduced system size and the communication volume. The second phase is an in-block row reordering method for decreasing the nonzero count of the reduced system. Extensive experiments on a dataset consisting of 359 sparse linear systems verify the effectiveness of the proposed partitioning and reordering model in terms of reducing the communication and the sequential computational overheads. Parallel experiments on 12 large systems using up to 320 cores demonstrate that the proposed model significantly improves the scalability of dmpGS.

Modeling of the Scattering Field of an FGM-148 Javelin Anti-Tank Missile in Altair Feko

Introduction. Computer-aided design systems for microwave devices are an effective tool for assessing the backscattering characteristics of complex-shaped objects. However, these calculations are often associated with significant computational costs, especially at large values of the ratio of the characteristic dimensions of the object to the wavelength. The use of asymptotic methods in combination with the mesh coarsening of object partition can significantly reduce these costs. However, in each practical case, this leads to a deterioration in the accuracy of the estimates obtained, which is hard to predict.Aim. Comparative assessment of the results of modeling the scattering field in the CAD of microwave devices using various methods for calculating and detailing the object model in the decimeter and centimeter wavelength ranges.Materials and methods. The research object was an anti-tank guided missile FGM-148 Javelin. The scattering field of Altair FEKO microwave devices was modeled in CAD using the methods of moments and physical optics in the frequency range from 1 to 10 GHz and angles from 0 to 180°. A comparison of one-dimensional backscatter diagrams and radar images obtained using these methods was carried out.Results. For the class of objects under consideration, the method of physical optics provides acceptable accuracy at frequencies of 5 GHz and higher with a step of partitioning the model surface of the order of one centimeter and a total calculation duration of the order of several minutes (Intel Core i5-4460 PC / 3.2 GHz / 8 MB RAM). At lower frequencies, acceptable accuracy and a similar calculation duration are achieved when calculating by the method of moments and a partitioning step of about 20 cm. The possibility of using the Altair FEKO CAD system for modeling radar images of objects with a resolution of at least 20 cm is demonstrated.Conclusion. The results obtained complement the well-known studies in the field of comparative assessment of the time and accuracy characteristics of various methods for calculating the scattering field of objects in the CAD of microwave devices.

DBHC: A DBSCAN-based hierarchical clustering algorithm

Clustering is the process of partitioning objects of a dataset into some groups according to similarities and dissimilarities between its objects. DBSCAN is one of the most important clustering algorithms in the density based approach of clustering. In spite of the numerous advantages of the DBSCAN algorithm, it has two important input parameters, MinPts and Eps, which determining their values is still a great challenge. This problem arises because values of these parameters are heavily dependent on data distribution. To overcome this challenge, firstly features of these parameters are investigated and the data distribution are analyzed. Then a DBSCAN-based hierarchical clustering (DBHC) method is proposed in this paper in order to fix this challenge. For this purpose, DBHC first determines values of these parameters using the notion of k nearest neighbor and k-dist plot. Because most of the real world data is not distributed uniformly, it is needed to be produced several values for the Eps parameter. Then, DBHC executes the DBSCAN algorithm several times based on the number of Eps produced earlier. Finally, DBHC method merges obtained clusters if the number of produced clusters is larger than the number which has estimated by the user. To evaluate the performance of the DBHC method, several experiments were performed on some of benchmark datasets of UCI database. Obtained results were compared with other previous works. The obtained results consistently showed that the DBHC method led to better results in comparison to the other works.

AN EXPERIMENTAL ANALYSIS OF SPATIAL INDEXING ALGORITHMS FOR REAL TIME SAFETY CRITICAL MAP APPLICATION

Abstract. This paper presents a study that compares the three space partitioning and spatial indexing techniques, KD Tree, Quad KD Tree, and PR Tree. KD Tree is a data structure proposed by Bentley (Bentley and Friedman, 1979) that aims to cluster objects according to their spatial location. Quad KD Tree is a data structure proposed by Berezcky (Bereczky et al., 2014) that aims to partition objects using heuristic methods. Unlike Bereczky’s partitioning technique, a new partitioning technique is presented based on dividing objects according to space-driven, in the context of this study. PR Tree is a data structure proposed by Arge (Arge et al., 2008) that is an asymptotically optimal R-Tree variant, enables data-driven segmentation. This study mainly aimed to search and render big spatial data in real-time safety-critical avionics navigation map application. Such a real-time system needs to efficiently reach the required records inside a specific boundary. Performing range query during the runtime (such as finding the closest neighbors) is extremely important in performance. The most crucial purpose of these data structures is to reduce the number of comparisons to solve the range searching problem. With this study, the algorithms’ data structures are created and indexed, and worst-case analyses are made to cover the whole area to measure the range search performance. Also, these techniques’ performance is benchmarked according to elapsed time and memory usage. As a result of these experimental studies, Quad KD Tree outperformed in range search analysis over the other techniques, especially when the data set is massive and consists of different geometry types.

On utilizing the transitivity pursuit-enhanced object partitioning to optimize self-organizing lists-on-lists

In this paper, the Transitivity Pursuit-Enhanced Object Migration Automata (TPEOMA) is used to capture the dependence of elements in a hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) “adaptive” data structure. In doing so, the TPEOMA-enhanced hierarchical SLLs-on-SLLs learns the probability distribution of elements in a Non-stationary Environment. In this framework, we divide the hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) into an outer and inner list context. The inner-list context is itself a SLLs containing sub-elements of the list, while the outer-list context contains these sublist partitions as its primitive elements. The elements belonging to a particular sublist partition are determined using the TPEOMA reinforcement learning scheme from the theory of Learning Automata. The idea of Transitivity builds on the Pursuit concept that injects a noise filter into the EOMA to filter divergent queries from the Environment, thereby increasing the likelihood of training the Automaton to approximate the “true” distribution of the Environment. The Transitivity phenomenon can infer “dependent” query pairs from non-accessed elements in the transitivity relation based on the statistical distribution of the queried elements. The TPEOMA-enhanced hierarchical SLLs-on-SLLs schemes results in superior performances to the MTF and TR schemes as well as to the EOMA-enhanced hierarchical SLLs-on-SLLs schemes in NSEs.

K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony

K-Means Clustering is a popular technique in data analysis and data mining. To remedy the defects of relying on the initialization and converging towards the local minimum in the K-Means Clustering (KMC) algorithm, a chaotic adaptive artificial bee colony algorithm (CAABC) clustering algorithm is presented to optimally partition objects into K clusters in this study. This algorithm adopts the max–min distance product method for initialization. In addition, a new fitness function is adapted to the KMC algorithm. This paper also reports that the iteration abides by the adaptive search strategy, and Fuch chaotic disturbance is added to avoid converging on local optimum. The step length decreases linearly during the iteration. In order to overcome the shortcomings of the classic ABC algorithm, the simulated annealing criterion is introduced to the CAABC. Finally, the confluent algorithm is compared with other stochastic heuristic algorithms on the 20 standard test functions and 11 datasets. The results demonstrate that improvements in CAABA-K-means have an advantage on speed and accuracy of convergence over some conventional algorithms for solving clustering problems.

Comprehensive Review of K-Means Clustering Algorithms

This paper presents a comprehensive review of existing techniques of k-means clustering algorithms made at various times. The k-means algorithm is aimed at partitioning objects or points to be analyzed into well separated clusters. There are different algorithms for k-means clustering of objects such as traditional k-means algorithm, standard k-means algorithm, basic k-means algorithm and the conventional k-means algorithm, this are perhaps the most widely used versions of the k-means algorithms. These algorithms uses the Euclidean distance as its metric and minimum distance rule approach by assigning each data points (objects) to its closest centroids.

Learnable Weighting of Intra-Attribute Distances for Categorical Data Clustering with Nominal and Ordinal Attributes.

The success of categorical data clustering generally much relies on the distance metric that measures the dissimilarity degree between two objects. However, most of the existing clustering methods treat the two categorical subtypes, i.e., nominal and ordinal attributes, in the same way when calculating the dissimilarity without considering the relative order information of the ordinal values. Moreover, there would exist interdependence among the nominal and ordinal attributes, which is worth exploring for indicating the dissimilarity. This paper will therefore study the intrinsic difference and connection of nominal and ordinal attribute values from a perspective akin to the graph. Accordingly, we propose a novel distance metric to measure the intra-attribute distances of nominal and ordinal attributes in a unified way, meanwhile preserving the order relationship among ordinal values. Subsequently, we propose a new clustering algorithm to make the learning of intra-attribute distance weights and partitions of data objects into a single learning paradigm rather than two separate steps, whereby circumventing a suboptimal solution. Experiments show the efficacy of the proposed algorithm in comparison with the existing counterparts.

Multi-View Learning a Decomposable Affinity Matrix via Tensor Self-Representation on Grassmann Manifold

Multi-view clustering aims to partition objects into potential categories by utilizing cross-view information. One of the core issues is to sufficiently leverage different views to learn a latent subspace, within which the clustering task is performed. Recently, it has been shown that representing the multi-view data by a tensor and then learning a latent self-expressive tensor is effective. However, early works mainly focus on learning essential tensor representation from multi-view data and the resulted affinity matrix is considered as a byproduct or is computed by a simple average in Euclidean space, thereby destroying the intrinsic clustering structure. To that end, here we proposed a novel multi-view clustering method to directly learn a well-structured affinity matrix driven by the clustering task on Grassmann manifold. Specifically, we firstly employed a tensor learning model to unify multiple feature spaces into a latent low-rank tensor space. Then each individual view was merged on Grassmann manifold to obtain both an integrative subspace and a consensus affinity matrix, driven by clustering task. The two parts are modeled by a unified objective function and optimized jointly to mine a decomposable affinity matrix. Extensive experiments on eight real-world datasets show that our method achieves superior performances over other popular methods.

Determination of Body Parts in Holstein Friesian Cows Comparing Neural Networks and k Nearest Neighbour Classification.

Simple SummaryThe recognition of objects in three dimensional (3D) data is challenging, especially when it comes to the partition of objects into predefined segments. In this study, two machine learning approaches were applied to recognize the body parts head, rump, back, legs and udder of dairy cows in 3D data recorded with Microsoft Kinect V1, for usage in automated exterior evaluation. Five properties of data points were used as features in order to train a k nearest neighbour classifier and a neural network to determine the body part on which the point was located. Both algorithms used for this feature-based approach are computationally faster and more flexible compared to a model-based object detection priorly used for the same purpose. Both methods could be considered successful for the determination of body parts via pixel properties. Reaching high to very high overall accuracies and very small Hamming losses, the k nearest neighbour classification is superior to the neural network which reached medium to high evaluation metrics. However, k nearest neighbour classification is at runtime prone to higher costs regarding computational time and memory, while once trained, the neural network delivers the classification results very quickly. This needs also to be taken into account in the decision of which method should be implemented.Machine learning methods have become increasingly important in animal science, and the success of an automated application using machine learning often depends on the right choice of method for the respective problem and data set. The recognition of objects in 3D data is still a widely studied topic and especially challenging when it comes to the partition of objects into predefined segments. In this study, two machine learning approaches were utilized for the recognition of body parts of dairy cows from 3D point clouds, i.e., sets of data points in space. The low cost off-the-shelf depth sensor Microsoft Kinect V1 has been used in various studies related to dairy cows. The 3D data were gathered from a multi-Kinect recording unit which was designed to record Holstein Friesian cows from both sides in free walking from three different camera positions. For the determination of the body parts head, rump, back, legs and udder, five properties of the pixels in the depth maps (row index, column index, depth value, variance, mean curvature) were used as features in the training data set. For each camera positions, a k nearest neighbour classifier and a neural network were trained and compared afterwards. Both methods showed small Hamming losses (between 0.007 and 0.027 for k nearest neighbour (kNN) classification and between 0.045 and 0.079 for neural networks) and could be considered successful regarding the classification of pixel to body parts. However, the kNN classifier was superior, reaching overall accuracies 0.888 to 0.976 varying with the camera position. Precision and recall values associated with individual body parts ranged from 0.84 to 1 and from 0.83 to 1, respectively. Once trained, kNN classification is at runtime prone to higher costs in terms of computational time and memory compared to the neural networks. The cost vs. accuracy ratio for each methodology needs to be taken into account in the decision of which method should be implemented in the application.