A Local Cores-Based Hierarchical Clustering Algorithm for Data Sets with Complex Structures

Today, with the development of technology, the decision-making capabilities of machines have also increased. With their high analytical skills, computers can easily catch points and relationships that may escape the human eye. Thanks to these capabilities, machines are also widely used in the field of health. For example, many machine learning techniques developed on cancer prediction have been successfully applied. Early detection of cancer is crucial to survival. In the early diagnosis of cancer, the rates of drug treatment, chemotherapy or radiotherapy that the person will be exposed to are significantly reduced and the patient gets through this process with the least amount of wear and tear. Gene Expression Cancer RNA-Seq Dataset was used in this study. This data set includes gene expression values of 5 cancer types (BRCA, KIRC, LUAD, LUSC, UCEC). DNA sequences in the dataset were analyzed using k-means and hierarchical clustering algorithms, which are unsupervised machine learning methods. The aim of the study is to develop a usable machine learning model for early detection of cancer at the gene level. Adjusted Rand Index (ARI), Silhouette Score, and Accuracy metrics were used to evaluate the analysis results. The rand index calculates similarity between clusters by counting the binaries assigned to clusters. The adjusted Rand Index is a randomly adjusted version of the Rand Index. The silhouette score indicates how well a data point fits within its own set among separated datasets. The accuracy metric is obtained as a percentage of correctly clustered data points divided by all predictions. Different connection methods are used in the hierarchical clustering algorithm. These are 'complete', 'ward', 'average' and 'single'. As a result of the study, the accuracy in the k-means algorithm was 0.990, the Adjusted Rand Index was 0.79, and the Silhouette Score was 0.14. Looking at the hierarchical clustering, ward performed the best of the four linkage methods, with an ARI score of 0.76 and a silhouette score of 0.13. As a result of the study, the accuracy of in the hierarchical clustering algorithm was 0.999.

Clustering is one of the techniques used to obtain useful information from web log file for better understanding of customer behaviour. Two clustering techniques that commonly used are Greedy Hierarchical Item Set-Based Clustering (GHIC) algorithm and Hierarchical Clustering Algorithm (HCA). The algorithms, however, have its weaknesses in terms of processing times and time complexity. This paper proposes a new approach called Hierarchical Pattern-Based Clustering (HPBC) algorithm to improve the processing times based on the difference of mean support values of each cluster. The simulation revealed that the proposed algorithm outperformed the HCA and GHIC up to 100% and 50% respectively, with less time complexity.

There is a strong need for synthetic yet realistic distribution system test data sets that are as diverse, large, and complex to solve as real systems. Such data sets can facilitate the development of advanced algorithms and the assessment of emerging distributed energy resources while avoiding the need to acquire proprietary critical infrastructure or private data. Such synthetic data sets, however, are useful only if they are realistic enough to look and behave similarly to actual systems. This paper presents a comprehensive framework for validating synthetic distribution data sets using a three-pronged statistical, operational, and expert validation approach. It also presents a set of statistical and operational metric targets for achieving realistic data sets based on detailed characterization of more than 10,000 real U.S. utility feeders. The paper demonstrates the use of the proposed validation approach to validate three large-scale synthetic data sets developed by the authors representing Santa Fe, New Mexico; Greensboro, North Carolina; and the San Francisco Bay Area, California.

Empirical studies of some hashing functions

Improved partitioning technique for density cube-based spatio-temporal clustering method

In this paper, new parallel algorithms for single and complete link hierarchical agglomerative clustering are presented. The parallel algorithms have been mapped on a SIMD machine model with a linear interconnection network. The model consists of a linear array of N PE's, where N is the number of patterns, interfaced with a global host machine and the interconnection network provides inter-PE and PE-to-host/host-to-PE communication. The proposed algorithms are faster than previously known algorithms for hierarchical clustering. For clustering a data set with N patterns, using N PE's, the computation time for the single link clustering algorithm is shown to be O(NlogN) and that for the complete link clustering algorithm is shown to be O(N/sup 2/). The parallel algorithms have been verified through simulations on the Intel's iPSC/2 concurrent supercomputer.

We present an algorithm to simulate random sequential adsorption (random "parking") of discs on constant-curvature surfaces: the plane, sphere, hyperboloid, and projective plane, all embedded in three-dimensional space. We simulate complete parkings by explicitly calculating the boundary of the available area in which discs can park and concentrating new points in this area. This makes our algorithm efficient and also provides a diagnostic to determine when each parking is complete, so there is no need to extrapolate data from incomplete parkings to study questions of physical interest. We use our algorithm to study the number distribution and density of discs parked in each space, where for the plane and hyperboloid we consider two different periodic tilings each. We make several notable observations: (i) On the sphere, there is a critical disc radius such the number of discs parked is always exactly four: the random parking is actually deterministic. We prove this statement rigorously, and also show that random parking on the surface of a $d$-dimensional sphere would have deterministic behaviour at the same critical radius. (ii) The average number of parked discs does not always monotonically increase as the disc radius decreases: on the plane (square with periodic boundary conditions), there is an interval of decreasing radius over which the average *decreases*. We give a heuristic explanation for this counterintuitive finding. (iii) As the disc radius shrinks to zero, the density (average fraction of area covered by parked discs) appears to converge to the same constant for all spaces, though it is always slightly larger for a sphere and slightly smaller for a hyperboloid. Therefore, for parkings on a general curved surface we would expect higher local densities in regions of positive curvature and lower local densities in regions of negative curvature.

Two simplified one-dimensional models for waterlike particles are studied. One is referred to as the primitive model which is a simplified version of a model introduced by Ben-Naim in 1992 [Statistical Thermodynamics for Chemists and Biochemists (Plenum, New York, 1992)]. The second, referred to as the primitive cluster model, is a simplified version of the model used by Lovett and Ben-Naim in 1969 [J. Chem. Phys. 51, 3108 (1969)]. The two models are shown to be nearly equivalent and both exhibit some of the most characteristic behavior of liquid water. It is argued that a key feature of the molecular interactions--the correlation between the strong binding energy and low local density--is essential for the manifestation of the anomalous behavior of liquid water. It is also essential for the understanding of the outstanding behavior of liquid water.

We present a novel pairwise clustering method. Given a proximity matrix of pairwise relations (i.e. pairwise similarity or dissimilarity estimates) between data points, our algorithm extracts the two most prominent clusters in the data set. The algorithm, which is completely nonparametric, iteratively employs a two-step transformation on the proximity matrix. The first step of the transformation represents each point by its relation to all other data points, and the second step re-estimates the pairwise distances using a statistically motivated proximity measure on these representations. Using this transformation, the algorithm iteratively partitions the data points, until it finally converges to two clusters. Although the algorithm is simple and intuitive, it generates a complex dynamics of the proximity matrices. Based on this bipartition procedure we devise a hierarchical clustering algorithm, which employs the basic bipartition algorithm in a straightforward divisive manner. The hierarchical clustering algorithm copes with the model validation problem using a general cross-validation approach, which may be combined with various hierarchical clustering methods. We further present an experimental study of this algorithm. We examine some of the algorithm's properties and performance on some synthetic and ‘standard’ data sets. The experiments demonstrate the robustness of the algorithm and indicate that it generates a good clustering partition even when the data is noisy or corrupted.

Clustering is an effective unsupervised machine learning method that can be used as a stand-alone heuristic or as a part of a data mining process. The goal of clustering analysis is to partition data into groups with high intra-cluster association, and low inter-cluster association. Hierarchical clustering requires minimal parameters, has flexibility with similarity measure, and has strong visualization power, all of which makes it ideal for exploratory analysis. Hierarchical clustering is a particular branch of clustering algorithms where the results are not given as partitions, but rather a nested structure, which can represent the ordering among elements within a dataset. The study of the performance of hierarchical structure on time series data is limited. In this paper, we examine the hierarchical structure of time series datasets. The most popular hierarchical structured clustering heuristics include the Hierarchical Agglomerative Clustering, which is distance based; and Ordering Points To Identify the Clustering Structure, which is density based. Both share many similar characteristics and are suitable for time series data processing. We examine the performance of different hierarchical clustering algorithms with time series both internally as well as externally.

This work presents a study about dissimilarity measures for seismic signals, and their relation to clustering in the particular problem of the identification of earthquake focal mechanisms, i.e. the physical phenomena which have generated an earthquake. Starting from the assumption that waveform similarity implies similarity in the focal parameters, important details about them can be determined by studying waveforms related to the wave field produced by earthquakes and recorded by a seismic network. Focal mechanisms identification is currently investigated by clustering of seismic events, using mainly cross-correlation dissimilarity in conjunction with hierarchical clustering algorithm. By the way, it results that such adoptions have not been sufficiently validated. To shed light on this we have studied the cross correlation dissimilarity on simulated seismic signals in conjunction with hierarchical and partitional clustering algorithms, and compared its performance with a newly one recently introduced for the purpose called cumulative shape. In particular, we have properly created synthetic waveforms related to two types of focal mechanisms, showing that the cumulative shape perform better than cross-correlation in the identification of the expected clustering solution.

The matrix factorization (MF) technique has been widely adopted for solving the rating prediction problem in recommender systems. The MF technique utilizes the latent factor model to obtain static user preferences (user latent vectors) and item characteristics (item latent vectors) based on historical rating data. However, in the real world, user preferences are not static but full of dynamics. Though there are several previous works that addressed this time-varying issue of user preferences, it seems (to the best of our knowledge) that none of them are specifically designed for tracking concept drift in individual user preferences . Motivated by this, we develop a temporal MF approach for tracking concept drift in each individual user latent vector. There are two key innovative steps in our approach: 1) we develop a modified stochastic gradient descent method to learn an individual user latent vector at each time step and 2) by Lasso regression, we learn a linear model for the transition of the individual user latent vectors. We test our method on a synthetic data set and several real data sets. In comparison with the original MF, our experimental results show that our temporal method is able to achieve lower root mean square errors (RMSEs) for both the synthetic and real data sets. One interesting finding is that the performance gain in RMSE is mostly from those users who indeed have concept drift in their user latent vectors at the time of prediction. In particular, for the synthetic data set and the Ciao data set, there are quite a few users with that property and the performance gains for these two data sets are roughly 20% and 5%, respectively.

Hierarchical clustering algorithm is a very important method in data mining. The disadvantage of hierarchical clustering lies in the time complexity of the algorithm and the one-way irreversibility of the algorithm. The inaccuracy of the conditions for cluster termination is another major disadvantage of hierarchical clustering. Hierarchical clustering requires the final cluster number. But for most datasets, the number of clusters cannot be known in advance. Therefore, a method is proposed to combine the split-based and agglomeration-based hierarchical clustering algorithms to first quickly and uniformly partition the original dataset, and then make similar partitions adaptively merge based on the partition density and partition distance on the basis of these partitions. In this paper, aiming at these defects of hierarchical clustering, a hierarchical clustering algorithm based on fast and uniform segmentation is proposed.

The traditional stator single-phase-to-ground fault protective schemes are hard to completely satisfy the requirement of selectivity for bus-connected Powerformers. In order to overcome the aforementioned problem, a new stator single-phase-to-ground fault protective scheme based on the hierarchical clustering algorithm is proposed in this paper. The direction and magnitude of zero-sequence current and leakage current are discussed and selected as feature vectors. Then, the data set are divided into two groups by hierarchical clustering algorithm, and cluster center of each group is calculated. Finally, the space relative distance among detected pattern and two cluster centers is calculated to discriminate the faulty Powerformer. The fundamental component and the third harmonic component of the data set are combined to realize 100% coverage of fault detection for the stator windings of Powerformer. Simulation results have shown that, under different fault conditions, the new scheme can distinguish internal faults from external faults reliably, and can detect in which machine a stator single-phase-to-ground fault is occurring even if the fault resistance is at 5 kΩ.

Intrusion detection systems based on a hybrid approach have attracted considerable interest from researchers. Hybrid classifiers are able to provide improved detection accuracy, but usually have a complex structure and high computational costs. In this research, we propose a new and easy-to-implement hybrid learning method, named distance sum-based support vector machine (DSSVM), which can be used as an effective intrusion detection model. In DSSVM, we introduce the distance sum, a correlation between each data sample and cluster centers. Consider a data set represented by n-dimensional feature vectors, each distance sum for a data sample in the data set is obtained from the distances between this data sample and k?1 of k cluster centers found by a clustering algorithm. A new data set representing the features of these distance sums is formed and used to train a support vector machine classifier. By applying DSSVM to the KDD'99 data set, our experimental results show that the proposed hybrid method performs well in both detection performance and computational cost, which suggests it is a competitive candidate for intrusion detection. In addition, we also use six databases with different numbers of features, classes, and data samples to further validate the effectiveness of our method for some other pattern recognition problems.