Single-link Clustering Method Research Articles

Cluster-based foreshock discrimination model with flexible time horizon and mainshock magnitudes

Foreshock detection before mainshock occurrence is an important challenge limiting the short-term forecasts of large earthquakes. Various models for predicting mainshocks based on discrimination of foreshocks activity have been proposed, but many of them work in restricted scenarios and neglect foreshocks and mainshocks out of their scope. In disaster prevention, it is often necessary to change the forecast period and the magnitude of target mainshocks. This paper presents a cluster-based statistical discrimination of foreshocks which is applicable all over Japan and adjustable with respect to forecasting time span and mainshock magnitudes. Using the single-link clustering method, the model updates the expanding seismic clusters and determines in real time the probabilities that larger subsequent events will occur. The foreshock clusters and the others show different trends of certain feature statistics with respect to their magnitudes and spatiotemporal distances. Based on those features and the epicentral location, a nonlinear logistic regression model is used to evaluate the probabilities that growing seismic clusters are foreshocks that will trigger mainshocks within 30 days. The log of odds is estimated between the foreshock clusters and other clusters for respective feature values as nonlinear spline functions from a Japanese hypocenter catalog for the period 1926–1999. Based on the estimated odds functions, foreshock clusters tend to have smaller differences in their two largest magnitudes, shorter time durations, and slightly longer epicentral distances within the individual clusters. Given a potential foreshock cluster, its mainshock magnitude can be predicted by the Gutenberg–Richter law over the largest foreshock magnitude. The timing of mainshock occurrences from foreshocks is also predicted by multiplying the portion of mainshocks within a shorter span from those within 30 days by the evaluated foreshock probabilities. The predictive performance of our model is validated by the holdout method using a Japanese hypocenter catalog before and after 2000. The evaluated foreshock probabilities are roughly consistent with the actual portion of foreshocks in the validation catalog and could serve as an alert for large mainshocks.

Assessment of lake water quality using multivariate statistical techniques and chlorophyll-nutrient relationships: a case study of the Göksu Lake

This study aimed to evaluate the water quality of the Goksu Lake, which is located in Ankara, Turkey. For this purpose, multivariate statistical analyses, namely, principal component analysis/factor analysis, regression analysis and cluster analysis, and linear regression analysis, were used to determine the relationship between the nutrients. In order to evaluate the status of the lake water quality, the limiting nutrient element was determined using the total nitrogen to total phosphorus ratio (TN/TP). The water quality parameters were selected as pH, turbidity, chemical oxygen demand (COD), suspended solids (SS), dissolved oxygen (DO), biochemical oxygen demand (BOD), total nitrogen (TN), chlorophyll-a (Chl-a), total phosphorus (TP), color, fecal coliform (FC), and total coliform (TC) count. For the cluster analysis, the single-link clustering method using Euclidean distance criteria was preferred. Cluster I consisted of sites 1, 2, 3, and 4, while cluster II consisted of site 5. Two factors were obtained as a result of the factor analysis. These two factors explained 88.2% of the total variance. The first factor clarifies the 45.62% of total variance has pH, COD, DO, TN, TP, color, BOD, and TC strong positive load value. This factor was thought to represent domestic wastewater. The second factor that affects water quality clarifies the 42.54% of total variance has turbidity, SS, Chl-a, and FC strong positive load value. This factor was thought to represent the microbiological activities that occurred as a result of the mixing of wastewaters and also pollution accumulating in the bottom sediment. The nutrient-limiting elements in the water lake quality are determined with TN/TP ratio. Accordingly, the lake water quality was determined as N-limited at two points and co-limited at three points. The relationship between the nutrients was evaluated using regression analysis.

Damage evolution analysis of coal samples under cyclic loading based on single-link cluster method

In this paper, the acoustic emission (AE) response of coal samples under cyclic loading is measured. The results show that there is good positive relation between AE parameters and stress. The AE signal of coal samples under cyclic loading exhibits an obvious Kaiser Effect. The single-link cluster (SLC) method is applied to analyze the spatial evolution characteristics of AE events and the damage evolution process of coal samples. It is found that a subset scale of the SLC structure becomes smaller and smaller when the number of cyclic loading increases, and there is a negative linear relationship between the subset scale and the degree of damage. The spatial correlation length ξ of an SLC structure is calculated. The results show that ξ fluctuates around a certain value from the second cyclic loading process to the fifth cyclic loading process, but spatial correlation length ξ clearly increases in the sixth loading process. Based on the criterion of microcrack density, the coal sample failure process is the transformation from small-scale damage to large-scale damage, which is the reason for changes in the spatial correlation length. Through a systematic analysis, the SLC method is an effective method to research the damage evolution process of coal samples under cyclic loading, and will provide important reference values for studying coal bursts.

Fractal characteristics of acoustic emission events based on single-link cluster method during uniaxial loading of rock

A rock mechanics test system and an acoustic emission (AE) test system have been employed to conduct AE event location experiments on sandstone samples under uniaxial compression. According to the single-link cluster (SLC) method, an SLC structure is set up. Each single link is defined as a spatial vector, which can be calculated based on the spatial coordinates of the nearest neighbor of a certain AE event minus the spatial coordinates of this event. Based on the basic theory of fractal geometry, a spherical surface-covering method is proposed herein to analyze the fractal property of spatial vector direction in an SLC structure. To study the change in fractal dimension over time, a sliding event window is used. The results show that the window length and slide step length have little effect on the change in trend of fractal dimension. Before buckling failure of a rock sample, the fractal dimension curve shows a clear downward trend. The reason for the change in fractal dimension is related to the generation mechanism of AE events. Therefore, a clear decrease in fractal dimension can be taken as precursor to rock buckling failure under uniaxial compression. This research provides a new method for studying the evolution process of rock buckling failure and has important significance regarding the monitoring of rock stability and early warning of rock burst.

Effective data summarization for hierarchical clustering in large datasets

Cluster analysis in a large dataset is an interesting challenge in many fields of Science and Engineering. One important clustering approach is hierarchical clustering, which outputs hierarchical (nested) structures of a given dataset. The single-link is a distance-based hierarchical clustering method, which can find non-convex (arbitrary)-shaped clusters in a dataset. However, this method cannot be used for clustering large dataset as this method either keeps entire dataset in main memory or scans dataset multiple times from secondary memory of the machine. Both of them are potentially severe problems for cluster analysis in large datasets. One remedy for both problems is to create a summary of a given dataset efficiently, and the summary is subsequently used to speed up clustering methods in large datasets. In this paper, we propose a summarization scheme termed data sphere (ds) to speed up single-link clustering method in large datasets. The ds utilizes sequential leaders clustering method to collect important statistics of a given dataset. The single-link method is modified to work with ds. Modified clustering method is termed as summarized single-link (SSL). The SSL method is considerably faster than the single-link method applied directly to the dataset, and clustering results produced by SSL method are close to the clustering results produced by single-link method. The SSL method outperforms single-link using data bubble (summarization scheme) both in terms of clustering accuracy and computation time. To speed up proposed summarization scheme, a technique is introduced to reduce a large number of distance computations in leaders method. Experimental studies demonstrate effectiveness of the proposed summarization scheme for large datasets.

Location of acoustic emission events and changes of spatial correlation length in rock during uniaxial compression

Acoustic emission (AE) location technique was applied to study the three‐dimensional spatial evolutionary process of microcracks initiation, propagation and coalescence during rock failure process under uniaxial loading. Changes of spatial correlation length of AE events during fracture process of granite and marble specimens were acquired using the single link cluster method. Stiffness obtained by the moving point regression technique can clearly reflect the plastic phase. Two factors may influence the change of spatial correlation length in plastic phase: stress release, which leads to a decrease in correlation length, and stress redistribution, which leads to an increase in correlation length. During the rock fracture process, long range correlations are established by the redistribution of stress from smaller to larger scales. In this regard, the change of spatial correlation length reflects the long range transfer of stress field. The different characteristics of spatial correlation length during elastic and plastic phases may be used as an indicator for predicting failure of rock.

Temporal and Spatial Statistical Characteristics of Earthquakes in China by Single-Link Cluster Method

[1] A procedure of single-link cluster (SLC) analysis was provided according to the principle of minimal spanning tree, and applied to 9,556 earthquakes with mb of 4.0 or greater, occurred in China from January 1970 to March 1998. We have discussed three statistical characteristics of the resulting space-time SLC frame. One describes the distribution of clusters in the frame under different cutoff length, and if we choose about 70km as the cutoff length, the distribution of clusters obeys power decay law. The other two are for the distributions of cumulative lengths and frequency of links, and they reveal the following features for the total frame: (a)The cumulative distribution of lengths can be fit by Weibull function very well; (b)The cumulative distribution of frequency can also be fit by the same function, but failed to pass the Komogorov test; However, it successfully passed that test after removing the clustered pre-shocks and after-shocks from the catalog.

Copper(II) six-membered rings: a molecular mechanics and cluster analysis

An agglomerative, hierarchical single-link clustering method was used to separate the different conformations of all the saturated six-membered copper(II) rings found in the Cambridge Structure Database. Three percent of all rings were found to be in the sofa and twist-boat conformations, one percent were boats and the rest chairs. There was no correlation between the coordination geometry of the copper(II) ion and the conformation of the six-membered ring. Changing the ligating atoms from nitrogen to sulfur had no effect on the conformational distribution of the six-membered rings. Molecular mechanics calculations were used to establish the reasons why high energy non-chair conformations wre adopted in certain cases.

Cluster and Molecular Mechanical Analysis of the Conformations of All Six-Membered Cobalt(III) Diamine Rings in the Cambridge Structure Database

An agglomerative, single-link clustering method was used to separate all of the cobalt(III) diamine six-membered rings found in the Cambridge Structural Database into chair, boat, unsymmetric twist-boat, and δ and λ twist-boat conformations. Of all of the six-membered rings analyzed, 80% adopt the energetically favored chair conformation. Twist boats are favored for steric reasons, while the high-energy boats are only found when the six-membered ring is structurally prevented from adopting a chair or twist-boat conformation. This is the first inorganic cluster analysis to published. The conformations of all of the nonchairs, except one, could be found by generating all of the possible combinations of the different idealized conformations of five- and six-membered rings and minimizing them.

Single-link characteristics of a mode-seeking clustering algorithm

This paper demonstrates the similarity between the single-link clustering method and a recently proposed clustering method based on mode-seeking. A user of clustering algorithms should be aware of this fact when attempting to assess clusters from different points of view.

Document clustering: An evaluation of some experiments with the cranfield 1400 collection

The single-link cluster method is used to construct a hierarchic classification for the 1400 documents in the Cranfield test collection. A variety of retrieval strategies applied to this hierarchy are evaluated in terms of effectiveness and efficiency. Comparisons are made between our results and those of similar experiments in document clustering on the Smart project.

SLINK: An optimally efficient algorithm for the single-link cluster method

SLINK: An optimally efficient algorithm for the single-link cluster method