Robust initialisation of Gaussian radial basis function networks using partitioned k-means clustering

Radial basis function networks can be trained quickly using linear optimisation once centres and other associated parameters have been initialised. The authors propose a small adjustment to a well accepted initialisation algorithm which improves the network accuracy over a range of problems. The algorithm is described and results are presented.

Epidemic K-Means clustering

The K-Means algorithm for cluster analysis is one of the most influential and popular data mining methods. Its straightforward parallel formulation is well suited for distributed memory systems with reliable interconnection networks. However, in large-scale geographically distributed systems the straightforward parallel algorithm can be rendered useless by a single communication failure or high latency in communication paths. This work proposes a fully decentralised algorithm (Epidemic K-Means) which does not require global communication and is intrinsically fault tolerant. The proposed distributed K-Means algorithm provides a clustering solution which can approximate the solution of an ideal centralised algorithm over the aggregated data as closely as desired. A comparative performance analysis is carried out against the state of the art distributed K-Means algorithms based on sampling methods. The experimental analysis confirms that the proposed algorithm is a practical and accurate distributed K-Means implementation for networked systems of very large and extreme scale.

Fault tolerant decentralised K-Means clustering for asynchronous large-scale networks

The K-Means algorithm for cluster analysis is one of the most influential and popular data mining methods. Its straightforward parallel formulation is well suited for distributed memory systems with reliable interconnection networks, such as massively parallel processors and clusters of workstations. However, in large-scale geographically distributed systems the straightforward parallel algorithm can be rendered useless by a single communication failure or high latency in communication paths. The lack of scalable and fault tolerant global communication and synchronisation methods in large-scale systems has hindered the adoption of the K-Means algorithm for applications in large networked systems such as wireless sensor networks, peer-to-peer systems and mobile ad hoc networks. This work proposes a fully distributed K-Means algorithm (EpidemicK-Means) which does not require global communication and is intrinsically fault tolerant. The proposed distributed K-Means algorithm provides a clustering solution which can approximate the solution of an ideal centralised algorithm over the aggregated data as closely as desired. A comparative performance analysis is carried out against the state of the art sampling methods and shows that the proposed method overcomes the limitations of the sampling-based approaches for skewed clusters distributions. The experimental analysis confirms that the proposed algorithm is very accurate and fault tolerant under unreliable network conditions (message loss and node failures) and is suitable for asynchronous networks of very large and extreme scale.

Mean-tracking clustering algorithm for radial basis function centre selection

Radial basis functions can be combined into a network structure that has several advantages over conventional neural network solutions. However, to operate effectively the number and positions of the basis function centres must be carefully selected. Although no rigorous algorithm exists for this purpose, several heuristic methods have been suggested. In this paper a new method is proposed in which radial basis function centres are selected by the mean-tracking clustering algorithm. The mean-tracking algorithm is compared with k means clustering and it is shown that it achieves significantly better results in terms of radial basis function performance. As well as being computationally simpler, the mean-tracking algorithm in general selects better centre positions, thus providing the radial basis functions with better modelling accuracy

Neural network basis function center selection using cluster analysis

This paper deals with the selection of centres for radial basis function (RBF) networks. A novel mean-tracking clustering algorithm is described as a way in which centers can be chosen based on a batch of collected data. A direct comparison is made between the mean-tracking algorithm and k-means clustering and it is shown how mean-tracking clustering is significantly better in terms of achieving an RBF network which performs accurate function modelling.

Extreme wind storms over Europe in present and future climate: a cluster analysis approach

Boreal winter wind storm situations over Central Europe are investigated by means of an objective cluster analysis. Surface data from the NCEP-Reanalysis and ECHAM4/OPYC3-climate change GHG simulation (IS92a) are considered. To achieve an optimum separation of clusters of extreme storm conditions, 55 clusters of weather patterns are differentiated. To reduce the computational effort, a PCA is initially performed, leading to a data reduction of about 98 %. The clustering itself was computed on 3-day periods constructed with the first six PCs using "k-means" clustering algorithm. The applied method enables an evaluation of the time evolution of the synoptic developments. The climate change signal is constructed by a projection of the GCM simulation on the EOFs attained from the NCEP-Reanalysis. Consequently, the same clusters are obtained and frequency distributions can be compared. For Central Europe, four primary storm clusters are identified. These clusters feature almost 72 % of the historical extreme storms events and add only to 5 % of the total relative frequency. Moreover, they show a statistically significant signature in the associated wind fields over Europe. An increased frequency of Central European storm clusters is detected with enhanced GHG conditions, associated with an enhancement of the pressure gradient over Central Europe. Consequently, more intense wind events over Central Europe are expected. The presented algorithm will be highly valuable for the analysis of huge data amounts as is required for e.g. multi-model ensemble analysis, particularly because of the enormous data reduction.

Method for exploratory cluster analysis and visualisation of single-trial ERP ensembles

Background: The validity of ensemble averaging on event-related potential (ERP) data has been questioned, due to its assumption that the ERP is identical across trials. Thus, there is a need for preliminary testing for cluster structure in the data. New method: We propose a complete pipeline for the cluster analysis of ERP data. To increase the signalto-noise (SNR) ratio of the raw single-trials, we used a denoising method based on Empirical Mode Decomposition (EMD). Next, we used a bootstrap-based method to determine the number of clusters, through a measure called the Stability Index (SI). We then used a clustering algorithm based on a Genetic Algorithm (GA)to define initial cluster centroids for subsequent k-means clustering. Finally, we visualised the clustering results through a scheme based on Principal Component Analysis (PCA). Results: After validating the pipeline on simulated data, we tested it on data from two experiments – a P300 speller paradigm on a single subject and a language processing study on 25 subjects. Results revealed evidence for the existence of 6 clusters in one experimental condition from the language processing study. Further, a two-way chi-square test revealed an influence of subject on cluster membership.

Objective determination of the extratropical transition of tropical cyclones in the Northern Hemisphere

Extratropical transition (ET) has eluded objective identification since the realisation of its existence in the 1970s. Recent advances in numerical, computational models have provided data of higher resolution than previously available. In conjunction with this, an objective characterisation of the structure of a storm has now become widely accepted in the literature. Here we present a method of combining these two advances to provide an objective method for defining ET. The approach involves applying K-means clustering to isolate different life-cycle stages of cyclones and then analysing the progression through these stages. This methodology is then tested by applying it to five recent years from the European Centre of Medium-Range Weather Forecasting operational analyses. It is found that this method is able to determine the general characteristics for ET in the Northern Hemisphere. Between 2008 and 2012, 54% (±7, 32 of 59) of Northern Hemisphere tropical storms are estimated to undergo ET. There is great variability across basins and time of year. To fully capture all the instances of ET is necessary to introduce and characterise multiple pathways through transition. Only one of the three transition types needed has been previously well-studied. A brief description of the alternate types of transitions is given, along with illustrative storms, to assist with further study

Understanding climate change projections for precipitation over western Europe with a weather typing approach

Precipitation over western Europe (WE) is projected to increase (decrease) roughly northward (equatorward) of 50°N during the 21st century. These changes are generally attributed to alterations in the regional large-scale circulation, e.g., jet stream, cyclone activity, and blocking frequencies. A novel weather typing within the sector (30°W–10°E, 25–70°N) is used for a more comprehensive dynamical interpretation of precipitation changes. A k-means clustering on daily mean sea level pressure was undertaken for ERA-Interim reanalysis (1979–2014). Eight weather types are identified: S1, S2, S3 (summertime types), W1, W2, W3 (wintertime types), B1, and B2 (blocking-like types). Their distinctive dynamical characteristics allow identifying the main large-scale precipitation-driving mechanisms. Simulations with 22 Coupled Model Intercomparison Project 5 models for recent climate conditions show biases in reproducing the observed seasonality of weather types. In particular, an overestimation of weather type frequencies associated with zonal airflow is identified. Considering projections following the (Representative Concentration Pathways) RCP8.5 scenario over 2071–2100, the frequencies of the three driest types (S1, B2, and W3) are projected to increase (mainly S1, +4%) in detriment of the rainiest types, particularly W1 (−3%). These changes explain most of the precipitation projections over WE. However, a weather type-independent background signal is identified (increase/decrease in precipitation over northern/southern WE), suggesting modifications in precipitation-generating processes and/or model inability to accurately simulate these processes. Despite these caveats in the precipitation scenarios for WE, which must be duly taken into account, our approach permits a better understanding of the projected trends for precipitation over WE.

Scalability of efficient parallel K-Means

Clustering is defined as the grouping of similar items in a set, and is an important process within the field of data mining. As the amount of data for various applications continues to increase, in terms of its size and dimensionality, it is necessary to have efficient clustering methods. A popular clustering algorithm is K-Means, which adopts a greedy approach to produce a set of K-clusters with associated centres of mass, and uses a squared error distortion measure to determine convergence. Methods for improving the efficiency of K-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting a more efficient data structure, notably a multi-dimensional binary search tree (KD-Tree) to store either centroids or data points. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient K-Means techniques in parallel computational environments. In this work, we provide a parallel formulation for the KD-Tree based K-Means algorithm and address its load balancing issues.

Soft topographic map for clustering and classification of bacteria

In this work a new method for clustering and building a topographic representation of a bacteria taxonomy is presented. The method is based on the analysis of stable parts of the genome, the so-called “housekeeping genes”. The proposed method generates topographic maps of the bacteria taxonomy, where relations among different type strains can be visually inspected and verified. Two well known DNA alignement algorithms are applied to the genomic sequences. Topographic maps are optimized to represent the similarity among the sequences according to their evolutionary distances. The experimental analysis is carried out on 147 type strains of the Gammaprotebacteria class by means of the 16S rRNA housekeeping gene. Complete sequences of the gene have been retrieved from the NCBI public database. In the experimental tests the maps show clusters of homologous type strains and present some singular cases potentially due to incorrect classification or erroneous annotations in the database.

Space partitioning for scalable K-means

K-Means is a popular clustering algorithm which adopts an iterative refinement procedure to determine data partitions and to compute their associated centres of mass, called centroids. The straightforward implementation of the algorithm is often referred to as `brute force' since it computes a proximity measure from each data point to each centroid at every iteration of the K-Means process. Efficient implementations of the K-Means algorithm have been predominantly based on multi-dimensional binary search trees (KD-Trees). A combination of an efficient data structure and geometrical constraints allow to reduce the number of distance computations required at each iteration. In this work we present a general space partitioning approach for improving the efficiency and the scalability of the K-Means algorithm. We propose to adopt approximate hierarchical clustering methods to generate binary space partitioning trees in contrast to KD-Trees. In the experimental analysis, we have tested the performance of the proposed Binary Space Partitioning K-Means (BSP-KM) when a divisive clustering algorithm is used. We have carried out extensive experimental tests to compare the proposed approach to the one based on KD-Trees (KD-KM) in a wide range of the parameters space. BSP-KM is more scalable than KDKM, while keeping the deterministic nature of the `brute force' algorithm. In particular, the proposed space partitioning approach has shown to overcome the well-known limitation of KD-Trees in high-dimensional spaces and can also be adopted to improve the efficiency of other algorithms in which KD-Trees have been used.

Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

Efficient group communication for large-scale parallel clustering

Global communication requirements and load imbalance of some parallel data mining algorithms are the major obstacles to exploit the computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication cost in iterative parallel data mining algorithms. In particular, the analysis focuses on one of the most influential and popular data mining methods, the k-means algorithm for cluster analysis. The straightforward parallel formulation of the k-means algorithm requires a global reduction operation at each iteration step, which hinders its scalability. This work studies a different parallel formulation of the algorithm where the requirement of global communication can be relaxed while still providing the exact solution of the centralised k-means algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real world distributed applications or can be induced by means of multi-dimensional binary search trees. The approach can also be extended to accommodate an approximation error which allows a further reduction of the communication costs.

Serial clustering of extratropical cyclones

The clustering in time (seriality) of extratropical cyclones is responsible for large cumulative insured losses in western Europe, though surprisingly little scientific attention has been given to this important property. This study investigates and quantifies the seriality of extratropical cyclones in the Northern Hemisphere using a point-process approach. A possible mechanism for serial clustering is the time-varying effect of the large-scale flow on individual cyclone tracks. Another mechanism is the generation by one parent cyclone of one or more offspring through secondary cyclogenesis. A long cyclone-track database was constructed for extended October March winters from 1950 to 2003 using 6-h analyses of 850-mb relative vorticity derived from the NCEP NCAR reanalysis. A dispersion statistic based on the varianceto- mean ratio of monthly cyclone counts was used as a measure of clustering. It reveals extensive regions of statistically significant clustering in the European exit region of the North Atlantic storm track and over the central North Pacific. Monthly cyclone counts were regressed on time-varying teleconnection indices with a log-linear Poisson model. Five independent teleconnection patterns were found to be significant factors over Europe: the North Atlantic Oscillation (NAO), the east Atlantic pattern, the Scandinavian pattern, the east Atlantic western Russian pattern, and the polar Eurasian pattern. The NAO alone is not sufficient for explaining the variability of cyclone counts in the North Atlantic region and western Europe. Rate dependence on time-varying teleconnection indices accounts for the variability in monthly cyclone counts, and a cluster process did not need to be invoked.