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

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.

Modelling niches of arbitrary shape in genetic algorithms using Niche Linkage in the Dynamic Niche Clustering framework

We present some additions to a fuzzy variable radius niche technique called Dynamic Niche Clustering (DNC) (Gan and Warwick, 1999; 2000; 2001) that enable the identification and creation of niches of arbitrary shape through a mechanism called Niche Linkage. We show that by using this mechanism it is possible to attain better feature extraction from the underlying population.

Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs

This paper describes the recent developments and improvements made to the variable radius niching technique called Dynamic Niche Clustering (DNC). DNC is fitness sharing based technique that employs a separate population of overlapping fuzzy niches with independent radii which operate in the decoded parameter space, and are maintained alongside the normal GA population. We describe a speedup process that can be applied to the initial generation which greatly reduces the complexity of the initial stages. A split operator is also introduced that is designed to counteract the excessive growth of niches, and it is shown that this improves the overall robustness of the technique. Finally, the effect of local elitism is documented and compared to the performance of the basic DNC technique on a selection of 2D test functions. The paper is concluded with a view to future work to be undertaken on the technique.

The Spanish Ambassador and Samuel Daniel's Vision of the Twelve Goddesses: A New Document [with text]

The performance of Samuel Daniel's masque The Vision of the Twelve Goddesses at court on January 8, 1604 took place in the midst of the preliminary negotiations that would lead to the signing of the Anglo-Spanish peace at Somerset House the following August. Philip III sent a special ambassador to England to congratulate James on his accession, and a series of tussles between Juan de Tassis and his French counterpart ensued. As a recently-discovered document in the Archivo General de Simancas reveals, Anna of Denmark intervened personally to insure that de Tassis, and not the Frenchman, attended the masque. This was a clear signal of James and Anna's peace aims, which de Tassis conveyed to the King of Spain; moreover, he enclosed in his dispatch a text of Daniel's masque which he clearly considered both political intelligence and of interest to the theater-loving Hapsburg monarch. The Simancas text of the Daniel masque is a new version, hitherto unknown, which adds to our knowledge of the circumstances in which the first Stuart masque was performed. Here we present a transcription and annotated translation of both de Tassis' letter and the text of the masque he had compiled for Philip III. (B. C.-E. and M. H.)

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.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

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.

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