Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

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.

Environmental variables and multivariate seabed classification maps via k means clustering of Potter Cove, Antarctica, link to input and result files in GeoTIFF format

This study subdivides the Potter Cove, King George Island, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis includes in total 42 different environmental variables, interpolated based on samples taken during Australian summer seasons 2010/2011 and 2011/2012. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared and the most reasonable method has been applied. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested and 4, 7, 10 as well as 12 were identified as reasonable numbers for clustering the Potter Cove. Especially the results of 10 and 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.

Reliability of vegetation community information derived using decorana ordination and fuzzy c-means clustering

Descriptions of vegetation communities are often based on vague semantic terms describing species presence and dominance. For this reason, some researchers advocate the use of fuzzy sets in the statistical classification of plant species data into communities. In this study, spatially referenced vegetation abundance values collected from Greek phrygana were analysed by ordination (DECORANA), and classified on the resulting axes using fuzzy c-means to yield a point data-set representing local memberships in characteristic plant communities. The fuzzy clusters matched vegetation communities noted in the field, which tended to grade into one another, rather than occupying discrete patches. The fuzzy set representation of the community exploited the strengths of detrended correspondence analysis while retaining richer information than a TWINSPAN classification of the same data. Thus, in the absence of phytosociological benchmarks, meaningful and manageable habitat information could be derived from complex, multivariate species data. We also analysed the influence of the reliability of different surveyors' field observations by multiple sampling at a selected sample location. We show that the impact of surveyor error was more severe in the Boolean than the fuzzy classification. © 2007 Springer.

What to do when K-means clustering fails:a simple yet principled alternative algorithm

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

QK-Means: A clustering technique based on community detection and K-Means for deployment of cluster head nodes

Wireless Sensor Networks (WSN) are a special kind of ad-hoc networks that is usually deployed in a monitoring field in order to detect some physical phenomenon. Due to the low dependability of individual nodes, small radio coverage and large areas to be monitored, the organization of nodes in small clusters is generally used. Moreover, a large number of WSN nodes is usually deployed in the monitoring area to increase WSN dependability. Therefore, the best cluster head positioning is a desirable characteristic in a WSN. In this paper, we propose a hybrid clustering algorithm based on community detection in complex networks and traditional K-means clustering technique: the QK-Means algorithm. Simulation results show that QK-Means detect communities and sub-communities thus lost message rate is decreased and WSN coverage is increased. © 2012 IEEE.

Algorithms for time series clustering applied to biomedical signals

Thesis submitted in the fulfillment of the requirements for the Degree of Master in Biomedical Engineering

Algorithms for information extraction and signal annotation on long-term biosignals using clustering techniques

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Aggregation invariance in general clustering approaches

General clustering deals with weighted objects and fuzzy memberships. We investigate the group- or object-aggregation-invariance properties possessed by the relevant functionals (effective number of groups or objects, centroids, dispersion, mutual object-group information, etc.). The classical squared Euclidean case can be generalized to non-Euclidean distances, as well as to non-linear transformations of the memberships, yielding the c-means clustering algorithm as well as two presumably new procedures, the convex and pairwise convex clustering. Cluster stability and aggregation-invariance of the optimal memberships associated to the various clustering schemes are examined as well.

Management zones using fuzzy clustering based on spatial-temporal variability of soil and corn yield

Clustering soil and crop data can be used as a basis for the definition of management zones because the data are grouped into clusters based on the similar interaction of these variables. Therefore, the objective of this study was to identify management zones using fuzzy c-means clustering analysis based on the spatial and temporal variability of soil attributes and corn yield. The study site (18 by 250-m in size) was located in Jaboticabal, São Paulo/Brazil. Corn yield was measured in one hundred 4.5 by 10-m cells along four parallel transects (25 observations per transect) over five growing seasons between 2001 and 2010. Soil chemical and physical attributes were measured. SAS procedure MIXED was used to identify which variable(s) most influenced the spatial variability of corn yield over the five study years. Basis saturation (BS) was the variable that better related to corn yield, thus, semivariograms models were fitted for BS and corn yield and then, data values were krigged. Management Zone Analyst software was used to carry out the fuzzy c-means clustering algorithm. The optimum number of management zones can change over time, as well as the degree of agreement between the BS and corn yield management zone maps. Thus, it is very important take into account the temporal variability of crop yield and soil attributes to delineate management zones accurately.