Abstract
Online learning algorithms which address fast data streams should process examples at the rate they arrive, using a single scan of data and fixed memory, maintaining a decision model at any time and being able to adapt the model to the most recent data. These features yield the necessity of using approximate models. One problem that usually arises with approximate models is the definition of a minimum number of observations necessary to assure convergence, which implies a high risk since the system may have to decide based only on a small subset of the entire data. One approach is to apply techniques based on the Hoeffding bound to enforce decisions with a confidence level. In divisive clustering of time series, the goal is to find clusters of similar time series over time. In online approaches there are two decisions to make: when to split and how to assign variables to new clusters. We can define a confidence level to both the decision of splitting and the assignment of data variables to new clusters. Previous works have already addressed confident decisions on the moment of split. Our proposal is to include a confidence level to the assignment process. When a split point is reported, creating two new clusters, we can directly assign points which are confidently closer to one cluster than the other, having a different strategy for those variables which do not satisfy the confidence level. In this paper we propose to assign the unsure variables to a third cluster. Experimental evaluation is presented in the context of a recently proposed hierarchical algorithm, assessing the advantages of the proposal, revealing also advantages on memory usage reduction and processing speed. Although this proposal is evaluated under the scope of an existent method, it can be generalized to any divisive procedure.

Abstract
This paper addresses the space-time change detection problem in climate data over the Iberian Peninsula using a 50 years dataset. The data were analyzed concerning the temporal and geographical information, using the following methodology: information about space-time drifts in climate data was obtained by applying a change detection algorithm on all the temporal data available for each physical location considered in this study; the performance and the robustness of this algorithm were then assessed by the McNemar nonparametric statistical test on cluster structures; geographical correlations were inferred using visualization tools and graphical representations of data. Most of the space-temporal drifts detected by the algorithm were confirmed by the results of the McNemar test and are in accordance with visual and graphical representations, supporting the advantage of using inter-disciplinary methods. This analysis also shows that there are locations which do not reveal any change along all the observed years.

Abstract
In ubiquitous streaming data sources, such as sensor networks, clustering nodes by the data they produce is an important problem that gives insights on the phenomenon being monitored by such networks. However, if these techniques require data to be gathered centrally, communication and storage requirements are often unbounded. The goal of this paper is to assess the feasibility of computing local clustering at each node, using only neighbors' centroids, as an approximation of the global clustering computed by a centralized process. A local algorithm is proposed to perform clustering of sensors based on the moving average of each node's data over time: the moving average of each node is approximated using memory-less fading average; clustering is based on the furthest point algorithm applied to the centroids computed by the node's direct neighbors. The algorithm was evaluated on a state-of-the-art sensor network simulator, measuring the agreement between local and global clustering. Experimental work on synthetic data with spherical Gaussian clusters is consistently analyzed for different network size, number of clusters and cluster overlapping. Results show a high level of agreement between each node's clustering definitions and the global clustering definition, with special emphasis on separability agreement. Overall, local approaches are able to keep a good approximation of the global clustering, improving privacy among nodes, and decreasing communication and computation load in the network. Hence, the basic requirements for distributed clustering of streaming data sensors recommend that clustering on these settings should be performed locally. © 2011 ACM.

Abstract

Abstract

Abstract
Several predictive systems are nowadays vital for operations and decision support. The quality of these systems is most of the time defined by their average accuracy which has low or no information at all about the estimated error of each individual prediction. In these cases, users should be allowed to associate a measure of reliability to each prediction. However, with the advent of data streams, batch state-of-the-art reliability estimates need to be redefined. In this chapter we adapt and evaluate five empirical measures for online reliability estimation of individual predictions: similarity-based (k-NN) error, local sensitivity (bias and variance) and online bagging predictions (bias and variance). Evaluation is performed with a neural network base model on two different problems, with results showing that online bagging and k-NN estimates are consistently correlated with the error of the base model. Furthermore, we propose an approach for correcting individual predictions based on the CNK reliability estimate. Evaluation is done on a real-world problem (prediction of the electricity load for a selected European geographical region), using two different regression models: neural network and the k nearest neighbors algorithm. Comparison is performed with corrections based on the Kalman filter. The results show that our method performs better than the Kalman filter, significantly improving the original predictions to more accurate values.