Detection of elliptical shapes via cross-entropy clustering

The problem of finding elliptical shapes in an image will be considered. We discuss the solution which uses cross-entropy clustering. The proposed method allows the search for ellipses with predefined sizes and position in the space. Moreover, it works well for search of ellipsoids in higher dimensions

Fuzzy cluster validation using the partition negentropy criterion

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-04277-5_24Proceedings of the 19th International Conference, Limassol, Cyprus, September 14-17, 2009We introduce the Partition Negentropy Criterion (PNC) for cluster validation. It is a cluster validity index that rewards the average normality of the clusters, measured by means of the negentropy, and penalizes the overlap, measured by the partition entropy. The PNC is aimed at finding well separated clusters whose shape is approximately Gaussian. We use the new index to validate fuzzy partitions in a set of synthetic clustering problems, and compare the results to those obtained by the AIC, BIC and ICL criteria. The partitions are obtained by fitting a Gaussian Mixture Model to the data using the EM algorithm. We show that, when the real clusters are normally distributed, all the criteria are able to correctly assess the number of components, with AIC and BIC allowing a higher cluster overlap. However, when the real cluster distributions are not Gaussian (i.e. the distribution assumed by the mixture model) the PNC outperforms the other indices, being able to correctly evaluate the number of clusters while the other criteria (specially AIC and BIC) tend to overestimate it.This work has been partially supported with funds from MEC BFU2006-07902/BFI, CAM S-SEM-0255-2006 and CAM/UAM project CCG08-UAM/TIC-442

From energy behaviours to lifestyles: Contribution of behavioural archetypes to the description of energy consumption patterns in the residential sector

International audienceMany studies emphasise that household energy behaviour is a key determinant of domestic energy consumption, but few highlight the fact that it is fundamentally associated with lifestyle and housing context. Existing studies that address this issue perform clustering but use only restricted datasets and rarely describe the associated households and housings. In this study, we develop an original methodology to construct behavioural archetypes from qualitative and quantitative variables, opening up perspectives for a wider and more transparent use of survey data. The clustering is performed with 35 variables describing hygiene, food, heating, lighting and leisure practices and housing occupation. Seven homogeneous archetypes of domestic behaviours were constructed from a database describing 1363 households in the Ile de France region. The analysis of the related household profiles shows that the behavioural archetypes are related to specific housing contexts and energy consumption levels. The work also invites to stand back from the variables usually mobilized, such as income or tenure status, and used for the conception of targeted policies. In particular, the work highlights the value of the household life cycle in constructing a typology suitable for policy makers. Finally, this work opens up avenues for the construction of archetypal energy consumption models

Modeling and clustering water demand patterns from real-world smart meter data

Nowadays, drinking water utilities need an acute comprehension of the water demand on their distribution network, in order to efficiently operate the optimization of resources, manage billing and propose new customer services. With the emergence of smart grids, based on automated meter reading (AMR), a better understanding of the consumption modes is now accessible for smart cities with more granularities. In this context, this paper evaluates a novel methodology for identifying relevant usage profiles from the water consumption data produced by smart meters. The methodology is fully data-driven using the consumption time series which are seen as functions or curves observed with an hourly time step. First, a Fourier-based additive time series decomposition model is introduced to extract seasonal patterns from time series. These patterns are intended to represent the customer habits in terms of water consumption. Two functional clustering approaches are then used to classify the extracted seasonal patterns: the functional version of K-means, and the Fourier REgression Mixture (FReMix) model. The K-means approach produces a hard segmentation and K representative prototypes. On the other hand, the FReMix is a generative model and also produces K profiles as well as a soft segmentation based on the posterior probabilities. The proposed approach is applied to a smart grid deployed on the largest water distribution network (WDN) in France. The two clustering strategies are evaluated and compared. Finally, a realistic interpretation of the consumption habits is given for each cluster. The extensive experiments and the qualitative interpretation of the resulting clusters allow one to highlight the effectiveness of the proposed methodology