Clustering functional data using wavelets

We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first method uses the distribution of energy across scales generate a handy number of features that can be sufficient to still make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high dimensional populations. The second method uses dissimilarity measures between the whole time-scale representations and are based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these dissimilarities. Practical performance of these methods that jointly designs both the feature selection in the wavelet domain and the classification distance is demonstrated through simulations as well as daily profiles of the French electricity power demand

Non-Metric Multi-Dimensional Scaling for Distance-Based Privacy-Preserving Data Mining

Recent advances in the field of data mining have led to major concerns about privacy. Sharing data with external parties for analysis puts private information at risk. The original data are often perturbed before external release to protect private information. However, data perturbation can decrease the utility of the output. A good perturbation technique requires balance between privacy and utility. This study proposes a new method for data perturbation in the context of distance-based data mining. We propose the use of non-metric multi-dimensional scaling (MDS) as a suitable technique to perturb data that are intended for distance-based data mining. The basic premise of this approach is to transform the original data into a lower dimensional space and generate new data that protect private details while maintaining good utility for distance-based data mining analysis. We investigate the extent the perturbed data are able to preserve useful statistics for distance-based analysis and to provide protection against malicious attacks. We demonstrate that our method provides an adequate alternative to data randomisation approaches and other dimensionality reduction approaches. Testing is conducted on a wide range of benchmarked datasets and against some existing perturbation methods. The results confirm that our method has very good overall performance, is competitive with other techniques, and produces clustering and classification results at least as good, and in some cases better, than the results obtained from the original data

Laser Ultrasound Inspection Based on Wavelet Transform and Data Clustering for Defect Estimation in Metallic Samples

Laser-generated ultrasound is a modern non-destructive testing technique. It has been investigated over recent years as an alternative to classical ultrasonic methods, mainly in industrial maintenance and quality control procedures. In this study, the detection and reconstruction of internal defects in a metallic sample is performed by means of a time-frequency analysis of ultrasonic waves generated by a laser-induced thermal mechanism. In the proposed methodology, we used wavelet transform due to its multi-resolution time frequency characteristics. In order to isolate and estimate the corresponding time of flight of eventual ultrasonic echoes related to internal defects, a density-based spatial clustering was applied to the resulting time frequency maps. Using the laser scan beam’s position, the ultrasonic transducer’s location and the echoes’ arrival times were determined, the estimation of the defect’s position was carried out afterwards. Finally, clustering algorithms were applied to the resulting geometric solutions from the set of the laser scan points which was proposed to obtain a two-dimensional projection of the defect outline over the scan plane. The study demonstrates that the proposed method of wavelet transform ultrasonic imaging can be effectively applied to detect and size internal defects without any reference information, which represents a valuable outcome for various applications in the industry. View Full-TextPeer ReviewedPostprint (published version

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd