METHODS FOR AUTOMATIC ESTIMATION OF THE NUMBER OF CLUSTERS FOR K-MEANS ALGORITHM USED ON EEG SIGNAL: FEASIBILITY STUDY

Lots of brain diseases are recognized by EEG recording. EEG signal has a stochastic character, this stochastic nature makes the evaluation of EEG recording complicated. Therefore we use automatic classification methods for EEG processing. This methods help the expert to find significant or physiologically important segments in the EEG recording. The k-means algorithm is a frequently used method in practice for automatic classification. The main disadvantage of the k-means algorithm is the necessary determination of the number of clusters. So far there are many methods which try to determine optimal number of clusters for k-means algorithm. The aim of this study is to test functionality of the two most frequently used methods on EEG signals, concretely the elbow and the silhouette method. In this feasibility study we compared the results of both methods on simulated data and real EEG signal. We want to prove with the help of an expert the possibility to use these functions on real EEG signal. The results show that the silhouette method applied on EEG recordings is more time-consuming than the elbow method. Neither of the methods is able to correctly recognize the number of clusters in the EEG record by expert evaluation and therefore it is not applicable to the automatic classification of EEG based on k-means algorithm

MMKK++ algorithm for clustering heterogeneous images into an unknown number of clusters

In this paper we present an automatic clustering procedure with the main aim to predict the number of clusters of unknown, heterogeneous images. We used the Fisher-vector for mathematical representation of the images and these vectors were considered as input data points for the clustering algorithm. We implemented a novel variant of K-means, the kernel K-means++, furthermore the min-max kernel K-means plusplus (MMKK++) as clustering method. The proposed approach examines some candidate cluster numbers and determines the strength of the clustering to estimate how well the data fit into K clusters, as well as the law of large numbers was used in order to choose the optimal cluster size. We conducted experiments on four image sets to demonstrate the efficiency of our solution. The first two image sets are subsets of different popular collections; the third is their union; the fourth is the complete Caltech101 image set. The result showed that our approach was able to give a better estimation for the number of clusters than the competitor methods. Furthermore, we defined two new metrics for evaluation of predicting the appropriate cluster number, which are capable of measuring the goodness in a more sophisticated way, instead of binary evaluation

A New Reduction Scheme for Gaussian Sum Filters

In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF) provide the MMSE state estimate by tracking the GM posterior. However, since the number of the clusters of the GM posterior grows exponentially over time, suitable reduction schemes need to be used to maintain the size of the bank in GSF. In this work we propose a low computational complexity reduction scheme which uses an initial state estimation to find the active noise clusters and removes all the others. Since the performance of our proposed method relies on the accuracy of the initial state estimation, we also propose five methods for finding this estimation. We provide simulation results showing that with suitable choice of the initial state estimation (based on the shape of the noise models), our proposed reduction scheme provides better state estimations both in terms of accuracy and precision when compared with other reduction methods

Aerial moving target detection based on motion vector field analysis

An efficient automatic detection strategy for aerial moving targets in airborne forward-looking infrared (FLIR) imagery is presented in this paper. Airborne cameras induce a global motion over all objects in the image, that invalidates motion-based segmentation techniques for static cameras. To overcome this drawback, previous works compensate the camera ego-motion. However, this approach is too much dependent on the quality of the ego-motion compensation, tending towards an over-detection. In this work, the proposed strategy estimates a robust motion vector field, free of erroneous vectors. Motion vectors are classified into different independent moving objects, corresponding to background objects and aerial targets. The aerial targets are directly segmented using their associated motion vectors. This detection strategy has a low computational cost, since no compensation process or motion-based technique needs to be applied. Excellent results have been obtained over real FLIR sequences

Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering

This study introduces a new method for detecting and sorting spikes from multiunit recordings. The method combines the wavelet transform, which localizes distinctive spike features, with superparamagnetic clustering, which allows automatic classification of the data without assumptions such as low variance or gaussian distributions. Moreover, an improved method for setting amplitude thresholds for spike detection is proposed. We describe several criteria for implementation that render the algorithm unsupervised and fast. The algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings. For these data sets, we found that the proposed algorithm outperformed conventional methods

An Objective and Automatic Cluster Finder: An Improvement of the Matched-Filter Method

We describe an objective and automated method for detecting clusters of galaxies from optical imaging data. This method is a variant of the so-called `matched-filter' technique pioneered by Postman et al. (1996). With simultaneous use of positions and apparent magnitudes of galaxies, this method can, not only find cluster candidates, but also estimate their redshifts and richnesses as byproducts of detection. We examine errors in the estimation of cluster's position, redshift, and richness with a number of Monte Carlo simulations. No systematic discrepancies between the true and estimated values are seen for either redshift or richness. Spurious detection rate of the method is about less than 10% of those of conventional ones which use only surface density of galaxies. A cluster survey in the North Galactic Pole is executed to verify the performance characteristics of the method with real data. Two known real clusters are successfully detected. We expect these methods based on `matched-filter' technique to be essential tools for compiling large and homogeneous optically-selected cluster catalogs.Comment: 13 pages, 12 PostScript figures, uses LaTeX L-AA, A&AS accepte

Gravitational Clustering: A Simple, Robust and Adaptive Approach for Distributed Networks

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed algorithms have been proposed, which frame the signal/object labelling problem in terms of cluster analysis after extracting source-specific features, however, the number of clusters is assumed to be known. We propose a new method called Gravitational Clustering (GC) to adaptively estimate the time-varying number of clusters based on a set of feature vectors. The key idea is to exploit the physical principle of gravitational force between mass units: streaming-in feature vectors are considered as mass units of fixed position in the feature space, around which mobile mass units are injected at each time instant. The cluster enumeration exploits the fact that the highest attraction on the mobile mass units is exerted by regions with a high density of feature vectors, i.e., gravitational clusters. By sharing estimates among neighboring nodes via a diffusion-adaptation scheme, cooperative and distributed cluster enumeration is achieved. Numerical experiments concerning robustness against outliers, convergence and computational complexity are conducted. The application in a distributed cooperative multi-view camera network illustrates the applicability to real-world problems.Comment: 12 pages, 9 figure