Recently, independent component analysis (ICA) has been widely used in the analysis of brain imaging data. An important problem with most ICA algorithms is, however, that they are stochastic, i.e. their results may be somewhat different in different runs of the algorithm. Thus, the outputs of a single run of an ICA algorithm cannot be trusted, and some analysis of the algorithmic reliability of the components is needed. Moreover, as with any statistical method, the results are affected by the random sampling of the data, and some analysis of the statistical significance or reliability should be done as well. Here, we present a method for assessing both the algorithmic and statistical reliability of estimated independent components. The method is based on running the algorithm many times with slightly different conditions, and visualizing the clustering structure of the obtained components in the signal space. In experiments with MEG and fMRI data, the method was able to show that expected components are reliable; furthermore, it pointed out components whose interpretation was not obvious but whose reliability should incite the the experimenter to investigate the underlying technical or physical phenomena. The method is implemented in a sofware package called Icasso.

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channel data including path powers

This paper presents a complete solution to the problem of how to parametrise cluster-based stochastic MIMO channel models from measurement data, with minimum user intervention. The method comprises the following steps: (i) identify clusters in measurement data, (ii) identify the optimum number of clusters, (iii) track clusters over consecutive time snapshots, (iv) estimate cluster parameters. These parameters are given as estimated probability density functions of the cluster power, cluster positions, delay and angular spreads of clusters and the number of paths within a cluster. Applied to high-resolution indoor MIMO measurement data at 5.2 GHz and at 2.55 GHz, the method yields coherent results of the obtained cluster parameters.

Abstract—In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SAR-specific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation–maximization iterative methodology with the recently developed “method-of-log-cumulants ” for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data. Index Terms—Finite mixture models (FMMs), parametric estimation, probability density function (pdf) estimation, stochastic expectation maximization (SEM), synthetic aperture radar (SAR) images. I.

A major problem in application of independent component analysis (ICA) is that the reliability of the estimated independent components is not known. Firstly, the finite sample size induces statistical errors in the estimation. Secondly, as real data never exactly follows the ICA model, the contrast function used in the estimation may have many local minima which are all equally good, or the practical algorithm may not always perform properly, for example getting stuck in local minima with strongly suboptimal values of the contrast function. We present an explorative visualization method for investigating the relations between estimates from FastICA. The algorithmic and statistical reliability is investigated by running the algorithm many times with di#erent initial values or with di#erently bootstrapped data sets, respectively. Resulting estimates are compared by visualizing their clustering according to a suitable similarity measure. Reliable estimates correspond to tight clusters, and unreliable ones to points which do not belong to any such cluster. We have developed a software package called Icasso to implement these operations. We also present results of this method when applying Icasso on biomedical data.

Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.

Rapid advances of microarray technologies are making it possible to analyze and manipulate large amounts of gene expression data. Clustering algorithms, such as hierarchical clustering, self-organizing maps, k-means clustering and fuzzy k-means clustering, have become important tools for expression analysis of microarray data. However, the need of prior knowledge of the number of clusters, k, and the fuzziness parameter, b, limits the usage of fuzzy clustering. Few approaches have been proposed for assigning best possible values for such parameters. In this paper, we use simulated annealing and fuzzy k-means clustering to determine the optimal parameters, namely the number of clusters, k, and the fuzziness parameter, b. Our results show that a nearly-optimal pair of k and b can be obtained without exploring the entire search space.

This paper addresses the issue of assessing the quality of the clusters found by fuzzy and hard clustering algorithms. In particular, it seeks an answer to the question on how well cluster validity indexes can automatically determine the appropriate number of clusters that represent the data. The paper surveys several key existing solutions for cluster validity in the domain of image segmentation. In addition, it suggests two new indexes. The first one is based on Akaike’s information criterion (AIC). While AIC was devoted to other domains such as statistical estimation of model fitting, it is implemented here for the first time as a validation index. The second index is developed from the well-established idea of cross-validation. The existing and new indexes are evaluated and compared on several synthetic images corrupted with noise of varying levels and volumetric MR data. Index Terms—clustering, cluster validity, fuzzy clustering, image segmentation. 1.

Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.