Reliability of vegetation community information derived using decorana ordination and fuzzy c-means clustering

Descriptions of vegetation communities are often based on vague semantic terms describing species presence and dominance. For this reason, some researchers advocate the use of fuzzy sets in the statistical classification of plant species data into communities. In this study, spatially referenced vegetation abundance values collected from Greek phrygana were analysed by ordination (DECORANA), and classified on the resulting axes using fuzzy c-means to yield a point data-set representing local memberships in characteristic plant communities. The fuzzy clusters matched vegetation communities noted in the field, which tended to grade into one another, rather than occupying discrete patches. The fuzzy set representation of the community exploited the strengths of detrended correspondence analysis while retaining richer information than a TWINSPAN classification of the same data. Thus, in the absence of phytosociological benchmarks, meaningful and manageable habitat information could be derived from complex, multivariate species data. We also analysed the influence of the reliability of different surveyors' field observations by multiple sampling at a selected sample location. We show that the impact of surveyor error was more severe in the Boolean than the fuzzy classification. © 2007 Springer.

What to do when K-means clustering fails:a simple yet principled alternative algorithm

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

A hybrid generative/discriminative framework to train a semantic parser from an un-annotated corpus

We propose a hybrid generative/discriminative framework for semantic parsing which combines the hidden vector state (HVS) model and the hidden Markov support vector machines (HM-SVMs). The HVS model is an extension of the basic discrete Markov model in which context is encoded as a stack-oriented state vector. The HM-SVMs combine the advantages of the hidden Markov models and the support vector machines. By employing a modified K-means clustering method, a small set of most representative sentences can be automatically selected from an un-annotated corpus. These sentences together with their abstract annotations are used to train an HVS model which could be subsequently applied on the whole corpus to generate semantic parsing results. The most confident semantic parsing results are selected to generate a fully-annotated corpus which is used to train the HM-SVMs. The proposed framework has been tested on the DARPA Communicator Data. Experimental results show that an improvement over the baseline HVS parser has been observed using the hybrid framework. When compared with the HM-SVMs trained from the fully-annotated corpus, the hybrid framework gave a comparable performance with only a small set of lightly annotated sentences. © 2008. Licensed under the Creative Commons.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Fuzzy c-means variants for medical image segmentation

Segmentation is an important step in many medical imaging applications and a variety of image segmentation techniques exist. One group of segmentation algorithms is based on clustering concepts. In this article we investigate several fuzzy c-means based clustering algorithms and their application to medical image segmentation. In particular we evaluate the conventional hard c-means (HCM) and fuzzy c-means (FCM) approaches as well as three computationally more efficient derivatives of fuzzy c-means: fast FCM with random sampling, fast generalised FCM, and a new anisotropic mean shift based FCM. © 2010 by IJTS, ISDER.