Correlation-based Data Representation

The Dagstuhl Seminar \u27Similarity-based Clustering and its Application to Medicine and Biology\u27 (07131) held in March 25--30, 2007, provided an excellent atmosphere for in-depth discussions about the research frontier of computational methods for relevant applications of biomedical clustering and beyond. We address some highlighted issues about correlation-based data analysis in this seminar postribution. First, some prominent correlation measures are briefly revisited. Then, a focus is put on Pearson correlation, because of its widespread use in biomedical sciences and because of its analytic accessibility. A connection to Euclidean distance of z-score transformed data outlined. Cost function optimization of correlation-based data representation is discussed for which, finally, applications to visualization and clustering of gene expression data are given

Improved forecasts for the baryon acoustic oscillations and cosmological distance scale

We present the cosmological distance errors achievable using the baryon acoustic oscillations as a standard ruler. We begin from a Fisher matrix formalism that is upgraded from Seo & Eisenstein (2003). We isolate the information from the baryonic peaks by excluding distance information from other less robust sources. Meanwhile we accommodate the Lagrangian displacement distribution into the Fisher matrix calculation to reflect the gradual loss of information in scale and in time due to nonlinear growth, nonlinear bias, and nonlinear redshift distortions. We then show that we can contract the multi-dimensional Fisher matrix calculations into a 2-dimensional or even 1-dimensional formalism with physically motivated approximations. We present the resulting fitting formula for the cosmological distance errors from galaxy redshift surveys as a function of survey parameters and nonlinearity, which saves us going through the 12-dimensional Fisher matrix calculations. Finally, we show excellent agreement between the distance error estimates from the revised Fisher matrix and the precision on the distance scale recovered from N-body simulations.Comment: Submitted to ApJ, 21 pages, LaTe

Correlation-maximizing surrogate gene space for visual mining of gene expression patterns in developing barley endosperm tissue

<p>Abstract</p> <p>Background</p> <p>Micro- and macroarray technologies help acquire thousands of gene expression patterns covering important biological processes during plant ontogeny. Particularly, faithful visualization methods are beneficial for revealing interesting gene expression patterns and functional relationships of coexpressed genes. Such screening helps to gain deeper insights into regulatory behavior and cellular responses, as will be discussed for expression data of developing barley endosperm tissue. For that purpose, high-throughput multidimensional scaling (HiT-MDS), a recent method for similarity-preserving data embedding, is substantially refined and used for (a) assessing the quality and reliability of centroid gene expression patterns, and for (b) derivation of functional relationships of coexpressed genes of endosperm tissue during barley grain development (0–26 days after flowering).</p> <p>Results</p> <p>Temporal expression profiles of 4824 genes at 14 time points are faithfully embedded into two-dimensional displays. Thereby, similar shapes of coexpressed genes get closely grouped by a correlation-based similarity measure. As a main result, by using power transformation of correlation terms, a characteristic cloud of points with bipolar sandglass shape is obtained that is inherently connected to expression patterns of pre-storage, intermediate and storage phase of endosperm development.</p> <p>Conclusion</p> <p>The new HiT-MDS-2 method helps to create global views of expression patterns and to validate centroids obtained from clustering programs. Furthermore, functional gene annotation for developing endosperm barley tissue is successfully mapped to the visualization, making easy localization of major centroids of enriched functional categories possible.</p

Clustering and Classification Methods for Gene Expression Data Analysis

Efficient use of the large data sets generated by gene expression microarray experiments requires computerized data analysis approaches. In this chapter we briefly describe and illustrate two broad families of commonly used data analysis methods: class discovery and class prediction methods. A wide range of alternative approaches for clustering and classification of gene expression data are available. While differences in efficiency do exist, none of the well established approaches is uniformly superior to others. Choosing an approach requires consideration of the goals of the analysis, the background knowledge, and the specific experimental constraints. The quality of an algorithm is important, but is not in itself a guarantee of the quality of a specific data analysis. Uncertainty, sensitivity analysis and, in the case of classifiers, external validation or cross-validation should be used to support the legitimacy of results of microarray data analyses

A New Generation of Mixture-Model Cluster Analysis with Information Complexity and the Genetic EM Algorithm

In this dissertation, we extend several relatively new developments in statistical model selection and data mining in order to improve one of the workhorse statistical tools - mixture modeling (Pearson, 1894). The traditional mixture model assumes data comes from several populations of Gaussian distributions. Thus, what remains is to determine how many distributions, their population parameters, and the mixing proportions. However, real data often do not fit the restrictions of normality very well. It is likely that data from a single population exhibiting either asymmetrical or nonnormal tail behavior could be erroneously modeled as two populations, resulting in suboptimal decisions. To avoid these pitfalls, we develop the mixture model under a broader distributional assumption by fitting a group of multivariate elliptically-contoured distributions (Anderson and Fang, 1990; Fang et al., 1990). Special cases include the multivariate Gaussian and power exponential distributions, as well as the multivariate generalization of the Student’s T. This gives us the flexibility to model nonnormal tail and peak behavior, though the symmetry restriction still exists. The literature has many examples of research generalizing the Gaussian mixture model to other distributions (Farrell and Mersereau, 2004; Hasselblad, 1966; John, 1970a), but our effort is more general. Further, we generalize the mixture model to be non-parametric, by developing two types of kernel mixture model. First, we generalize the mixture model to use the truly multivariate kernel density estimators (Wand and Jones, 1995). Additionally, we develop the power exponential product kernel mixture model, which allows the density to adjust to the shape of each dimension independently. Because kernel density estimators enforce no functional form, both of these methods can adapt to nonnormal asymmetric, kurtotic, and tail characteristics. Over the past two decades or so, evolutionary algorithms have grown in popularity, as they have provided encouraging results in a variety of optimization problems. Several authors have applied the genetic algorithm - a subset of evolutionary algorithms - to mixture modeling, including Bhuyan et al. (1991), Krishna and Murty (1999), and Wicker (2006). These procedures have the benefit that they bypass computational issues that plague the traditional methods. We extend these initialization and optimization methods by combining them with our updated mixture models. Additionally, we “borrow” results from robust estimation theory (Ledoit and Wolf, 2003; Shurygin, 1983; Thomaz, 2004) in order to data-adaptively regularize population covariance matrices. Numerical instability of the covariance matrix can be a significant problem for mixture modeling, since estimation is typically done on a relatively small subset of the observations. We likewise extend various information criteria (Akaike, 1973; Bozdogan, 1994b; Schwarz, 1978) to the elliptically-contoured and kernel mixture models. Information criteria guide model selection and estimation based on various approximations to the Kullback-Liebler divergence. Following Bozdogan (1994a), we use these tools to sequentially select the best mixture model, select the best subset of variables, and detect influential observations - all without making any subjective decisions. Over the course of this research, we developed a full-featured Matlab toolbox (M3) which implements all the new developments in mixture modeling presented in this dissertation. We show results on both simulated and real world datasets. Keywords: mixture modeling, nonparametric estimation, subset selection, influence detection, evidence-based medical diagnostics, unsupervised classification, robust estimation

Polyphonic music information retrieval based on multi-label cascade classification system

Recognition and separation of sounds played by various instruments is very useful in labeling audio files with semantic information. This is a non-trivial task requiring sound analysis, but the results can aid automatic indexing and browsing music data when searching for melodies played by user specified instruments. Melody match based on pitch detection technology has drawn much attention and a lot of MIR systems have been developed to fulfill this task. However, musical instrument recognition remains an unsolved problem in the domain. Numerous approaches on acoustic feature extraction have already been proposed for timbre recognition. Unfortunately, none of those monophonic timbre estimation algorithms can be successfully applied to polyphonic sounds, which are the more usual cases in the real music world. This has stimulated the research on multi-labeled instrument classification and new features development for content-based automatic music information retrieval. The original audio signals are the large volume of unstructured sequential values, which are not suitable for traditional data mining algorithms; while the acoustical features are sometime not sufficient for instrument recognition in polyphonic sounds because they are higher-level representatives of raw signal lacking details of original information. In order to capture the patterns which evolve on the time scale, new temporal features are introduced to supply more temporal information for the timbre recognition. We will introduce the multi-labeled classification system to estimate multiple timbre information from the polyphonic sound by classification based on acoustic features and short-term power spectrum matching. In order to achieve higher estimation rate, we introduced the hierarchically structured cascade classification system under the inspiration of the human perceptual process. This cascade classification system makes a first estimate on the higher level decision attribute, which stands for the musical instrument family. Then, the further estimation is done within that specific family range. Experiments showed better performance of a hierarchical system than the traditional flat classification method which directly estimates the instrument without higher level of family information analysis. Traditional hierarchical structures were constructed in human semantics, which are meaningful from human perspective but not appropriate for the cascade system. We introduce the new hierarchical instrument schema according to the clustering results of the acoustic features. This new schema better describes the similarity among different instruments or among different playing techniques of the same instrument. The classification results show the higher accuracy of cascade system with the new schema compared to the traditional schemas. The query answering system is built based on the cascade classifier

Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping

The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series is determining their pairwise similarity, i.e., the degree to which a given time series resembles another. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. Elastic metrics such as dynamic time warping (DTW) offer a promising approach, but are limited by their computational complexity, non-differentiability and sensitivity to noise and outliers. This thesis proposes novel elastic alignment methods that use parametric \& diffeomorphic warping transformations as a means of overcoming the shortcomings of DTW-based metrics. The proposed method is differentiable \& invertible, well-suited for deep learning architectures, robust to noise and outliers, computationally efficient, and is expressive and flexible enough to capture complex patterns. Furthermore, a closed-form solution was developed for the gradient of these diffeomorphic transformations, which allows an efficient search in the parameter space, leading to better solutions at convergence. Leveraging the benefits of these closed-form diffeomorphic transformations, this thesis proposes a suite of advancements that include: (a) an enhanced temporal transformer network for time series alignment and averaging, (b) a deep-learning based time series classification model to simultaneously align and classify signals with high accuracy, (c) an incremental time series clustering algorithm that is warping-invariant, scalable and can operate under limited computational and time resources, and finally, (d) a normalizing flow model that enhances the flexibility of affine transformations in coupling and autoregressive layers.Comment: PhD Thesis, defended at the University of Navarra on July 17, 2023. 277 pages, 8 chapters, 1 appendi