Statistics for Spatial Data.

The present historical moment may seem a particularly inopportune time to review Bowling Alone, Robert Putnam's latest exploration of civic decline in America. After all, the outpouring of volunteerism, solidarity, patriotism, and self-sacrifice displayed by Americans in the wake of the September 11 terrorist attacks appears to fly in the face of Putnam's central argument: that \"social capital\" -defined as \"social networks and the norms of reciprocity and trustworthiness that arise from them\" (p. 19)'has declined to dangerously low levels in America over the last three decades. However, Putnam is not fazed in the least by the recent effusion of solidarity. Quite the contrary, he sees in it the potential to \"reverse what has been a 30to 40-year steady decline in most measures of connectedness or community.\"' As an example of how the current \"war on terrorism\" could generate a durable civic renewal, Putnam points to the burst in civic practices that occurred during and after World War II, which he says \"permanently marked\" the generation that lived through it and had a \"terrific effect on American public life over the last half-century.\" 3 If Americans can follow this example and channel their current civic

Bowling alone: The collapse and revival of American community

Images containing faces are essential to intelligent vision-based human-computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation and expression recognition. However, many reported methods assume that the faces in an image or an image sequence have been identified and localized. To build fully automated systems that analyze the information contained in face images, robust and efficient face detection algorithms are required. Given a single image, the goal of face detection is to identify all image regions which contain a face, regardless of its 3D position, orientation and lighting conditions. Such a problem is challenging because faces are non-rigid and have a high degree of variability in size, shape, color and texture. Numerous techniques have been developed to detect faces in a single image, and the purpose of this paper is to categorize and evaluate these algorithms. We also discuss relevant issues such as data collection, evaluation metrics and benchmarking. After analyzing these algorithms and identifying their limitations, we conclude with several promising directions for future research.

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Detecting faces in images: a survey

Using a differential-geometric treatment of planar shapes, we present tools for: 1) hierarchical clustering of imaged objects according to the shapes of their boundaries, 2) learning of probability models for clusters of shapes, and 3) testing of newly observed shapes under competing probability models. Clustering at any level of hierarchy is performed using a minimum variance type criterion and a Markov process. Statistical means of clusters provide shapes to be clustered at the next higher level, thus building a hierarchy of shapes. Using finite-dimensional approximations of spaces tangent to the shape space at sample means, we (implicitly) impose probability models on the shape space, and results are illustrated via random sampling and classification (hypothesis testing). Together, hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval. Examples are presented using shapes and images from ETH, Surrey, and AMCOM databases.

Statistical shape analysis: clustering, learning, and testing

The first edition of "Geometric Morphometrics for Biologists" has been the primary resource for teaching modern geometric methods of shape analysis to biologists who have a stronger background in biology than in multivariate statistics and matrix algebra. These geometric methods are appealing to biologists who approach the study of shape from a variety of perspectives, from clinical to evolutionary, because they incorporate the geometry of organisms throughout the data analysis. The second edition of this book retains the emphasis on accessible explanations, and the copious illustrations and examples of the first, updating the treatment of both theory and practice. The second edition represents the current state-of-the-art and adds new examples and summarizes recent literature, as well as provides an overview of new software and step-by-step guidance through details of carrying out the analyses. This title contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics. It offers a reorganization of chapters to streamline learning basic concepts. It presents detailed instructions for conducting analyses with freely available, easy to use software. It provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results.

Geometric morphometrics for biologists: a primer

Preliminaries: Size Measures and Shape Coordinates. Preliminaries: Planar Procrustes Analysis. Shape Space and Distance. General Procrustes Methods. Shape Models for Two Dimensional Data. Tangent Space Inference. Size--and--Shape. Distributions for Higher Dimensions. Deformations and Describing Shape Change. Shape in Images. Additional Topics. References and Author Index. Index.

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Statistical Shape Analysis: With Applications in R

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes Anisotropy is discussed.

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Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

A general framework for a novel non-geodesic decomposition of high-dimensional spheres or high-dimensional shape spaces for planar landmarks is discussed. The decomposition, principal nested spheres, leads to a sequence of submanifolds with decreasing intrinsic dimensions, which can be interpreted as an analogue of principal component analysis. In a number of real datasets, an apparent one-dimensional mode of variation curving through more than one geodesic component is captured in the one-dimensional component of principal nested spheres. While analysis of principal nested spheres provides an intuitive and flexible decomposition of the high-dimensional sphere, an interesting special case of the analysis results in finding principal geodesics, similar to those from previous approaches to manifold principal component analysis. An adaptation of our method to Kendall’s shape space is discussed, and a computational algorithm for fitting principal nested spheres is proposed. The result provides a coordinate system to visualize the data structure and an intuitive summary of principal modes of variation, as exemplified by several datasets.

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Analysis of principal nested spheres

Purpose Currently known serum biomarkers do not predict clinical outcome in melanoma. S100- is widely established as a reliable prognostic indicator in patients with advanced metastatic disease but is of limited predictive value in tumor-free patients. This study was aimed to determine whether molecular profiling of the serum proteome could discriminate between early- and late-stage melanoma and predict disease progression. Patients and Methods Two hundred five serum samples from 101 early-stage (American Joint Committee on Cancer [AJCC] stage I) and 104 advanced stage (AJCC stage IV) melanoma patients were analyzed by matrix-assisted laser desorption/ionisation (MALDI) time-of-flight (ToF; MALDIToF) mass spectrometry utilizing protein chip technology and artificial neural networks (ANN). Serum samples from 55 additional patients after complete dissection of regional lymph node metastases (AJCC stage III), with 28 of 55 patients relapsing within the first year of follow-up, were analyzed in an attempt to predict disease recurrence. Serum S100- was measured using a sandwich immunoluminometric assay. Results Analysis of 205 stage I/IV serum samples, utilizing a training set of 94 of 205 and a test set of 15 of 205 samples for 32 different ANN models, revealed correct stage assignment in 84 (88%) of 96 of a blind set of 96 of 205 serum samples. Forty-four (80%) of 55 stage III serum samples could be correctly assigned as progressors or nonprogressors using random sample cross-validation statistical methodologies. Twenty-three (82%) of 28 stage III progressors were correctly identified by MALDI-ToF combined with ANN, whereas only six (21%) of 28 could be detected by S100-. Conclusion Validation of these findings may enable proteomic profiling to become a valuable tool for identifying high-risk melanoma patients eligible for adjuvant therapeutic interventions.

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Serum Proteomic Fingerprinting Discriminates Between Clinical Stages and Predicts Disease Progression in Melanoma Patients

fMRI studies of brain activity at rest study slow (<0.1 Hz) intrinsic fluctuations in the blood- oxygenation-level-dependent (BOLD) signal that are observed in a temporal scale of several minutes. The origin of these fluctuations is not clear but has previously been associated with slow changes in rhythmic neuronal activity resulting from changes in cortical excitability or neuronal synchronization. In this work, we show that individual spontaneous BOLD events occur during rest, in addition to slow fluctuations. Individual spontaneous BOLD events were identified by deconvolving the hemodynamic impulse response function for each time point in the fMRI time series, thus requiring no information on timing or a-priori spatial information of events. The patterns of activation detected were related to the motor, visual, default-mode, and dorsal attention networks. The correspondence between spontaneous events and slow fluctuations in these networks was assessed using a sliding window, seed-correlation analysis, where seed regions were selected based on the individual spontaneous event BOLD activity maps. We showed that the correlation varied considerably over time, peaking at the time of spontane- ous events in these networks. By regressing spontaneous events out of the fMRI signal, we showed that both the correlation strength and the power in spectral frequencies <0.1 Hz decreased, indicating that spontaneous activation events contribute to low-frequency fluctuations observed in resting state net- works with fMRI. This work provides new insights into the origin of signals detected in fMRI studies of functional connectivity. Hum Brain Mapp 00:000-000, 2012. V C 2012 Wiley Periodicals, Inc.

Ian L. Dryden

Papers

Statistical Shape Analysis: With Applications in R

Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

Analysis of principal nested spheres

Serum Proteomic Fingerprinting Discriminates Between Clinical Stages and Predicts Disease Progression in Melanoma Patients

Periods of rest in fMRI contain individual spontaneous events which are related to slowly fluctuating spontaneous activity.