The geometry of kernelized spectral clustering

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clustering in recovering the latent labels of i.i.d. samples from a finite mixture of nonparametric distributions. The difficulty of this label recovery problem depends on the overlap between mixture components and how easily a mixture component is divided into two nonoverlapping components. When the overlap is small compared to the indivisibility of the mixture components, the principal eigenspace of the population-level normalized Laplacian operator is approximately spanned by the square-root kernelized component densities. In the finite sample setting, and under the same assumption, embedded samples from different components are approximately orthogonal with high probability when the sample size is large. As a corollary we control the fraction of samples mislabeled by spectral clustering under finite mixtures with nonparametric components.Comment: Published at http://dx.doi.org/10.1214/14-AOS1283 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Superresolution without Separation

This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of M shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from 2M + 1 observations. This recovery is achieved by solving a a weighted version of basis pursuit over a continuous dictionary. Our methods combine classical polynomial interpolation techniques with contemporary tools from compressed sensing.Comment: 23 pages, 8 figure

Gendered innovation in health and medicine

"'Gendered Innovations' integrates sex and gender analysis into all phases of biomedical and health research to assure excellence and quality in outcomes. This article reports on the interdisciplinary, international collaboration that produced: 1) state-of-the-art methods of sex and gender analysis for health and medicine; and 2) case studies to illustrate how gender analysis leads to discovery in biomedicine and better outcomes in health research: osteoporosis research in men, the genetics of sex determination, heart disease in women, stem cell research, animal research, nutrigenomics and degendering knee implants. The article concludes with a short review of policy at the Canadian, US, and European institutes of health, medical curricula, and policies for peer-reviewed journals in relation to reporting sex/gender analysis in research." (Autorenreferat)"'Gendered Innovations' integriert eine Sex und Genderanalyse in alle Phasen der biomedizinischen und Gesundheitsforschung, um Exzellenz und Qualität auf Ergebnisseite zu sichern. Der Beitrag stellt die interdisziplinären internationalen Kooperationsbemühungen dar, in deren Rahmen sowohl zeitgemäße Methoden der geschlechterfokussierten Analyse im Bereich von Gesundheit und Medizin entwickelt als auch Fallstudien durchgeführt wurden: zur Osteoporoseforschung bei Männern, zu genetischen Faktoren der Geschlechtsbestimmung, Herzerkrankungen bei Frauen, Stammzellenforschung, Tierversuchen, Nutrigenomik und zum 'Degendering' bei Knieimplantaten. Der Beitrag schließt mit einem kurzen Blick auf kanadische, US-amerikanische und europäische Gesundheitsinstitute, medizinische Curricula und den Umgang peer-reviewter Zeitschriften mit Forschungsberichten über Sex-/Genderanalysen" (Autorenreferat

Agnotology: The Making and Unmaking of Ignorance

"This volume emerged from workshops held at Pennsylvania State University in 2003 and Stanford University in 2005"--P. vii