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

Useful knowledge, 'industrial enlightenment', and the place of India

Research is now turning to the missing place of technology and ‘useful knowledge’ in the debate on the ‘great divergence’ between East and West. Parallel research in the history of science has sought the global dimensions of European knowledge. Joel Mokyr's recent The Enlightened Economy (2009) argued the place of an exceptional ‘industrial enlightenment’ in Europe in explaining industrialization there, but neglected the wide geographic framework of European investigation of the arts and manufactures. This article presents two case studies of European industrial travellers who accessed and described Indian crafts and industries at the time of Britain's industrial revolution and Europe's Enlightenment discourse on crafts and manufactures. The efforts of Anton Hove and Benjamin Heyne to ‘codify’ the ‘tacit’ knowledge of a part of the world distant from Europe were hindered by the English East India Company and the British state. Their accounts, only published much later, provide insight into European perceptions of India's ‘useful knowledge’

Plant capitalism and company science: the Indian career of Nathaniel Wallich

The career of the Danish-born botanist Nathaniel Wallich, superintendent of the Calcutta Botanic Garden from 1815 to 1846, illustrates the complex nature of botanical science under the East India Company and shows how the plant life of South Asia was used as a capital resource both in the service of the Company's economic interests and for Wallich's own professional advancement and international reputation. Rather than seeing him as a pioneer of modern forest conservation or an innovative botanist, Wallich's attachment to the ideology of ‘improvement’ and the Company's material needs better explain his longevity as superintendent of the Calcutta garden. Although aspects of Wallich's career and botanical works show the importance of circulation between Europe and India, more significant was the hierarchy of knowledge in which indigenous plant lore and illustrative skill were subordinated to Western science and in which colonial science frequently lagged behind that of the metropolis

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