Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space. However, since these manifolds belong to non-Euclidean topological spaces, exploiting their structures is computationally expensive, especially when one considers the clustering analysis of massive amounts of data. To this end, we propose an efficient framework to address the clustering problem on Riemannian manifolds. This framework implements random projections for manifold points via kernel space, which can preserve the geometric structure of the original space, but is computationally efficient. Here, we introduce three methods that follow our framework. We then validate our framework on several computer vision applications by comparing against popular clustering methods on Riemannian manifolds. Experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases

Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are verified by numerical simulations

The Atacama Cosmology Telescope: Extragalactic Sources at 148 GHz in the 2008 Survey

We report on extragalactic sources detected in a 455 square-degree map of the southern sky made with data at a frequency of 148 GHz from the Atacama Cosmology Telescope 2008 observing season. We provide a catalog of 157 sources with flux densities spanning two orders of magnitude: from 15 to 1500 mJy. Comparison to other catalogs shows that 98% of the ACT detections correspond to sources detected at lower radio frequencies. Three of the sources appear to be associated with the brightest cluster galaxies of low redshift X-ray selected galaxy clusters. Estimates of the radio to mm-wave spectral indices and differential counts of the sources further bolster the hypothesis that they are nearly all radio sources, and that their emission is not dominated by re-emission from warm dust. In a bright (>50 mJy) 148 GHz-selected sample with complete cross-identifications from the Australia Telescope 20 GHz survey, we observe an average steepening of the spectra between 5, 20, and 148 GHz with median spectral indices of $\alpha_{\rm 5-20} = -0.07 \pm 0.06$, $\alpha_{\rm 20-148} = -0.39 \pm0.04$, and $\alpha_{\rm 5-148} = -0.20 \pm 0.03$. When the measured spectral indices are taken into account, the 148 GHz differential source counts are consistent with previous measurements at 30 GHz in the context of a source count model dominated by radio sources. Extrapolating with an appropriately rescaled model for the radio source counts, the Poisson contribution to the spatial power spectrum from synchrotron-dominated sources with flux density less than 20 mJy is C^{\rm Sync} = (2.8 \pm 0.3) \times 10^{-6} \micro\kelvin^2.Comment: Accepted to Ap

Sunyaev-Zel'dovich clusters reconstruction in multiband bolometer camera surveys

We present a new method for the reconstruction of Sunyaev-Zel'dovich (SZ) galaxy clusters in future SZ-survey experiments using multiband bolometer cameras such as Olimpo, APEX, or Planck. Our goal is to optimise SZ-Cluster extraction from our observed noisy maps. We wish to emphasize that none of the algorithms used in the detection chain is tuned on prior knowledge on the SZ -Cluster signal, or other astrophysical sources (Optical Spectrum, Noise Covariance Matrix, or covariance of SZ Cluster wavelet coefficients). First, a blind separation of the different astrophysical components which contribute to the observations is conducted using an Independent Component Analysis (ICA) method. Then, a recent non linear filtering technique in the wavelet domain, based on multiscale entropy and the False Discovery Rate (FDR) method, is used to detect and reconstruct the galaxy clusters. Finally, we use the Source Extractor software to identify the detected clusters. The proposed method was applied on realistic simulations of observations. As for global detection efficiency, this new method is impressive as it provides comparable results to Pierpaoli et al. method being however a blind algorithm. Preprint with full resolution figures is available at the URL: w10-dapnia.saclay.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=728Comment: Submitted to A&A. 32 Pages, text onl

Extragalactic millimeter-wave sources in South Pole Telescope survey data: source counts, catalog, and statistics for an 87 square-degree field

We report the results of an 87 square-degree point-source survey centered at R.A. 5h30m, decl. -55 deg. taken with the South Pole Telescope (SPT) at 1.4 and 2.0 mm wavelengths with arc-minute resolution and milli-Jansky depth. Based on the ratio of flux in the two bands, we separate the detected sources into two populations, one consistent with synchrotron emission from active galactic nuclei (AGN) and one consistent with thermal emission from dust. We present source counts for each population from 11 to 640 mJy at 1.4 mm and from 4.4 to 800 mJy at 2.0 mm. The 2.0 mm counts are dominated by synchrotron-dominated sources across our reported flux range; the 1.4 mm counts are dominated by synchroton-dominated sources above ~15 mJy and by dust-dominated sources below that flux level. We detect 141 synchrotron-dominated sources and 47 dust-dominated sources at S/N > 4.5 in at least one band. All of the most significantly detected members of the synchrotron-dominated population are associated with sources in previously published radio catalogs. Some of the dust-dominated sources are associated with nearby (z << 1) galaxies whose dust emission is also detected by the Infrared Astronomy Satellite (IRAS). However, most of the bright, dust-dominated sources have no counterparts in any existing catalogs. We argue that these sources represent the rarest and brightest members of the population commonly referred to as sub-millimeter galaxies (SMGs). Because these sources are selected at longer wavelengths than in typical SMG surveys, they are expected to have a higher mean redshift distribution and may provide a new window on galaxy formation in the early universe.Comment: 35 emulateapj pages, 12 figures, 5 table

Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of "ambiguous" modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into "pure" E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.Comment: Minor changes to previous version. Accepted for publication in Phys. Rev.

GOODS-HerschelHerschel: identification of the individual galaxies responsible for the 80-290μ\mum cosmic infrared background

We propose a new method of pushing $Herschel$ to its faintest detection limits using universal trends in the redshift evolution of the far infrared over 24$\mu$m colours in the well-sampled GOODS-North field. An extension to other fields with less multi-wavelength information is presented. This method is applied here to raise the contribution of individually detected $Herschel$ sources to the cosmic infrared background (CIRB) by a factor 5 close to its peak at 250$\mu$m and more than 3 in the 350$\mu$m and 500$\mu$m bands. We produce realistic mock $Herschel$ images of the deep PACS and SPIRE images of the GOODS-North field from the GOODS-$Herschel$ Key Program and use them to quantify the confusion noise at the position of individual sources, i.e., estimate a "local confusion noise". Two methods are used to identify sources with reliable photometric accuracy extracted using 24$\mu$m prior positions. The clean index (CI), previously defined but validated here with simulations, which measures the presence of bright 24$\mu$m neighbours and the photometric accuracy index (PAI) directly extracted from the mock $Herschel$ images. After correction for completeness, thanks to our mock $Herschel$ images, individually detected sources make up as much as 54% and 60% of the CIRB in the PACS bands down to 1.1 mJy at 100$\mu$m and 2.2 mJy at 160$\mu$m and 55, 33, and 13% of the CIRB in the SPIRE bands down to 2.5, 5, and 9 mJy at 250$\mu$m, 350$\mu$m, and 500$\mu$m, respectively. The latter depths improve the detection limits of $Herschel$ by factors of 5 at 250$\mu$m, and 3 at 350$\mu$m and 500$\mu$m as compared to the standard confusion limit. Interestingly, the dominant contributors to the CIRB in all $Herschel$ bands appear to be distant siblings of the Milky Way ($z$$\sim$0.96 for $\lambda$$<$300$\mu$m) with a stellar mass of $M_{\star}$$\sim$9$\times$10$^{10}$M$_{\odot}$.Comment: 22 pages, 16 figures. Accepted for publication by Astronomy and Astrophysic