HIERARCHICAL CLUSTERING USING LEVEL SETS

Over the past several decades, clustering algorithms have earned their place as a go-to solution for database mining. This paper introduces a new concept which is used to develop a new recursive version of DBSCAN that can successfully perform hierarchical clustering, called Level- Set Clustering (LSC). A level-set is a subset of points of a data-set whose densities are greater than some threshold, ‘t’. By graphing the size of each level-set against its respective ‘t,’ indents are produced in the line graph which correspond to clusters in the data-set, as the points in a cluster have very similar densities. This new algorithm is able to produce the clustering result with the same O(n log n) time complexity as DBSCAN and OPTICS, while catching clusters the others missed

Weak Lensing Peak Finding: Estimators, Filters, and Biases

Large catalogs of shear-selected peaks have recently become a reality. In order to properly interpret the abundance and properties of these peaks, it is necessary to take into account the effects of the clustering of source galaxies, among themselves and with the lens. In addition, the preferred selection of lensed galaxies in a flux- and size-limited sample leads to fluctuations in the apparent source density which correlate with the lensing field (lensing bias). In this paper, we investigate these issues for two different choices of shear estimators which are commonly in use today: globally-normalized and locally-normalized estimators. While in principle equivalent, in practice these estimators respond differently to systematic effects such as lensing bias and cluster member dilution. Furthermore, we find that which estimator is statistically superior depends on the specific shape of the filter employed for peak finding; suboptimal choices of the estimator+filter combination can result in a suppression of the number of high peaks by orders of magnitude. Lensing bias generally acts to increase the signal-to-noise \nu of shear peaks; for high peaks the boost can be as large as \Delta \nu ~ 1-2. Due to the steepness of the peak abundance function, these boosts can result in a significant increase in the abundance of shear peaks. A companion paper (Rozo et al., 2010) investigates these same issues within the context of stacked weak lensing mass estimates.Comment: 11 pages, 8 figures; comments welcom

Determining cosmic microwave background structure from its peak distribution

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering - analogously to galaxies, the 2-point angular correlation function, $\xi_\nu(\theta)$. We show that for increasing peak threshold, $\nu$, the $\xi_\nu(\theta)$ is strongly amplified and becomes measurable for $\nu\geq$1 on angular scales $\leq 10^\circ$. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, $C(\theta)$, and thus the measured $\xi_\nu$ can be uniquely inverted to obtain $C(\theta)$ and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only $[f(\nu)]^2N^2$ operations where $f(\nu)$ is the fraction of pixels with $|\delta T|\geq\nu$ standard deviations in the map of $N$ pixels and is e.g. 0.045 and 0.01 for $\nu$=2 and 2.5 respectively. We develop theoretical formalism for the method and show with detailed simulations, using MAP mission parameters, that this method allows to determine very accurately the CMB power spectrum from the upcoming CMB maps in only $\sim(10^{-4}-10^{-3})\times N^2$ operations.Comment: To be published in Ap.J. Letters. Minor changes to match the journal versio

The clustering of galaxies at z~0.5 in the SDSS-III Data Release 9 BOSS-CMASS sample: a test for the LCDM cosmology

We present results on the clustering of 282,068 galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) sample of massive galaxies with redshifts 0.4<z<0.7 which is part of the Sloan Digital Sky Survey III project. Our results cover a large range of scales from ~0.5 to ~90 Mpc/h. We compare these estimates with the expectations of the flat LCDM cosmological model with parameters compatible with WMAP7 data. We use the MultiDark cosmological simulation together with a simple halo abundance matching technique, to estimate galaxy correlation functions, power spectra, abundance of subhaloes and galaxy biases. We find that the LCDM model gives a reasonable description to the observed correlation functions at z~0.5, which is a remarkably good agreement considering that the model, once matched to the observed abundance of BOSS galaxies, does not have any free parameters. However, we find a deviation (>~10%) in the correlation functions for scales less than ~1 Mpc/h and ~10-40 Mpc/h. A more realistic abundance matching model and better statistics from upcoming observations are needed to clarify the situation. We also estimate that about 12% of the "galaxies" in the abundance-matched sample are satellites inhabiting central haloes with mass M>~1e14 M_sun/h. Using the MultiDark simulation we also study the real space halo bias b(r) of the matched catalogue finding that b=2.00+/-0.07 at large scales, consistent with the one obtained using the measured BOSS projected correlation function. Furthermore, the linear large-scale bias depends on the number density n of the abundance-matched sample as b=-0.048-(0.594+/-0.02)*log(n/(h/Mpc)^3). Extrapolating these results to BAO scales we measure a scale-dependent damping of the acoustic signal produced by non-linear evolution that leads to ~2-4% dips at ~3 sigma level for wavenumbers k>~0.1 h/Mpc in the linear large-scale bias.Comment: Replaced to match published version. Typos corrected; 25 pages, 17 figures, 9 tables. To appear in MNRAS. Correlation functions (projected and redshift-space) and correlation matrices of CMASS presented in Appendix B. Correlation and covariance data for the combined CMASS sample can be downloaded from http://www.sdss3.org/science/boss_publications.ph

Two 100 Mpc-scale structures in the 3-D distribution of radio galaxies and their implications

We present unequivocal evidence for a huge (~80 x 100 x 100 Mpc^3) super-structure at redshift z=0.27 in the 3-D distribution of radio galaxies from the TONS08 sample, confirming tentative evidence for such a structure from the 7C redshift survey (7CRS). A second, newly discovered super-structure is also less securely found at redshift 0.35 (of dimensions ~100 x 100 x 100 Mpc^3). We present full observational details on the TONS08 sample which was constructed to probe structures in the redshift range 0 < z < 0.5 by matching NVSS sources with objects in APM catalogues to obtain a sample of optically bright (E ~ R 3 mJy) radio galaxies in the same 25 deg^2 area as part-II of the 7CRS. Out of the total sample size of 84 radio galaxies, at least 25 are associated with the two ~100 Mpc-scale super-structures. We use quasi-linear structure formation theory to estimate the number of such structures expected in the TONS08 volume if the canonical value for radio galaxy bias is assumed. Under this assumption, the structures represent ~ 4-5 sigma peaks in the primordial density field and their expected number is low (~10^-2 - 10^-4). Fortunately, there are several plausible explanations (many of which are testable) for these low probabilities in the form of potential mechanisms for boosting the bias on large scales. These include: the association of radio galaxies with highly biased rich clusters in super-structures, enhanced triggering by group/group mergers, and enhanced triggering and/or redshift space distortion in collapsing systems as the growth of super-structures moves into the non-linear regime (abridged).Comment: Accepted for publication in MNRAS. 26 pages,16 figures. spectra can be found in: http://www-astro.physics.ox.ac.uk/~brand/08_paper.ps.g

A GMBCG Galaxy Cluster Catalog of 55,424 Rich Clusters from SDSS DR7

We present a large catalog of optically selected galaxy clusters from the application of a new Gaussian Mixture Brightest Cluster Galaxy (GMBCG) algorithm to SDSS Data Release 7 data. The algorithm detects clusters by identifying the red sequence plus Brightest Cluster Galaxy (BCG) feature, which is unique for galaxy clusters and does not exist among field galaxies. Red sequence clustering in color space is detected using an Error Corrected Gaussian Mixture Model. We run GMBCG on 8240 square degrees of photometric data from SDSS DR7 to assemble the largest ever optical galaxy cluster catalog, consisting of over 55,000 rich clusters across the redshift range from 0.1 < z < 0.55. We present Monte Carlo tests of completeness and purity and perform cross-matching with X-ray clusters and with the maxBCG sample at low redshift. These tests indicate high completeness and purity across the full redshift range for clusters with 15 or more members.Comment: Updated to match the published version. The catalog can be accessed from: http://home.fnal.gov/~jghao/gmbcg_sdss_catalog.htm