10,582 research outputs found
Structure in the 3D Galaxy Distribution: I. Methods and Example Results
Three methods for detecting and characterizing structure in point data, such
as that generated by redshift surveys, are described: classification using
self-organizing maps, segmentation using Bayesian blocks, and density
estimation using adaptive kernels. The first two methods are new, and allow
detection and characterization of structures of arbitrary shape and at a wide
range of spatial scales. These methods should elucidate not only clusters, but
also the more distributed, wide-ranging filaments and sheets, and further allow
the possibility of detecting and characterizing an even broader class of
shapes. The methods are demonstrated and compared in application to three data
sets: a carefully selected volume-limited sample from the Sloan Digital Sky
Survey redshift data, a similarly selected sample from the Millennium
Simulation, and a set of points independently drawn from a uniform probability
distribution -- a so-called Poisson distribution. We demonstrate a few of the
many ways in which these methods elucidate large scale structure in the
distribution of galaxies in the nearby Universe.Comment: Re-posted after referee corrections along with partially re-written
introduction. 80 pages, 31 figures, ApJ in Press. For full sized figures
please download from: http://astrophysics.arc.nasa.gov/~mway/lss1.pd
The Loss Rank Principle for Model Selection
We introduce a new principle for model selection in regression and
classification. Many regression models are controlled by some smoothness or
flexibility or complexity parameter c, e.g. the number of neighbors to be
averaged over in k nearest neighbor (kNN) regression or the polynomial degree
in regression with polynomials. Let f_D^c be the (best) regressor of complexity
c on data D. A more flexible regressor can fit more data D' well than a more
rigid one. If something (here small loss) is easy to achieve it's typically
worth less. We define the loss rank of f_D^c as the number of other
(fictitious) data D' that are fitted better by f_D'^c than D is fitted by
f_D^c. We suggest selecting the model complexity c that has minimal loss rank
(LoRP). Unlike most penalized maximum likelihood variants (AIC,BIC,MDL), LoRP
only depends on the regression function and loss function. It works without a
stochastic noise model, and is directly applicable to any non-parametric
regressor, like kNN. In this paper we formalize, discuss, and motivate LoRP,
study it for specific regression problems, in particular linear ones, and
compare it to other model selection schemes.Comment: 16 page
Supervised cross-modal factor analysis for multiple modal data classification
In this paper we study the problem of learning from multiple modal data for
purpose of document classification. In this problem, each document is composed
two different modals of data, i.e., an image and a text. Cross-modal factor
analysis (CFA) has been proposed to project the two different modals of data to
a shared data space, so that the classification of a image or a text can be
performed directly in this space. A disadvantage of CFA is that it has ignored
the supervision information. In this paper, we improve CFA by incorporating the
supervision information to represent and classify both image and text modals of
documents. We project both image and text data to a shared data space by factor
analysis, and then train a class label predictor in the shared space to use the
class label information. The factor analysis parameter and the predictor
parameter are learned jointly by solving one single objective function. With
this objective function, we minimize the distance between the projections of
image and text of the same document, and the classification error of the
projection measured by hinge loss function. The objective function is optimized
by an alternate optimization strategy in an iterative algorithm. Experiments in
two different multiple modal document data sets show the advantage of the
proposed algorithm over other CFA methods
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