18,538 research outputs found
Sampling-based optimization with mixtures
Sampling-based Evolutionary Algorithms (EA) are of great use when dealing with a highly non-convex and/or noisy optimization task, which is the kind of task we often have to solve in Machine Learning. Two derivative-free examples of such methods are Estimation of Distribution Algorithms (EDA) and techniques based on the Cross-Entropy Method (CEM). One of the main problems these algorithms have to solve is finding a good surrogate model for the normalized target function, that is, a model which has sufficient complexity to fit this target function, but which keeps the computations simple enough. Gaussian mixture models have been applied in practice with great success, but most of these approaches lacked a solid theoretical founding. In this paper we describe a sound mathematical justification for Gaussian mixture surrogate models, more precisely we propose a proper derivation of an EDA/CEM algorithm with mixture updates using Expectation Maximization techniques. It will appear that this algorithm resembles the recent Population MCMC schemes, thus reinforcing the link between Monte- Carlo integration methods and sampling-based optimization. We will concentrate throughout this paper on continuous optimization
Application of the Gaussian mixture model in pulsar astronomy -- pulsar classification and candidates ranking for {\it Fermi} 2FGL catalog
Machine learning, algorithms to extract empirical knowledge from data, can be
used to classify data, which is one of the most common tasks in observational
astronomy. In this paper, we focus on Bayesian data classification algorithms
using the Gaussian mixture model and show two applications in pulsar astronomy.
After reviewing the Gaussian mixture model and the related
Expectation-Maximization algorithm, we present a data classification method
using the Neyman-Pearson test. To demonstrate the method, we apply the
algorithm to two classification problems. Firstly, it is applied to the well
known period-period derivative diagram, where we find that the pulsar
distribution can be modeled with six Gaussian clusters, with two clusters for
millisecond pulsars (recycled pulsars) and the rest for normal pulsars. From
this distribution, we derive an empirical definition for millisecond pulsars as
. The two
millisecond pulsar clusters may have different evolutionary origins, since the
companion stars to these pulsars in the two clusters show different chemical
composition. Four clusters are found for normal pulsars. Possible implications
for these clusters are also discussed. Our second example is to calculate the
likelihood of unidentified \textit{Fermi} point sources being pulsars and rank
them accordingly. In the ranked point source list, the top 5% sources contain
50% known pulsars, the top 50% contain 99% known pulsars, and no known active
galaxy (the other major population) appears in the top 6%. Such a ranked list
can be used to help the future follow-up observations for finding pulsars in
unidentified \textit{Fermi} point sources.Comment: 9 pages, 4 figures, accepted by MNRA
Paired Comparisons-based Interactive Differential Evolution
We propose Interactive Differential Evolution (IDE) based on paired
comparisons for reducing user fatigue and evaluate its convergence speed in
comparison with Interactive Genetic Algorithms (IGA) and tournament IGA. User
interface and convergence performance are two big keys for reducing Interactive
Evolutionary Computation (IEC) user fatigue. Unlike IGA and conventional IDE,
users of the proposed IDE and tournament IGA do not need to compare whole
individuals each other but compare pairs of individuals, which largely
decreases user fatigue. In this paper, we design a pseudo-IEC user and evaluate
another factor, IEC convergence performance, using IEC simulators and show that
our proposed IDE converges significantly faster than IGA and tournament IGA,
i.e. our proposed one is superior to others from both user interface and
convergence performance points of view
A Comparison of Nature Inspired Algorithms for Multi-threshold Image Segmentation
In the field of image analysis, segmentation is one of the most important
preprocessing steps. One way to achieve segmentation is by mean of threshold
selection, where each pixel that belongs to a determined class islabeled
according to the selected threshold, giving as a result pixel groups that share
visual characteristics in the image. Several methods have been proposed in
order to solve threshold selectionproblems; in this work, it is used the method
based on the mixture of Gaussian functions to approximate the 1D histogram of a
gray level image and whose parameters are calculated using three nature
inspired algorithms (Particle Swarm Optimization, Artificial Bee Colony
Optimization and Differential Evolution). Each Gaussian function approximates
thehistogram, representing a pixel class and therefore a threshold point.
Experimental results are shown, comparing in quantitative and qualitative
fashion as well as the main advantages and drawbacks of each algorithm, applied
to multi-threshold problem.Comment: 16 pages, this is a draft of the final version of the article sent to
the Journa
A New Generation of Mixture-Model Cluster Analysis with Information Complexity and the Genetic EM Algorithm
In this dissertation, we extend several relatively new developments in statistical model selection and data mining in order to improve one of the workhorse statistical tools - mixture modeling (Pearson, 1894). The traditional mixture model assumes data comes from several populations of Gaussian distributions. Thus, what remains is to determine how many distributions, their population parameters, and the mixing proportions. However, real data often do not fit the restrictions of normality very well. It is likely that data from a single population exhibiting either asymmetrical or nonnormal tail behavior could be erroneously modeled as two populations, resulting in suboptimal decisions. To avoid these pitfalls, we develop the mixture model under a broader distributional assumption by fitting a group of multivariate elliptically-contoured distributions (Anderson and Fang, 1990; Fang et al., 1990). Special cases include the multivariate Gaussian and power exponential distributions, as well as the multivariate generalization of the Student’s T. This gives us the flexibility to model nonnormal tail and peak behavior, though the symmetry restriction still exists. The literature has many examples of research generalizing the Gaussian mixture model to other distributions (Farrell and Mersereau, 2004; Hasselblad, 1966; John, 1970a), but our effort is more general. Further, we generalize the mixture model to be non-parametric, by developing two types of kernel mixture model. First, we generalize the mixture model to use the truly multivariate kernel density estimators (Wand and Jones, 1995). Additionally, we develop the power exponential product kernel mixture model, which allows the density to adjust to the shape of each dimension independently. Because kernel density estimators enforce no functional form, both of these methods can adapt to nonnormal asymmetric, kurtotic, and tail characteristics. Over the past two decades or so, evolutionary algorithms have grown in popularity, as they have provided encouraging results in a variety of optimization problems. Several authors have applied the genetic algorithm - a subset of evolutionary algorithms - to mixture modeling, including Bhuyan et al. (1991), Krishna and Murty (1999), and Wicker (2006). These procedures have the benefit that they bypass computational issues that plague the traditional methods. We extend these initialization and optimization methods by combining them with our updated mixture models. Additionally, we “borrow” results from robust estimation theory (Ledoit and Wolf, 2003; Shurygin, 1983; Thomaz, 2004) in order to data-adaptively regularize population covariance matrices. Numerical instability of the covariance matrix can be a significant problem for mixture modeling, since estimation is typically done on a relatively small subset of the observations. We likewise extend various information criteria (Akaike, 1973; Bozdogan, 1994b; Schwarz, 1978) to the elliptically-contoured and kernel mixture models. Information criteria guide model selection and estimation based on various approximations to the Kullback-Liebler divergence. Following Bozdogan (1994a), we use these tools to sequentially select the best mixture model, select the best subset of variables, and detect influential observations - all without making any subjective decisions. Over the course of this research, we developed a full-featured Matlab toolbox (M3) which implements all the new developments in mixture modeling presented in this dissertation. We show results on both simulated and real world datasets. Keywords: mixture modeling, nonparametric estimation, subset selection, influence detection, evidence-based medical diagnostics, unsupervised classification, robust estimation
A Survey on Soft Subspace Clustering
Subspace clustering (SC) is a promising clustering technology to identify
clusters based on their associations with subspaces in high dimensional spaces.
SC can be classified into hard subspace clustering (HSC) and soft subspace
clustering (SSC). While HSC algorithms have been extensively studied and well
accepted by the scientific community, SSC algorithms are relatively new but
gaining more attention in recent years due to better adaptability. In the
paper, a comprehensive survey on existing SSC algorithms and the recent
development are presented. The SSC algorithms are classified systematically
into three main categories, namely, conventional SSC (CSSC), independent SSC
(ISSC) and extended SSC (XSSC). The characteristics of these algorithms are
highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
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