73,079 research outputs found
Clustering for Different Scales of Measurement - the Gap-Ratio Weighted K-means Algorithm
This paper describes a method for clustering data that are spread out over
large regions and which dimensions are on different scales of measurement. Such
an algorithm was developed to implement a robotics application consisting in
sorting and storing objects in an unsupervised way. The toy dataset used to
validate such application consists of Lego bricks of different shapes and
colors. The uncontrolled lighting conditions together with the use of RGB color
features, respectively involve data with a large spread and different levels of
measurement between data dimensions. To overcome the combination of these two
characteristics in the data, we have developed a new weighted K-means
algorithm, called gap-ratio K-means, which consists in weighting each dimension
of the feature space before running the K-means algorithm. The weight
associated with a feature is proportional to the ratio of the biggest gap
between two consecutive data points, and the average of all the other gaps.
This method is compared with two other variants of K-means on the Lego bricks
clustering problem as well as two other common classification datasets.Comment: 13 pages, 6 figures, 2 tables. This paper is under the review process
for AIAP 201
Using interval weights in MADM problems
The choice of weights vectors in multiple attribute decision making (MADM) problems has generated an important literature, and a large number of methods have been proposed for this task. In some situations the decision maker (DM) may not be willing or able to provide exact values of the weights, but this difficulty can be avoided by allowing the DM to give some variability in the weights. In this paper we propose a model where the weights are not fixed, but can take any value from certain intervals, so the score of each alternative is the maximum value that the weighted mean can reach when the weights belong to those intervals. We provide a closed-form expression for the scores achieved by the alternatives so that they can be ranked them without solving the proposed model, and apply this new method to an MADM problem taken from the literature.Este trabajo forma parte del proyecto de investigación: MEC-FEDER Grant ECO2016-77900-P
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results
We compute the pointwise asymptotics of orthogonal polynomials with respect
to a general class of pure point measures supported on finite sets as both the
number of nodes of the measure and also the degree of the orthogonal
polynomials become large. The class of orthogonal polynomials we consider
includes as special cases the Krawtchouk and Hahn classical discrete orthogonal
polynomials, but is far more general. In particular, we consider nodes that are
not necessarily equally spaced. The asymptotic results are given with error
bound for all points in the complex plane except for a finite union of discs of
arbitrarily small but fixed radii. These exceptional discs are the
neighborhoods of the so-called band edges of the associated equilibrium
measure. As applications, we prove universality results for correlation
functions of a general class of discrete orthogonal polynomial ensembles, and
in particular we deduce asymptotic formulae with error bound for certain
statistics relevant in the random tiling of a hexagon with rhombus-shaped
tiles.
The discrete orthogonal polynomials are characterized in terms of a a
Riemann-Hilbert problem formulated for a meromorphic matrix with certain pole
conditions. By extending the methods of [17, 22], we suggest a general and
unifying approach to handle Riemann-Hilbert problems in the situation when
poles of the unknown matrix are accumulating on some set in the asymptotic
limit of interest.Comment: 28 pages, 7 figure
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