3,380 research outputs found
Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm
Over the past five decades, k-means has become the clustering algorithm of
choice in many application domains primarily due to its simplicity, time/space
efficiency, and invariance to the ordering of the data points. Unfortunately,
the algorithm's sensitivity to the initial selection of the cluster centers
remains to be its most serious drawback. Numerous initialization methods have
been proposed to address this drawback. Many of these methods, however, have
time complexity superlinear in the number of data points, which makes them
impractical for large data sets. On the other hand, linear methods are often
random and/or sensitive to the ordering of the data points. These methods are
generally unreliable in that the quality of their results is unpredictable.
Therefore, it is common practice to perform multiple runs of such methods and
take the output of the run that produces the best results. Such a practice,
however, greatly increases the computational requirements of the otherwise
highly efficient k-means algorithm. In this chapter, we investigate the
empirical performance of six linear, deterministic (non-random), and
order-invariant k-means initialization methods on a large and diverse
collection of data sets from the UCI Machine Learning Repository. The results
demonstrate that two relatively unknown hierarchical initialization methods due
to Su and Dy outperform the remaining four methods with respect to two
objective effectiveness criteria. In addition, a recent method due to Erisoglu
et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms
(Springer, 2014). arXiv admin note: substantial text overlap with
arXiv:1304.7465, arXiv:1209.196
A Comparative Study of Efficient Initialization Methods for the K-Means Clustering Algorithm
K-means is undoubtedly the most widely used partitional clustering algorithm.
Unfortunately, due to its gradient descent nature, this algorithm is highly
sensitive to the initial placement of the cluster centers. Numerous
initialization methods have been proposed to address this problem. In this
paper, we first present an overview of these methods with an emphasis on their
computational efficiency. We then compare eight commonly used linear time
complexity initialization methods on a large and diverse collection of data
sets using various performance criteria. Finally, we analyze the experimental
results using non-parametric statistical tests and provide recommendations for
practitioners. We demonstrate that popular initialization methods often perform
poorly and that there are in fact strong alternatives to these methods.Comment: 17 pages, 1 figure, 7 table
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (âefficientâ) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find âquicklyâ (reasonable run-times), with âhighâ probability, provable âgoodâ solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
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Variable neighbourhood search based heuristic for K-harmonic means clustering
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Although there has been a rapid development of technology and increase of computation speeds, most of the real-world optimization problems still cannot be solved in a reasonable time. Some times it is impossible for them to be optimally solved, as there are many instances of real problems which cannot be addressed by computers at their present speed. In such cases, the heuristic approach can be used. Heuristic research has been used by many researchers to supply this need. It gives a sufficient solution in reasonable time. The clustering problem is one example of this, formed in many applications.
In this thesis, I suggest a Variable Neighbourhood Search (VNS) to improve a recent clustering local search called K-Harmonic Means (KHM).Many experiments are presented to show the strength of my code compared with some algorithms from the literature.
Some counter-examples are introduced to show that KHM may degenerate entirely, in either one or more runs. Furthermore, it degenerates and then stops in some familiar datasets, which significantly affects the final solution. Hence, I present a removing degeneracy code for KHM. I also apply VNS to improve the code of KHM after removing the evidence of degeneracy
Fast training of self organizing maps for the visual exploration of molecular compounds
Visual exploration of scientific data in life science
area is a growing research field due to the large amount of
available data. The Kohonenâs Self Organizing Map (SOM) is
a widely used tool for visualization of multidimensional data.
In this paper we present a fast learning algorithm for SOMs
that uses a simulated annealing method to adapt the learning
parameters. The algorithm has been adopted in a data analysis
framework for the generation of similarity maps. Such maps
provide an effective tool for the visual exploration of large and
multi-dimensional input spaces. The approach has been applied
to data generated during the High Throughput Screening
of molecular compounds; the generated maps allow a visual
exploration of molecules with similar topological properties.
The experimental analysis on real world data from the
National Cancer Institute shows the speed up of the proposed
SOM training process in comparison to a traditional approach.
The resulting visual landscape groups molecules with similar
chemical properties in densely connected regions
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