15 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 reduction for efficient LDA topic reconstruction
We present a novel approach for LDA (Latent Dirichlet Allocation) topic reconstruction. The main technical idea is to show that the distribution over the documents generated by LDA can be transformed into a distribution for a much simpler generative model in which documents are generated from the same set of topics but have a much simpler structure: documents are single topic and topics are chosen uniformly at random. Furthermore, this reduction is approximation preserving, in the sense that approximate distributions - the only ones we can hope to compute in practice - are mapped into approximate distribution in the simplified world. This opens up the possibility of efficiently reconstructing LDA topics in a roundabout way. Compute an approximate document distribution from the given corpus, transform it into an approximate distribution for the single-topic world, and run a reconstruction algorithm in the uniform, single-topic world - a much simpler task than direct LDA reconstruction. We show the viability of the approach by giving very simple algorithms for a generalization of two notable cases that have been studied in the literature, p-separability and matrix-like topics
Self-Repairing systems modeling and verification using AGG
Self-Repairing (or healing) systems are systems
equipped with a mechanism that monitors the system behaviour
to determine whether it behaves within prefixed parameters.
If a deviation exists, then the system itself is in charge of
adapting its configuration. In this paper we show how to model
self-repairing systems by means of Dynamic Software Architectures (DSAs). DSAs are formalized as Typed (hyper) Graph Grammars (TGGs) and this formalization enables verification of correctness and completeness of self-repairing systems. DSAs are modeled and verified by using the Attributed Graph Grammar system (AGG). The overall approach is applied to a traffic light system case study