1,238 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
Towards optimal symbolization for time series comparisons
The abundance and value of mining large time series data sets has long been acknowledged. Ubiquitous in fields ranging from astronomy, biology and web science the size and number of these datasets continues to increase, a situation exacerbated by the exponential growth of our digital footprints. The prevalence and potential utility of this data has led to a vast number of time-series data mining techniques, many of which require symbolization of the raw time series as a pre-processing step for which a number of well used, pre-existing approaches from the literature are typically employed. In this work we note that these standard approaches are sub-optimal in (at least) the broad application area of time series comparison leading to unnecessary data corruption and potential performance loss before any real data mining takes place. Addressing this we present a novel quantizer based upon optimization of comparison fidelity and a computationally tractable algorithm for its implementation on big datasets. We demonstrate empirically that our new approach provides a statistically significant reduction in the amount of error introduced by the symbolization process compared to current state-of-the-art. The approach therefore provides a more accurate input for the vast number of data mining techniques in the literature, providing the potential of increased real world performance across a wide range of existing data mining algorithms and applications
Adaptive Speech Compression Based on Discrete Wave Atoms Transform
This paper proposes a new adaptive speech compression system based on discrete wave atoms transform. First, the signal is decomposed on wave atoms, then wave atom coefficients are truncated using a new adaptive thresholding which depends on the SNR estimation. The thresholded coefficients are quantized using Max Lloyd scalar quantizer. Besides, they are encoded using zero run length encoding followed by Huffman coding. Numerous simulations are performed to prove the robustness of our approach. The results of current work are compared with wavelet based compression by using objective criteria, namely CR, SNR, PSNR and NRMSE. This study shows that the wave atoms transform is more appropriate than wavelets transform since it offers a higher compression ratio and a better speech quality
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