From Aggregation Operators to Soft Learning Vector Quantization and Clustering Algorithms

Karayiannis, N.B.

doi:10.1016/b978-044450270-4/50004-8

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…Using the weighted norm in Eq. (15) to perform clustering of the original set of feature vectors {x i ∈ X ⊂ R n×1 } is equivalent to using the Euclidean norm to perform clustering of a new set of vectors { x i ∈ X ⊂ R n×1 } produced through the linear transformation…”

Section: Reformulation Functions Based On Weighted Normsmentioning

confidence: 99%

“…This motivated the development of fuzzy and, more recently, soft clustering algorithms. Soft clustering algorithms can be seen as the essential generalization of fuzzy clustering algorithms and include fuzzy clustering algorithms as special cases [13][14][15]17,18,[21][22][23]. Fuzzy and soft clustering algorithms typically outperform hard clustering algorithms because they quantify the uncertainty associated with the partition of feature vectors into clusters and they exploit this uncertainty to benefit cluster formation.…”

Section: Introductionmentioning

confidence: 99%

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Non-Euclidean c-means clustering algorithms

Karayiannis

Randolph-Gips

2003

IDA

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This paper introduces non-Euclidean c-means clustering algorithms. These algorithms rely on weighted norms to measure the distance between the feature vectors and the prototypes that represent the clusters. The proposed algorithms are developed by solving a constrained minimization problem in an iterative fashion. The norm weights are determined from the data in an attempt to produce partitions of the feature vectors that are consistent with the structure of the feature space. A series of experiments on three different data sets reveal that the proposed non-Euclidean c-means algorithms provide an attractive alternative to Euclidean c-means clustering in applications that involve data sets containing clusters of different shapes and sizes.

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Section: Reformulation Functions Based On Weighted Normsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Euclidean c-means clustering algorithms

Karayiannis

Randolph-Gips

2003

IDA

Self Cite

View full text Add to dashboard Cite

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The Dynamic Character Curve Adjusting Model of Electric Load Based on Data Mining Theory

Zhang

Ren

Liu

et al. 2005

Advanced Data Mining and Applications

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Soft Learning Vector Quantization and Clustering Algorithms Based on Non-Euclidean Norms: Single-Norm Algorithms

Karayiannis

Randolph-Gips

2005

IEEE Trans. Neural Netw.

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This paper presents the development of soft clustering and learning vector quantization (LVQ) algorithms that rely on a weighted norm to measure the distance between the feature vectors and their prototypes. The development of LVQ and clustering algorithms is based on the minimization of a reformulation function under the constraint that the generalized mean of the norm weights be constant. According to the proposed formulation, the norm weights can be computed from the data in an iterative fashion together with the prototypes. An error analysis provides some guidelines for selecting the parameter involved in the definition of the generalized mean in terms of the feature variances. The algorithms produced from this formulation are easy to implement and they are almost as fast as clustering algorithms relying on the Euclidean norm. An experimental evaluation on four data sets indicates that the proposed algorithms outperform consistently clustering algorithms relying on the Euclidean norm and they are strong competitors to non-Euclidean algorithms which are computationally more demanding.

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From Aggregation Operators to Soft Learning Vector Quantization and Clustering Algorithms

Cited by 3 publications

References 7 publications

Non-Euclidean c-means clustering algorithms

Non-Euclidean c-means clustering algorithms

The Dynamic Character Curve Adjusting Model of Electric Load Based on Data Mining Theory

Soft Learning Vector Quantization and Clustering Algorithms Based on Non-Euclidean Norms: Single-Norm Algorithms

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