### Citations

562 | Lectures on functional equations and their applications, - Aczel - 1966 |

110 |
T.Ando, Means of positive linear operators,
- Kubo
- 1980
(Show Context)
Citation Context ... distances to the cluster centers. These pairwise distances form a distance matrix, one for each data point. The matrix analog of the harmonic mean is the parallel sum, see, e.g., [2], [3], [4], [8], =-=[10]-=- and [11]. An analogous theory of contour approximation can be developed using the parallel sum of the distance matrices, but the computations involved are complicated. (b) Harmonic means play an impo... |

21 |
Harmonic mean measure of animal activity areas.
- Dixon, Chapman
- 1980
(Show Context)
Citation Context ...(areas of activity) of animals are based on the harmonic mean of areal moments in much the same way, and for similar reasons that contour approximation uses the harmonic mean of distances, see, e.g., =-=[7]-=-. (c) A unified optimization framework for distance clustering, employing quasi– linear means and other functions of distances, is given in [12]. Acknowledgement. Thanks to Dr. Cem Iyigun for the grap... |

15 | A unified continuous optimization framework for center-based clustering methods, - Teboulle - 2007 |

7 | Probabilistic distance clustering,
- Ben-Israel, Iyigun
- 2008
(Show Context)
Citation Context ...e). (2) The cluster sizes qk are assumed known. The purpose of this paper is to study a new kind of data approximation suggested by the joint distance function (JDF) used in probabilistic clustering, =-=[6, 9]-=-. The JDF, Mathematics subject classification (2000): 62–07, 26E60, 91C20, 47A64. Key words and phrases: Harmonic mean, quasi-linear mean, clustering, contour approximation of data, distance functions... |

5 |
Shorted operators
- Jr, Trapp
- 1975
(Show Context)
Citation Context ...ata points, not just distances to the cluster centers. These pairwise distances form a distance matrix, one for each data point. The matrix analog of the harmonic mean is the parallel sum, see, e.g., =-=[2]-=-, [3], [4], [8], [10] and [11]. An analogous theory of contour approximation can be developed using the parallel sum of the distance matrices, but the computations involved are complicated. (b) Harmon... |

2 |
Probabilistic distance clustering with cluster sizes, Probab
- Iyigun, Ben-Israel
(Show Context)
Citation Context ...e). (2) The cluster sizes qk are assumed known. The purpose of this paper is to study a new kind of data approximation suggested by the joint distance function (JDF) used in probabilistic clustering, =-=[6, 9]-=-. The JDF, Mathematics subject classification (2000): 62–07, 26E60, 91C20, 47A64. Key words and phrases: Harmonic mean, quasi-linear mean, clustering, contour approximation of data, distance functions... |

2 |
Parallel summation, Maxwell’s principle and the infimum of projections
- MORLEY
- 1979
(Show Context)
Citation Context ...s to the cluster centers. These pairwise distances form a distance matrix, one for each data point. The matrix analog of the harmonic mean is the parallel sum, see, e.g., [2], [3], [4], [8], [10] and =-=[11]-=-. An analogous theory of contour approximation can be developed using the parallel sum of the distance matrices, but the computations involved are complicated. (b) Harmonic means play an important rol... |

1 |
Series and parallel of matrices
- DUFFIN
- 1969
(Show Context)
Citation Context ...oints, not just distances to the cluster centers. These pairwise distances form a distance matrix, one for each data point. The matrix analog of the harmonic mean is the parallel sum, see, e.g., [2], =-=[3]-=-, [4], [8], [10] and [11]. An analogous theory of contour approximation can be developed using the parallel sum of the distance matrices, but the computations involved are complicated. (b) Harmonic me... |

1 |
Network Models, Mathematical Aspects of Electrical Network Analysis
- DUFFIN
- 1971
(Show Context)
Citation Context ... just distances to the cluster centers. These pairwise distances form a distance matrix, one for each data point. The matrix analog of the harmonic mean is the parallel sum, see, e.g., [2], [3], [4], =-=[8]-=-, [10] and [11]. An analogous theory of contour approximation can be developed using the parallel sum of the distance matrices, but the computations involved are complicated. (b) Harmonic means play a... |