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Harmonic Mean for Subspace Selection
"... Under the homoscedastic Gaussian assumption, it has been shown that Fisher’s linear discriminant analysis (FLDA) suffers from the class separation problem when the dimensionality of subspace selected by FLDA is strictly less than the class number minus 1, i.e., the projection to a subspace tends to ..."
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Cited by 7 (2 self)
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to merge close class pairs. A recent result shows that maximizing the geometric mean of KullbackLeibler (KL) divergences of class pairs can significantly reduce this problem. In this paper, to further reduce the class separation problem, the harmonic mean is applied to replace the geometric mean
On the Harmonic Means of Branching Processes
"... The random variable X plays the role of 1 + Z in the eBMP context. Thus, m corresponds to 1 + = (1 p) 1 , and p 1 in this note is p 0 in Piau (2001b), and so on. 0.2 Results Joe (1993) mentions, as an unpublished result, the fact that, for any a > 0, E (S a n ) 6 c q n for any q > max ..."
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Cited by 1 (1 self)
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The random variable X plays the role of 1 + Z in the eBMP context. Thus, m corresponds to 1 + = (1 p) 1 , and p 1 in this note is p 0 in Piau (2001b), and so on. 0.2 Results Joe (1993) mentions, as an unpublished result, the fact that, for any a > 0, E (S a n ) 6 c q n for any q > maxfp 1 ; m a g; where c is independent of n. In the same vein, Athreya (1994) shows that, if p 1 m a > 1, then p n 1 E(S a n j S 0 = 1) is a nondecreasing sequence, t
Geometric and harmonic means
"... J is used for the development of algorithms for a variety of statistical calculations including means, medians and quartiles, frequency tabulations, variances and covariances, regression analysis, graphical presentation, analysis of variance, random number generation and simulation, nonparametric te ..."
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J is used for the development of algorithms for a variety of statistical calculations including means, medians and quartiles, frequency tabulations, variances and covariances, regression analysis, graphical presentation, analysis of variance, random number generation and simulation, nonparametric
ArithmeticGeometricHarmonic Mean
, 2007
"... vol. 10, iss. 4, art. 117, 2009 Title Page Contents ..."
CONTOUR APPROXIMATION OF DATA AND THE HARMONIC MEAN
"... Abstract. A contour approximation of data is a function capturing the data points in its lower level–sets. Desirable properties of contour approximation are posited, and shown to be satisfied uniquely (up to a multiplicative constant) by the weighted harmonic mean of distances to the cluster centers ..."
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Abstract. A contour approximation of data is a function capturing the data points in its lower level–sets. Desirable properties of contour approximation are posited, and shown to be satisfied uniquely (up to a multiplicative constant) by the weighted harmonic mean of distances to the cluster
Some More Results on Harmonic Mean Graphs
, 2012
"... A GraphG = (V, E) with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x ∈ V with distinct labels f (x) from 1, 2,..., q + 1 in such a way that when each edge e = uv is labeled with f (uv) = 2 f (u) f (v) f (u)+ f (v) or 2 f (u) f (v) f (u)+ f (v) then ..."
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A GraphG = (V, E) with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x ∈ V with distinct labels f (x) from 1, 2,..., q + 1 in such a way that when each edge e = uv is labeled with f (uv) = 2 f (u) f (v) f (u)+ f (v) or 2 f (u) f (v) f (u)+ f (v
Harmonic mean, random polynomials and stochastic matrices, preprint
, 2001
"... Abstract. Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our ..."
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Cited by 10 (5 self)
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our results extend to other distributions). This, in turn, requires the study of the statistical behavior of the harmonic mean of random variables as above, and that, in turn, leads us to delicate question of the rate of convergence to stable laws and tail estimates for stable laws.
Ensemble based distributed kharmonic means clustering
 International Journal of Recent Trends in Engineering
, 2009
"... Abstract—Due to the explosion in the number of autonomous data sources, there is a growing need for effective approaches for distributed knowledge discovery and data mining. The distributed clustering algorithm is used to cluster the distributed datasets without necessarily downloading all the data ..."
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Cited by 2 (0 self)
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sensitive to centroid initialization. It is demonstrated that KHarmonic Means is essentially insensitive to centroid initialization. In this paper, a novel ensemble based distributed clustering algorithm using KHarmonic Means is proposed. The simulated experiments described in this paper confirm robust
A representation formula for the inverse harmonic mean curvature
, 2005
"... Abstract. Let be a smooth family of embedded, strictly convex hypersurfaces in ℝ +1 evolving by the inverse harmonic mean curvature flow = ℋ −1 . Surprisingly, we can determine the explicit solution of this nonlinear parabolic equation with some Fourier analysis. More precisely, there exists a repr ..."
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Cited by 6 (0 self)
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Abstract. Let be a smooth family of embedded, strictly convex hypersurfaces in ℝ +1 evolving by the inverse harmonic mean curvature flow = ℋ −1 . Surprisingly, we can determine the explicit solution of this nonlinear parabolic equation with some Fourier analysis. More precisely, there exists a
Results 1  10
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2,821