• Title/Summary/Keyword: Generalized means

Search Result 243, Processing Time 0.03 seconds

Pre-Adjustment of Incomplete Group Variable via K-Means Clustering

  • Hwang, S.Y.;Hahn, H.E.
    • Journal of the Korean Data and Information Science Society
    • /
    • v.15 no.3
    • /
    • pp.555-563
    • /
    • 2004
  • In classification and discrimination, we often face with incomplete group variable arising typically from many missing values and/or incredible cases. This paper suggests the use of K-means clustering for pre-adjusting incompleteness and in turn classification based on generalized statistical distance is performed. For illustrating the proposed procedure, simulation study is conducted comparatively with CART in data mining and traditional techniques which are ignoring incompleteness of group variable. Simulation study manifests that our methodology out-performs.

  • PDF

ON GENERALIZED FINSLER STRUCTURES WITH A VANISHING hυ-TORSION

  • Ichijyo, Yoshihiro;Lee, Il-Yong;Park, Hong-Suh
    • Journal of the Korean Mathematical Society
    • /
    • v.41 no.2
    • /
    • pp.369-378
    • /
    • 2004
  • A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

A NOTE ON TWO NEW CLOSED-FORM EVALUATIONS OF THE GENERALIZED HYPERGEOMETRIC FUNCTION 5F4 WITH ARGUMENT $\frac{1}{256}$

  • B. R. Srivatsa Kumar;Dongkyu Lim;Arjun K. Rathie
    • The Pure and Applied Mathematics
    • /
    • v.30 no.2
    • /
    • pp.131-138
    • /
    • 2023
  • The aim of this note is to provide two new and interesting closed-form evaluations of the generalized hypergeometric function 5F4 with argument $\frac{1}{256}$. This is achieved by means of separating a generalized hypergeometric function into even and odd components together with the use of two known sums (one each) involving reciprocals of binomial coefficients obtained earlier by Trif and Sprugnoli. In the end, the results are written in terms of two interesting combinatorial identities.

THE INCOMPLETE GENERALIZED τ-HYPERGEOMETRIC AND SECOND τ-APPELL FUNCTIONS

  • Parmar, Rakesh Kumar;Saxena, Ram Kishore
    • Journal of the Korean Mathematical Society
    • /
    • v.53 no.2
    • /
    • pp.363-379
    • /
    • 2016
  • Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

Extensions of X-means with Efficient Learning the Number of Clusters (X-means 확장을 통한 효율적인 집단 개수의 결정)

  • Heo, Gyeong-Yong;Woo, Young-Woon
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.12 no.4
    • /
    • pp.772-780
    • /
    • 2008
  • K-means is one of the simplest unsupervised learning algorithms that solve the clustering problem. However K-means suffers the basic shortcoming: the number of clusters k has to be known in advance. In this paper, we propose extensions of X-means, which can estimate the number of clusters using Bayesian information criterion(BIC). We introduce two different versions of algorithm: modified X-means(MX-means) and generalized X-means(GX-means), which employ one full covariance matrix for one cluster and so can estimate the number of clusters efficiently without severe over-fitting which X-means suffers due to its spherical cluster assumption. The algorithms start with one cluster and try to split a cluster iteratively to maximize the BIC score. The former uses K-means algorithm to find a set of optimal clusters with current k, which makes it simple and fast. However it generates wrongly estimated centers when the clusters are overlapped. The latter uses EM algorithm to estimate the parameters and generates more stable clusters even when the clusters are overlapped. Experiments with synthetic data show that the purposed methods can provide a robust estimate of the number of clusters and cluster parameters compared to other existing top-down algorithms.

Exact stochastic solution of beams subjected to delta-correlated loads

  • Falsone, G.;Settineri, D.
    • Structural Engineering and Mechanics
    • /
    • v.47 no.3
    • /
    • pp.307-329
    • /
    • 2013
  • The bending problem of Euler-Bernoulli discontinuous beams is dealt with, in which the discontinuities are due to the loads and eventually to essential constrains applied along the beam axis. In particular, the loads are modelled as random delta-correlated processes acting along the beam axis, while the ulterior eventual discontinuities are produced by the presence of external rollers applied along the beam axis. This kind of structural model can be considered in the static study of bridge beams. In the present work the exact expression of the response quantities are given in terms of means and variances, thanks to the use of the stochastic analysis rules and to the use of the generalized functions. The knowledge of the means and the variances of the internal forces implies the possibility of applying the reliability ${\beta}$-method for verifying the beam.

The Generation Method to Generalized Reed-Muller Coefficients over GF(3) by means of the Comparison of the Polarity (극수비교에 의한 GF(3)의 일반화된 Reed-Muller 계수 생성 방법)

  • Lee, Chol-U;Kim, Heung-Soo
    • Journal of IKEEE
    • /
    • v.3 no.2 s.5
    • /
    • pp.285-294
    • /
    • 1999
  • This paper presents a method for the generation of GRM coefncients over GF(3) by using a comparison of polarity. In general production method to GRM coefficients over GF(3) is searching for pn different polarity of an n-variable and from these optimal function according to the maximum number of zero coefficients is selected. This paper presents a method for the generation of GRM coefficients by means of compare to the number of zero coefficients without constructing the whole polarity GRM coefficients.

  • PDF

ON A GENERALIZED UPPER BOUND FOR THE EXPONENTIAL FUNCTION

  • Kim, Seon-Hong
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.1
    • /
    • pp.7-10
    • /
    • 2009
  • With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

  • PDF