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The Applications of Moments and Cluster Analysis to Reproductive Cycles

IP.com Disclosure Number: IPCOM000128506D
Original Publication Date: 1972-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 7 page(s) / 28K

Publishing Venue

Software Patent Institute

Related People

Allen R. Hanson, Ph.D: AUTHOR [+4]

Abstract

in this discussion we are considering the application of moments and cluster analysis for the purpose of obtaining insight into and classification of the important mechanisms of problems in chronobiology, in general, and those involving reproductive cycles, in particular. The procedures that we present should be Interpreted as being empirical and not statistical in nature.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

The Applications of Moments and Cluster Analysis to Reproductive Cycles

by

Allen R. Hanson, Ph.D. Jay A. Leavitt, Ph.D.

Technical Report 72-11 October, 1972

Abstract

in this discussion we are considering the application of moments and cluster analysis for the purpose of obtaining insight into and classification of the important mechanisms of problems in chronobiology, in general, and those involving reproductive cycles, in particular. The procedures that we present should be Interpreted as being empirical and not statistical in nature.

Section I. Generalized Moments

Generalized moments have been employed in a wide variety of problems because of their ability to reflect geometric features. Applications cover diverse fields of study ranging from ship identification j1J to alphanumeric character recognition [2,3]. Loosely, we define a generalized moment as a paramter we obtain when we form the convolution of a function f(t) we wish to analyze with one of a set of trial. functions

(Equation Omitted)

Ordinarily, if the function is defined by a set of data points, f(tj) , the ith moment

(Equation Omitted)

Typical choices of gilt) include

powers, ti , trigonometric functions, piecewise constant functions, and pyramid functions. If we are using (ti} as the set of trial functions MO is related to the arithmetic mean of f(t); M1 is related to its center of mass. A moment may be thought of as a weighted average. The purpose of introducing moments is to reduce the dimensionality of the space we are investigating. For example, if we were testing subjects so that we had 100 data points, we would not want to have to consider how each subject at each point behaved. Instead properties describing the mean, symmetry, etc. of the data constitute a smaller set of attributes which could be easier to analyze. Moments appear in a natural way in linear least squares problems fox they are the inhomogeneous terms that appear in the resulting equations (see Appendix). However, unlike the parameters which are obtained in a least squares fit the moments are independent of the number of terms used and of the other functions in the set. Furthermore, this implies that they are independent of the quality of fit. Thus they form an ideal set of parameters which may be used for subsequent analysis of f(t) . The relation between standard experimental procedures

University of Minnesota Page 1 Dec 31, 1972

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The Applications of Moments and Cluster Analysis to Reproductive Cycles

and the proposed method is summarized in Figure 1. In the classical experimental procedure (Figure la) before one

2 _ can analyze the data, a fit is obtained and the analysis is based on properties of the fit. This implies that the poorer the quality of the fit, the poorer our ability to analyze. The object of the proposed procedure (Figure lb) is to avoid this difficulty, that is to avoid the necessity of obtaining a fit....