Pattern Recognition in Chemistry by Kurt Varmuza (auth.)

By Kurt Varmuza (auth.)

Analytical chemistry of the hot years is strongly prompted through automation. information acquisition from analytica~ tools - and a few­ occasions additionally controlling of tools - by way of a working laptop or computer are mostly solved considering a long time. Availability of microcomputers made those projects additionally possible from the industrial standpoint. along with those simple purposes of desktops in chemical measurements scientists built desktop courses for fixing extra refined difficulties for which a few form of "intelligence" is mostly imagined to be valuable. damage­ much less numerical experiments in this subject ended in passionate discussions concerning the subject matter "which jobs can't be performed by means of a working laptop or computer yet basically by way of human mind ?~. If this query turns out to be useful in any respect it may now not be ans­ wered a priori. program of pcs in chemistry is an issue of application, occasionally it's a social challenge, however it is rarely a query of piety for the human mind. computerized tools and the need to paintings on advanced seasoned­ blems better the advance of computerized equipment for the relief and interpretation of huge facts units. a number of equipment from arithmetic, information, details conception, and machine technology were exten­ sively investigated for the elucidation of chemical info; a brand new self-discipline "chemometrics" has been tested. 3 diverse methods were used for computer-assisted interpretations of chemical info. 1. Heuristic tools try and formu­ overdue laptop courses operating similarly as a chemist may clear up the matter. 2.

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1 k = for all dimensions r/ \r-u- ( 18) V i~1 xi PATTERN POI N TS ,, ""/ ' . ~----f---. . ,~ 6c ~' . , ,, HYPERSPHERE FIGURE 1~. The distance between the centre of gravity ~ and the surface of the sphere is a criterion for the tightness of the cluster. All pattern points have been normalized to constant length. 25 If all pattern points lie on the surface of the sphere, then the centre of gravity of a cluster lies inside the sphere (Figure 14). The distance between the centre of gravity and the surface is a measure of the compactness of the cluster [54J.

2. Centres of Gravity in a d-Dimensional Space The coordinates c 1 , c 2 , ••• cd of the centre of gravity c in a d-dimensional hyperspace are calculated in the same way as for 2 dimensions. Each coordinate c i is the arithmetic average of the components xi summed over all patterns j (j = 1 ••• n) of a distinct class. Thus the centre of gravity is the mean of all patterns belonging to the same class. n c. 1 Ci n x ij n~ j=1 x .. 3. Classification by Distance Measurements For distance measurements between two points in the d-dimensional hyperspace usually the Euclidean distance D is used.

25 If all pattern points lie on the surface of the sphere, then the centre of gravity of a cluster lies inside the sphere (Figure 14). The distance between the centre of gravity and the surface is a measure of the compactness of the cluster [54J. 8. Distance Measurements in Pattern Space (Overview) In this Chapter some often used distance measurements in a sional space are summarized. d-dimen~ Let x(x 1 ' x 2 ' ••• x d ), z(z1' z2' ••• zd)' and U(U 1 ' u 2 ' ••• u d ) be three points in a d-dimensional space.

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