General Classification Problems Research Articles

Activation analysis: A basis for chemical similarity and classification

It is shown that activation analysis is especially suited to serve as a basis for determining the chemical similarity between samples defined by their trace element concentration patterns. The general problem of classification and identification is discussed. The nature of possible classification structures and their approriate clustering strategies is considered. A practical computer method is suggested and its application as well as the graphical representation of classification results are given. The possibility for classification using information theory is mentioned. Classification of chemical elements is discussed and practically realized after Hadamard transformation of the concerntration variation patterns in a series of samples.

Comments on "The Application of Filtered Transforms to the General Classification Problem"

Comments on "The Application of Filtered Transforms to the General Classification Problem"

The Application of Filtered Transforms to the General Classification Problem

An image classification model based on nearest prototypes in filtered Fourier and Walsh transform domains is presented. A computer simulation of the model applied to handwritten English letters, Russian letters, numerals, and electromagnetic signals is also presented. Experiments to date fail to refute the working hypothesis that generalized harmonic analysis can be used to reliably classify alphabet characters, time-varying signals, and other images.

A classification of immersions of the two-sphere

An immersion of one C' differentiable manifold in another is a regular map (a C' map whose Jacobian is of maximum rank) of the first into the second. A homotopy of an immersion is called regular if at each stage it is regular and if the induced homotopy of the tangent bundle is continuous. Little is known about the general problem of classification of immersions under regular homotopy. Whitney [5] has shown that two immersions of a k-dimensional manifold in an n-dimensional manifold, n>2k+2, are regularly homotopic if and only if they are homotopic. The Whitney-Graustein Theorem [4] classifies immersions of the circle S in the plane E2. In my thesis [3] this theorem is extended to the case where E2 is replaced byany C2 manifold Mn, n> 1. As far as I know, these are the only known results. In this paper we give a classification of immersions of the 2-sphere S2 in Euclidean n-space E , n>2, with respect to regular homotopy. Let V.,2 be the Stiefel manifold of all 2-frames in En. If f and g are two immersions of S2 in En, an invariant Q(f, g) Cw2(Vn,2) is defined.

A TEST FOR HOMOGENEITY OF THE MARGINAL DISTRIBUTIONS IN A TWO-WAY CLASSIFICATION

There are several circumstances in which we may wish to test the homogeneity of the two sets of marginal probabilities in a two-way classification. For example, a sample from a bivariate distribution (say height of father, height of son) may be classified into a two-way table with identical (height) groupings in each margin. Or a similar classification may be possible for a non-measurable variable (say strength of right hand - strength of left hand). Again, in surveys of the same sample (a 'panel') on two different occasions, the interrelation of the results on the two occasions may be displayed in a two-way table, with one margin corresponding to each occasion. In all these cases, the question may arise: are the two sets of marginal probabilities identical? If the variable is measurable, we may test the difference between the means of the two marginal distributions by a large-sample standard-error test. However, we may be interested in the overall distributions, rather than only in their means. For the more stringent hypothesis of homogeneity, a test exists if we have two completely independent samples. when an ordinary x2 test of homogeneity may be applied (Cramer, 1946, p. 445). This test does not meet the essentially bivariate situations described above, where non-independence of the marginal distributions is a fundamental feature of the problem. When the classification is a double dichotomy, the problem of testing marginal homogeneity is simple, and its solution is a special case of the large-sample solution of the more general 2K classification problem given by Cochran (1950). Bowker (1948) gave a largesample test for complete symmetry in a two-way classification, a more restrictive hypothesis which is concerned with the entire set of probabilities in the classification, and not only with the marginal probabilities as we are here. In the present paper, a large-sample test for marginal homogeneity is derived and illustrated.

Note on a certain type of parabola

In the development of the geometry of the complex domain, there has been a tendency to pass over problems of a relatively elementary character, despite their central position and importance. It is the purpose of this note to call attention to one of these problems, namely that of the classification of complex conies with respect to the group of complex rigid motions. A systematic study of this problem brings to light two special types of non-degenerate conies: the non-degenerate central conies which contain just one circular point at infinity, and the non-degenerate parabolas which are tangent to the line at infinity at a circular point. These special conies have already been considered, from a different point of view, in this Bulletin, f It is not our intention to go into detail, either in connection with the general problem of classification or in consideration of the special conies. We propose merely to discuss certain particularly striking properties of the special parabolas. I t is evident that the complex conic (1) Ax + Bxy + Cy + Dx + Ey + F = 0,

Is Classification by Mental Ages and Intelligence Quotients Worth While?

The advantages of classification have been generally accepted both in theory and in practice. There is a growing tendency at the present time, however, to consider the classification of pupils merely as an administrative device preceding a more complete program of differentiation. During the present period of adjust ment when the matter of differentiation of curricula, differentia tion of progress, and individual instruction are in the foreground, it may not be amiss to evaluate some objective evidence relating to the general problem of classification and placement of pupils. Classification is not an end in itself. But if pupils are classi fied with no further differentiation of progress or of curricula, can we expect any measurable gain in educational efficiency? This article attempts, in part, to answer this question. The term classification here means the grouping of pupils within a given into sections according to ability; intelli gence quotients and educational quotients are used as bases for classification. Classification according to mental age and educa tional age will be specifically referred to as grade placement. The effect of classification upon pupil promotion will first be considered.1 Do classification and proper placement of pupils reduce failures? Table I offers some objective evidence. Grade placement on the basis of mental age and educational age was limited to the first six grades ; reference to the table shows a greater reduction of failures in the elementary grades. The percent of failures after classification represents the average over a period of three years. These results indicate that better classification and the proper placement of pupils did ma terially reduce failures.