Classification of medullary lesions among paraplegic patients by the likelihood of the links method

We consider the problem submitted by Garcia and Proth and we propose for it a solution obtained by simply applying our very general method of hierarchical classification based on the likelihood of the links, in thc case of an incidence table of data. This application is done on each of the two sides of the incidence data table. In our approach, the common number p of classes has not to be fixed arbitrarily, but is an observed possible result-provided by the notions of 'significant' levels and nodes of the classification tree-for the 'natural' association between two partitions. We compare our solution with the previous one. KEY WORDS Group technology Production management Hierarchical and non-hierarchical clustering RECALL OF THE SETTING OF THE PROBLEMA working process is a sequence of tasks which are performed in order to manufacture a part. We distinguish the type of a part and we say that two parts belong to the same part type if their working processes are the same.We are looking for a pair of associated partitions, the first on the set of tasks and the second on the set of part types. A given class of tasks is called a production subsystem and a given class of part types is called a family. The numbers of classes of the two associated partitions are the same and the researched correspondence between the production subsystems and the families is one-one. These partitions must be determined in order to minimize the number of tasks performed in the production of part types which-respectively-do not belong to the families associated with the production subsystems including the concerned tasks.This problem has been submitted by Garcia and Proth in a preceding issue of this journal. They have introduced the following notations, that we adopt for reasons of conformity:Let X be the set of n part types and let Y be the set of rn tasks. We define the incidence matrix A = [ ajj I 1 < i < n , 1 < j < m ) , with n rows and m columns, where 1 if the working process of a part belonging to the part type i includes the task j .The goal is to determine a pair (X, y ) of partitions on X and Y, with the same number p(1) I 0 if not. aij =

Section: The Crossing Table: Discussionmentioning

confidence: 99%

Group methodology in production management: A solution based on a hierarchical classification method

Lerman

1986

Study of the plant recolonization process in a burnt heathland using a method of hierarchical classification

Tallur

Forgeard

1988

The reinstallation of different plant‐species and their evolution during a ten‐year period in a heathland after a fire accident has been studied by using the algorithm of heirarchical classification based on correlation (ABC) introduced by Tallur.1 Classification under contiguity restraint of the set of observation points (subintervals of an experimental observation line) enables one to determine the ‘patches’ having uniform vegetation structure. Lerman's ‘local’ and ‘global’ statistics are used to condense the classification tree to its significant nodes and to choose the most significant partition. x2 statistics are proposed to test whether a given patch has a ‘significant’ vegetation structure and if the association between a patch and a plant species is significant. Evolution of the horizontal structure of vegetation is studied by comparing the sets of patches obtained at successive observation dates and the corresponding dominant species.

Clusterwise aggregation of relations

Gaul

Schader

1988

SUMMARYIn this paper we handle the general problem of finding q( > 1) central relations on a set of objects which best fit the information contained in a finite number of given relations on that set. The proposed CAR (clusterwise aggregation of relations) algorithm allows one to consider the well-known situation of determining a single central relation as a special case ( q = 1) and takes into account the fact that the rcpresentation of appropriately selected subsets of relations by different central relations can provide additional insights into whether different clusters or segments of relations exist in the given set of relations. Two examples demonstrate the usefulness of the suggested approach.