L. Kaufman

Fuzzy clustering algorithms based on the maximum likelihood principle

Abstract A number of hard clustering algorithms have been shown to be derivable from the maximum likelihood principle. The only corresponding fuzzy algorithm are the well known fuzzy k-means or fuzzy isodata of Dunn and its generalizations by Bezdek and by Gustafson and Kessel. The authors show how to generate two other fuzzy algorithms which are analogous of known hard algorithms: the minimization of the fuzzy determinant and of the product of fuzzy determinants. By comparison between the hard and fuzzy methods it appears that the latter yield more often the global optimum, rather than merely a local optimum. This result and the comparison between the different algorithms, together with their specific domains of application, are illustrated by a few numerical examples.

Fuzzy clustering using scatter matrices

Abstract Starting from the well-known fuzzy k-means method, which was mainly intended for spherical clusters, several methods are considered which incorporate cluster-specific scatter matrices. This enables them to describe elliptical clusters with different orientation. The distinction between these methods lies in the way they deal with clusters of different volume, cardinality, and density. Some industrial examples show that different applications may lead to different goals and preferences, which affect the choice of the clustering method.

Multivariate analysis of CCSEM auto emission data

Abstract Computer-controlled scanning electron microscopy (CCSEM) has proven to be a powerful tool in the characterization of individual particles and the source apportionment of ambient aerosol mass. The method can measure both physical properties of the particle including maximum and minimum diameters and area, as well as determine the major elemental composition of each particle. The particle volume and density can be estimated and the particle mass calculated. There are also powerful multivariate statistical procedures that can be directly applied to the individual particle data to assign any particular particle to the identified classes. The purpose of the current study was to explore the use of various hierarchical and non-hierarchical cluster analysis methods to define the number of distinct particle classes within an auto emission source sample. Each class was then separately modeled using a disjoint principal component procedure and membership of each particle in defined classes was tested. Mass fractions of each particle class and their uncertainties were calculated. These methods are being tested using auto emission source data from El Paso Quantitative Microscopy Study to identify sources of TSP and lead.

Fuzzy clustering with high contrast

In a fuzzy clustering an object typically receives strictly positive memberships to all clusters, even when the object clearly belongs to one particular cluster. Consequently, each clusters estimated center and scatter matrix are influenced by many objects that have small positive memberships to it. This effect may keep the fuzzy method from finding the true clusters. We analyze the cause and propose a remedy, which is a modification of the objective function and the corresponding algorithm. The resulting clustering has a high contrast in the sense that outlying and bridging objects remain fuzzy, whereas the other objects become crisp. The enhanced version of fuzzy k-means is illustrated with an example, as well as the enhanced version of the fuzzy minimum volume method.

Feasibility study concerning the use of expert systems for the development of procedures in pharmaceutical analysis

The feasibility of using expert systems for the development of analytical procedures is investigated. A system for the computer generation of procedures to determine active drug substances in commercial formulations is proposed. It is shown that in nearly 85% of the cases investigated the present system immediately yields a correct procedure or conclusion. It is concluded that selecting methods and developing procedures with the use of expert systems is difficult but feasible.

Clustering on a microcomputer with an application to the classification of coals

Abstract The widespread introduction of microcmputers in laboratories where large data sets are more and more frequently gathered, makes it necessary to be able to use adapted statistical software. This paper describes a BASIC program for the Macnaughton-Smith clustering method adapted to the Apple II microcomputer. Experience is reported of an application of the program to the classification of a set of coals.

Optimisation of flow schemes for ion-exchange separations by dynamic programming

Zusammenfassung2 Methoden zur Auswahl des optimalen Fließdiagramms für Trennungsverfahren werden verglichen, wobei gezeigt wird, daß die dynamische Programmierung mehr Vorteile bietet als die Anwendung der Graphentheorie.SummaryThis article compares two operational research methods for the choice of the optimal flow scheme in separation chemistry. It is concluded that dynamic programming offers more advantages than the application of the theory of graphs.

Brainstem electric response audiometry in newborns

Abstract Brainstem electric response audiometry (BERA) was performed as a screening procedure for the assessment of hearing of 523 neonates. It is shown that binaural stimulation gives a higher percentage of interpretable records. A statistical analysis was made of CT3 (I–III) and CT5 (I–V) as a function of gestational age, conceptional age, birth weight, sex, Apgar score, bilirubinaemia and perinatal pathology.