Small sample results for a linear discriminant function estimated from a mixture of normal populations

Gànesalingam, S.; McLachlan, Geoffrey J.

doi:10.1080/00949657908810306

Cited by 43 publications

(18 citation statements)

References 5 publications

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“…For the cluster analysis problem where there are no classified data, Ganesalingam and McLachlan (1979a) have reported some very encouraging results in the univariate and bivariate cases for forming a linear discriminant function which provides adequate separation even in small samples from populations close together. They noted, however, as did Day (1969),…”

Section: Simulation Resultsmentioning

confidence: 99%

Updating a discriminant function on the basis of unclassified data

McLachlan

Gànesalingam

1982

Communications in Statistics - Simulation and Computation

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Section: Simulation Resultsmentioning

confidence: 99%

Updating a discriminant function on the basis of unclassified data

McLachlan

Gànesalingam

1982

Communications in Statistics - Simulation and Computation

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“…Although the mixture approach may not give accurate estimates of the posterior probabilities, 8,, , for the observations in the sample, it may still provide a satisfactory clustering of the data (Ganesalingam and McLachlan 1979). The case study of Hernandez-Avila ( 1979) suggests that the mixture approach applied, assuming multivariate normal densities, may well be reasonably robust from the cluster analysis viewpoint of separating samples in the presence of multimodality.…”

Section: Estimators Of Allocation Ratesmentioning

confidence: 93%

“…An allocation rule based on the estimated posterior probabilities can then be found for assigning the observations to the various populations. The properties of the mixture approach have been considered by Day (1969), Wolfe (1970), Hosmer (1973, O'Neill (1978), Ganesalingam and McLachlan (1978, 1980a,b, 1981, Aitkin (1980), Mezzich and Solomon (1980), Aitkin et al (1981), Symons (1981), Everitt and Hand (1981), and McLachlan (1982), among others. Hawkins et al (1982) strongly supported the increasing emphasis on such an approach to clustering because it is model based.…”

Section: Introductionmentioning

confidence: 98%

“…A technique based on averaging appropriate functions of the maximum of the posterior probabilities was suggested by Ganesalingam and McLachlan (1980b) to estimate the overall error rate of the mixture approach. It worked well on a real data set-consisting of a mixture of two bivariate normal populations-reported in an unpublished Ph.D. dissertation by Ganesalingam.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Allocation Rates in a Cluster Analysis Context

Basford

McLachlan

1985

Journal of the American Statistical Association

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A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the maximum of these posterior probabilities. The estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering. The bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained. Results are reported for three real data sets and a simulation study. It is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach. Encouraging results are obtained for the bootstrap method of bias correction applied to the estimates of the individual and overall allocation rates.

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“…If the two Gaussians are somewhat well-separated, the asymptotic gain of using unlabeled samples is very significant. For details, see [21,13,14]. McLachlan [18] gives a practical algorithm for this case which is essentially a "hard" version of EM, i.e.…”

Section: The Idea Of Using Em On a Joint Generative Model To Train Onmentioning

confidence: 99%

A Taxonomy for Semi-Supervised Learning Methods

Seeger¹

2006

Semi-Supervised Learning

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We propose a simple taxonomy of probabilistic graphical models for the semi-supervised learning problem. We give some broad classes of algorithms for each of the families and point to specific realizations in the literature. Finally, we shed more detailed light on the family of methods using input-dependent regularization (or conditional prior distributions) and show parallels to the Co-training paradigm.

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Small sample results for a linear discriminant function estimated from a mixture of normal populations

Cited by 43 publications

References 5 publications

Updating a discriminant function on the basis of unclassified data

Updating a discriminant function on the basis of unclassified data

Estimation of Allocation Rates in a Cluster Analysis Context

A Taxonomy for Semi-Supervised Learning Methods

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