Biomedical subjects

Marie Cottrell

Publications and source records attributed to Marie Cottrell.

4 recordsLinked to original sources

PubMed2006

Batch and median neural gas.

Neural Gas (NG) constitutes a very robust clustering algorithm given Euclidean data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.

Algorithms↗

PubMedDate not supplied

SOM-based algorithms for qualitative variables.

It is well known that the SOM algorithm achieves a clustering of data which can be interpreted as an extension of Principal Component Analysis, because of its topology-preserving property. But the SOM algorithm can only process real-valued data. In previous papers, we have proposed several methods based on the SOM algorithm to analyze categorical data, which is the case in survey data. In this paper, we present these methods in a unified manner. The first one (Kohonen Multiple Correspondence Analysis, KMCA) deals only with the modalities, while the two others (Kohonen Multiple Correspondence Analysis with individuals, KMCA_ind, Kohonen algorithm on DISJonctive table, KDISJ) can take into account the individuals, and the modalities simultaneously.

Algorithms↗

PubMedDate not supplied

Double quantization of the regressor space for long-term time series prediction: method and proof of stability.

The Kohonen self-organization map is usually considered as a classification or clustering tool, with only a few applications in time series prediction. In this paper, a particular time series forecasting method based on Kohonen maps is described. This method has been specifically designed for the prediction of long-term trends. The proof of the stability of the method for long-term forecasting is given, as well as illustrations of the utilization of the method both in the scalar and vectorial cases.

Forecasting↗

PubMedDate not supplied

Statistical tools to assess the reliability of self-organizing maps.

Results of neural network learning are always subject to some variability, due to the sensitivity to initial conditions, to convergence to local minima, and, sometimes more dramatically, to sampling variability. This paper presents a set of tools designed to assess the reliability of the results of self-organizing maps (SOM), i.e. to test on a statistical basis the confidence we can have on the result of a specific SOM. The tools concern the quantization error in a SOM, and the neighborhood relations (both at the level of a specific pair of observations and globally on the map). As a by-product, these measures also allow to assess the adequacy of the number of units chosen in a map. The tools may also be used to measure objectively how the SOM are less sensitive to non-linear optimization problems (local minima, convergence, etc.) than other neural network models.

Databases as Topic↗