Marie Cottrell | Université Paris 1 - Panthéon-Sorbonne (original) (raw)

Papers by Marie Cottrell

HAL (Le Centre pour la Communication Scientifique Directe), Apr 28, 2010

Self Organizing Maps (SOM) have been successfully applied in a lot of real world hard problems si... more Self Organizing Maps (SOM) have been successfully applied in a lot of real world hard problems since their apparition. In this paper we present new topologies for SOM based on a planar graph. The design of a specific graph to encode prior information on the dataset topology is the central question addressed in this paper. In this context, star-shaped graphs are advocated for health monitoring applications, leading to a new kind of SOM that we denote by Self Organizing Star (SOS). Experiments using aircraft engine measurements show that SOS lead to meaningful and natural dataset representation.

arXiv (Cornell University), Jan 8, 2007

Kohonen self-organisation maps are a well know classification tool, commonly used in a wide varie... more Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for multi-dimensional long-term trends prediction, with a double application of the Kohonen algorithm. Practical applications of the method are also presented.

HAL (Le Centre pour la Communication Scientifique Directe), 2006

Special issue of Neural Networks Journal after the WSOM 05 ConferenceSpecial issue of Neural Netw... more Special issue of Neural Networks Journal after the WSOM 05 ConferenceSpecial issue of Neural Networks Journal after the WSOM 05 ConferenceNeural Networks Volume 19, Issues 6-7, Pages 721-976 (July-August 2006) Advances in Self Organising Maps - WSOM'05 Edited by Marie Cottrell and Michel Verleysen 1. Advances in Self-Organizing Maps Pages 721-722 Marie Cottrell and Michel Verleysen 2. Self-organizing neural projections Pages 723-733 Teuvo Kohonen 3. Homeostatic synaptic scaling in self-organizing maps Pages 734-743 Thomas J. Sullivan and Virginia R. de Sa 4. Topographic map formation of factorized Edgeworth-expanded kernels Pages 744-750 Marc M. Van Hulle 5. Large-scale data exploration with the hierarchically growing hyperbolic SOM Pages 751-761 Jörg Ontrup and Helge Ritter 6. Batch and median neural gas Pages 762-771 Marie Cottrell, Barbara Hammer, Alexander Hasenfuß and Thomas Villmann 7. Fuzzy classification by fuzzy labeled neural gas Pages 772-779 Th. Villmann, B. Hammer, F. Schleif, T. Geweniger and W. Herrmann 8. On the equivalence between kernel self-organising maps and self-organising mixture density networks Pages 780-784 Hujun Yin 9. Adaptive filtering with the self-organizing map: A performance comparison Pages 785-798 Guilherme A. Barreto and Luís Gustavo M. Souza 10. The Self-Organizing Relationship (SOR) network employing fuzzy inference based heuristic evaluation Pages 799-811 Takanori Koga, Keiichi Horio and Takeshi Yamakawa 11. SOM's mathematics Pages 812-816 J.C. Fort 12. Performance analysis of LVQ algorithms: A statistical physics approach Pages 817-829 Anarta Ghosh, Michael Biehl and Barbara Hammer 13. Self-organizing map algorithm and distortion measure Pages 830-837 Joseph Rynkiewicz 14. Understanding and reducing variability of SOM neighbourhood structure Pages 838-846 Patrick Rousset, Christiane Guinot and Bertrand Maillet 15. Assessing self organizing maps via contiguity analysis Pages 847-854 Ludovic Lebart 16. Fast algorithm and implementation of dissimilarity self-organizing maps Pages 855-863 Brieuc Conan-Guez, Fabrice Rossi and Aïcha El Golli 17. Graph-based normalization and whitening for non-linear data analysis Pages 864-876 Catherine Aaron 18. Unfolding preprocessing for meaningful time series clustering Pages 877-888 Geoffroy Simon, John A. Lee and Michel Verleysen 19. Local multidimensional scaling Pages 889-899 Jarkko Venna and Samuel Kaski 20. Spherical self-organizing map using efficient indexed geodesic data structure Pages 900-910 Yingxin Wu and Masahiro Takatsuka 21. Advanced visualization of Self-Organizing Maps with vector fields Pages 911-922 Georg Pölzlbauer, Michael Dittenbach and Andreas Rauber 22. Online data visualization using the neural gas network Pages 923-934 Pablo A. Estévez and Cristián J. Figueroa 23. TreeSOM: Cluster analysis in the self-organizing map Pages 935-949 Elena V. Samsonova, Joost N. Kok and Ad P. IJzerman 24. Self-organizing neural networks to support the discovery of DNA-binding motifs Pages 950-962 Shaun Mahony, Panayiotis V. Benos, Terry J. Smith and Aaron Golden 25. A descriptive method to evaluate the number of regimes in a switching autoregressive model Pages 963-972 Madalina Oltean

International audienceSegregation phenomena have long been a concern for policy makers and urban ... more International audienceSegregation phenomena have long been a concern for policy makers and urban planners, and much attention has been devoted to their study, especially in the fields of quantitative sociology and geography. Perhaps the most common example of urban segregation corresponds to different groups living in different neighbourhoods across a city, with very few neighbourhoods where all groups are represented in roughly the same proportions as in the whole city itself. The social groups in question are usually defined according to one variable: ethnic group, income category, religious group, electoral group, age... In this paper, we introduce a novel, multidimensional approach based on the Self-Organizing Map algorithm (SOM). Working with public data available for the city of Paris, we illustrate how this method allows one to describe the complex interplay between social groups’ residential patterns and the geography of metropolitan facilities and services

Neural Computing and Applications, May 27, 2019

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation ... more We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census blocks or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

The European Symposium on Artificial Neural Networks, 1997

Besides their topological properties, Kohonen maps are often used for vector quantization only. T... more Besides their topological properties, Kohonen maps are often used for vector quantization only. These auto-organised networks are often compared to other standard and/or adaptive vector quantization methods, and, according to the large literature on the subject, show either better or worst properties in terms of quantization, speed of convergence, approximation of probability densities, clustering,… The purpose of this paper is to define more precisely some commonly encountered problems, and to try to give some answers through well-known theoretical arguments or simulations on simple examples.

Springer eBooks, Apr 28, 2019

For aircraft engineers, detecting abnormalities in a large dataset of recorded flights and unders... more For aircraft engineers, detecting abnormalities in a large dataset of recorded flights and understanding the reasons for these are crucial development and monitoring issues. The main difficulty comes from the fact that flights have unequal lengths, and data is usually high dimensional, with a variety of recorded signals. This question is addressed here by introducing a new methodology, combining time series partitioning, relational clustering and the stochasticity of the online self-organizing maps (SOM) algorithm. Our method allows to compress long and highfrequency bivariate time series corresponding to real flights into a sequence of categorical labels, which are next clustered using relational SOM. Eventually, by training SOM with a large number of initial configurations and by taking advantage of the stability of the clusters, we are able to isolate the most atypical flights, and, thanks to discussions with experts, understand what makes a flight an "abnormal" data.

Springer eBooks, 2019

The anomaly detection problem for univariate or multivariate time series is a critical question i... more The anomaly detection problem for univariate or multivariate time series is a critical question in many practical applications as industrial processes control, biological measures, engine monitoring, supervision of all kinds of behavior. In this paper we propose an empirical approach to detect anomalies in the behavior of multivariate time series. The approach is based on the empirical estimation of conditional quantiles. The method is tested on artificial data and its effectiveness is proven in the real framework of aircraft-engines monitoring.

Springer eBooks, 2014

We develop an application of SOM for the task of anomaly detection and visualization. To remove t... more We develop an application of SOM for the task of anomaly detection and visualization. To remove the effect of exogenous independent variables, we use a correction model which is more accurate than the usual one, since we apply different linear models in each cluster of context. We do not assume any particular probability distribution of the data and the detection method is based on the distance of new data to the Kohonen map learned with corrected healthy data. We apply the proposed method to the detection of aircraft engine anomalies.

Neural Networks, Jul 1, 2006

Advances in data analysis and classification, May 25, 2013

Model-based clustering is a popular tool which is renowned for its probabilistic foundations and ... more Model-based clustering is a popular tool which is renowned for its probabilistic foundations and its flexibility. However, model-based clustering techniques usually perform poorly when dealing with high-dimensional data streams, which are nowadays a frequent data type. To overcome this limitation of model-based clustering, we propose an online inference algorithm for the mixture of probabilistic PCA model. The proposed algorithm relies on an EM-based procedure and on a probabilistic and incremental version of PCA. Model selection is also considered in the online setting through parallel computing. Numerical experiments on simulated and real data demonstrate the effectiveness of our approach and compare it to state-of-the-art online EMbased algorithms.

Neurocomputing, 2004

Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring ... more Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for their more classical vector quantization property. We show in this paper that using SOM instead of the more classical Simple Competitive Learning (SCL) algorithm drastically increases the speed of convergence of the vector quantization process. This fact is demonstrated through extensive simulations on artificial and real examples, with specific SOM (fixed and decreasing neighborhoods) and SCL algorithms.

Neural Networks, Oct 1, 2002

Results of neural network learning are always subject to some variability, due to the sensitivity... more 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.

arXiv (Cornell University), May 9, 2017

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation ... more We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

International Conference on Artificial Intelligence and Statistics, Jan 4, 2001

Artificial Neural Networks in Pattern Recognition, 2003

Kohonen self-organisation maps are a well know classification tool, commonly used in a wide varie... more Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for long-term trends prediction, with a double application of the Kohonen algorithm. We also consider practical issues for the use of the method.

The European Symposium on Artificial Neural Networks, 1999

In a previous paper ([1], ESANN'97), we compared the Kohonen algorithm (SOM) to Simple Competitiv... more In a previous paper ([1], ESANN'97), we compared the Kohonen algorithm (SOM) to Simple Competitive Learning Algorithm (SCL) when the goal is to reconstruct an unknown density. We showed that for that purpose, the SOM algorithm quickly provides an excellent approximation of the initial density, when the frequencies of each class are taken into account to weight the quantifiers of the classes. Another important property of the SOM is the well known topology conservation, which implies that neighbor data are classified into the same class (as usual) or into neighbor classes. In this paper, we study another interesting property of the SOM algorithm, that holds for any fixed number of quantifiers. We show that even we use those approaches only for quantization, the SOM algorithm can be successfully used to accelerate in a very large proportion the speed of convergence of the classical Simple Competitive Learning Algorithm (SCL).

Springer eBooks, 2001

Making results reliable is one of the major concerns in artificial neural networks research. It i... more Making results reliable is one of the major concerns in artificial neural networks research. It is often argued that Self-Organizing Maps are less sensitive than other neural paradigms to problems related to convergence, local minima, etc. This paper introduces objective statistical measures that can be used to assess the stability of the results of SOM, both on the distortion and on the topology preservation points of views.

HAL (Le Centre pour la Communication Scientifique Directe), Apr 28, 2010

Self Organizing Maps (SOM) have been successfully applied in a lot of real world hard problems si... more Self Organizing Maps (SOM) have been successfully applied in a lot of real world hard problems since their apparition. In this paper we present new topologies for SOM based on a planar graph. The design of a specific graph to encode prior information on the dataset topology is the central question addressed in this paper. In this context, star-shaped graphs are advocated for health monitoring applications, leading to a new kind of SOM that we denote by Self Organizing Star (SOS). Experiments using aircraft engine measurements show that SOS lead to meaningful and natural dataset representation.

arXiv (Cornell University), Jan 8, 2007

Kohonen self-organisation maps are a well know classification tool, commonly used in a wide varie... more Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for multi-dimensional long-term trends prediction, with a double application of the Kohonen algorithm. Practical applications of the method are also presented.

HAL (Le Centre pour la Communication Scientifique Directe), 2006

Special issue of Neural Networks Journal after the WSOM 05 ConferenceSpecial issue of Neural Netw... more Special issue of Neural Networks Journal after the WSOM 05 ConferenceSpecial issue of Neural Networks Journal after the WSOM 05 ConferenceNeural Networks Volume 19, Issues 6-7, Pages 721-976 (July-August 2006) Advances in Self Organising Maps - WSOM'05 Edited by Marie Cottrell and Michel Verleysen 1. Advances in Self-Organizing Maps Pages 721-722 Marie Cottrell and Michel Verleysen 2. Self-organizing neural projections Pages 723-733 Teuvo Kohonen 3. Homeostatic synaptic scaling in self-organizing maps Pages 734-743 Thomas J. Sullivan and Virginia R. de Sa 4. Topographic map formation of factorized Edgeworth-expanded kernels Pages 744-750 Marc M. Van Hulle 5. Large-scale data exploration with the hierarchically growing hyperbolic SOM Pages 751-761 Jörg Ontrup and Helge Ritter 6. Batch and median neural gas Pages 762-771 Marie Cottrell, Barbara Hammer, Alexander Hasenfuß and Thomas Villmann 7. Fuzzy classification by fuzzy labeled neural gas Pages 772-779 Th. Villmann, B. Hammer, F. Schleif, T. Geweniger and W. Herrmann 8. On the equivalence between kernel self-organising maps and self-organising mixture density networks Pages 780-784 Hujun Yin 9. Adaptive filtering with the self-organizing map: A performance comparison Pages 785-798 Guilherme A. Barreto and Luís Gustavo M. Souza 10. The Self-Organizing Relationship (SOR) network employing fuzzy inference based heuristic evaluation Pages 799-811 Takanori Koga, Keiichi Horio and Takeshi Yamakawa 11. SOM's mathematics Pages 812-816 J.C. Fort 12. Performance analysis of LVQ algorithms: A statistical physics approach Pages 817-829 Anarta Ghosh, Michael Biehl and Barbara Hammer 13. Self-organizing map algorithm and distortion measure Pages 830-837 Joseph Rynkiewicz 14. Understanding and reducing variability of SOM neighbourhood structure Pages 838-846 Patrick Rousset, Christiane Guinot and Bertrand Maillet 15. Assessing self organizing maps via contiguity analysis Pages 847-854 Ludovic Lebart 16. Fast algorithm and implementation of dissimilarity self-organizing maps Pages 855-863 Brieuc Conan-Guez, Fabrice Rossi and Aïcha El Golli 17. Graph-based normalization and whitening for non-linear data analysis Pages 864-876 Catherine Aaron 18. Unfolding preprocessing for meaningful time series clustering Pages 877-888 Geoffroy Simon, John A. Lee and Michel Verleysen 19. Local multidimensional scaling Pages 889-899 Jarkko Venna and Samuel Kaski 20. Spherical self-organizing map using efficient indexed geodesic data structure Pages 900-910 Yingxin Wu and Masahiro Takatsuka 21. Advanced visualization of Self-Organizing Maps with vector fields Pages 911-922 Georg Pölzlbauer, Michael Dittenbach and Andreas Rauber 22. Online data visualization using the neural gas network Pages 923-934 Pablo A. Estévez and Cristián J. Figueroa 23. TreeSOM: Cluster analysis in the self-organizing map Pages 935-949 Elena V. Samsonova, Joost N. Kok and Ad P. IJzerman 24. Self-organizing neural networks to support the discovery of DNA-binding motifs Pages 950-962 Shaun Mahony, Panayiotis V. Benos, Terry J. Smith and Aaron Golden 25. A descriptive method to evaluate the number of regimes in a switching autoregressive model Pages 963-972 Madalina Oltean

International audienceSegregation phenomena have long been a concern for policy makers and urban ... more International audienceSegregation phenomena have long been a concern for policy makers and urban planners, and much attention has been devoted to their study, especially in the fields of quantitative sociology and geography. Perhaps the most common example of urban segregation corresponds to different groups living in different neighbourhoods across a city, with very few neighbourhoods where all groups are represented in roughly the same proportions as in the whole city itself. The social groups in question are usually defined according to one variable: ethnic group, income category, religious group, electoral group, age... In this paper, we introduce a novel, multidimensional approach based on the Self-Organizing Map algorithm (SOM). Working with public data available for the city of Paris, we illustrate how this method allows one to describe the complex interplay between social groups’ residential patterns and the geography of metropolitan facilities and services

Neural Computing and Applications, May 27, 2019

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation ... more We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census blocks or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

The European Symposium on Artificial Neural Networks, 1997

Besides their topological properties, Kohonen maps are often used for vector quantization only. T... more Besides their topological properties, Kohonen maps are often used for vector quantization only. These auto-organised networks are often compared to other standard and/or adaptive vector quantization methods, and, according to the large literature on the subject, show either better or worst properties in terms of quantization, speed of convergence, approximation of probability densities, clustering,… The purpose of this paper is to define more precisely some commonly encountered problems, and to try to give some answers through well-known theoretical arguments or simulations on simple examples.

Springer eBooks, Apr 28, 2019

For aircraft engineers, detecting abnormalities in a large dataset of recorded flights and unders... more For aircraft engineers, detecting abnormalities in a large dataset of recorded flights and understanding the reasons for these are crucial development and monitoring issues. The main difficulty comes from the fact that flights have unequal lengths, and data is usually high dimensional, with a variety of recorded signals. This question is addressed here by introducing a new methodology, combining time series partitioning, relational clustering and the stochasticity of the online self-organizing maps (SOM) algorithm. Our method allows to compress long and highfrequency bivariate time series corresponding to real flights into a sequence of categorical labels, which are next clustered using relational SOM. Eventually, by training SOM with a large number of initial configurations and by taking advantage of the stability of the clusters, we are able to isolate the most atypical flights, and, thanks to discussions with experts, understand what makes a flight an "abnormal" data.

Springer eBooks, 2019

The anomaly detection problem for univariate or multivariate time series is a critical question i... more The anomaly detection problem for univariate or multivariate time series is a critical question in many practical applications as industrial processes control, biological measures, engine monitoring, supervision of all kinds of behavior. In this paper we propose an empirical approach to detect anomalies in the behavior of multivariate time series. The approach is based on the empirical estimation of conditional quantiles. The method is tested on artificial data and its effectiveness is proven in the real framework of aircraft-engines monitoring.

Springer eBooks, 2014

We develop an application of SOM for the task of anomaly detection and visualization. To remove t... more We develop an application of SOM for the task of anomaly detection and visualization. To remove the effect of exogenous independent variables, we use a correction model which is more accurate than the usual one, since we apply different linear models in each cluster of context. We do not assume any particular probability distribution of the data and the detection method is based on the distance of new data to the Kohonen map learned with corrected healthy data. We apply the proposed method to the detection of aircraft engine anomalies.

Neural Networks, Jul 1, 2006

Advances in data analysis and classification, May 25, 2013

Model-based clustering is a popular tool which is renowned for its probabilistic foundations and ... more Model-based clustering is a popular tool which is renowned for its probabilistic foundations and its flexibility. However, model-based clustering techniques usually perform poorly when dealing with high-dimensional data streams, which are nowadays a frequent data type. To overcome this limitation of model-based clustering, we propose an online inference algorithm for the mixture of probabilistic PCA model. The proposed algorithm relies on an EM-based procedure and on a probabilistic and incremental version of PCA. Model selection is also considered in the online setting through parallel computing. Numerical experiments on simulated and real data demonstrate the effectiveness of our approach and compare it to state-of-the-art online EMbased algorithms.

Neurocomputing, 2004

Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring ... more Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for their more classical vector quantization property. We show in this paper that using SOM instead of the more classical Simple Competitive Learning (SCL) algorithm drastically increases the speed of convergence of the vector quantization process. This fact is demonstrated through extensive simulations on artificial and real examples, with specific SOM (fixed and decreasing neighborhoods) and SCL algorithms.

Neural Networks, Oct 1, 2002

Results of neural network learning are always subject to some variability, due to the sensitivity... more 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.

arXiv (Cornell University), May 9, 2017

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation ... more We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

International Conference on Artificial Intelligence and Statistics, Jan 4, 2001

Artificial Neural Networks in Pattern Recognition, 2003

Kohonen self-organisation maps are a well know classification tool, commonly used in a wide varie... more Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for long-term trends prediction, with a double application of the Kohonen algorithm. We also consider practical issues for the use of the method.

The European Symposium on Artificial Neural Networks, 1999

In a previous paper ([1], ESANN'97), we compared the Kohonen algorithm (SOM) to Simple Competitiv... more In a previous paper ([1], ESANN'97), we compared the Kohonen algorithm (SOM) to Simple Competitive Learning Algorithm (SCL) when the goal is to reconstruct an unknown density. We showed that for that purpose, the SOM algorithm quickly provides an excellent approximation of the initial density, when the frequencies of each class are taken into account to weight the quantifiers of the classes. Another important property of the SOM is the well known topology conservation, which implies that neighbor data are classified into the same class (as usual) or into neighbor classes. In this paper, we study another interesting property of the SOM algorithm, that holds for any fixed number of quantifiers. We show that even we use those approaches only for quantization, the SOM algorithm can be successfully used to accelerate in a very large proportion the speed of convergence of the classical Simple Competitive Learning Algorithm (SCL).

Springer eBooks, 2001

Making results reliable is one of the major concerns in artificial neural networks research. It i... more Making results reliable is one of the major concerns in artificial neural networks research. It is often argued that Self-Organizing Maps are less sensitive than other neural paradigms to problems related to convergence, local minima, etc. This paper introduces objective statistical measures that can be used to assess the stability of the results of SOM, both on the distortion and on the topology preservation points of views.