Emergence in Self Organizing Feature Maps

This paper sheds some light on the differences between SOM and emergent SOM (ESOM). The discussion in philosophy and epistemology about Emergence is summarized in the form of postulates. The properties of SOM are compared to these postulates. SOM fulfill most of the postulates. The epistemological postulates regarding this issue are hard, if not impossible, to prove. An alternative postulate relying on semiotic concepts, called "semiotic irreducibility" is proposed here. This concept is applied to U-Matrix on SOM with many neurons. This leads to the definition of ESOM as SOM producing a nontrivial U-Matrix on which the terms "watershed" and "catchment basin" are meaningful and which are cluster conform. The usefulness of the approach is demonstrated with an ESOM clustering algorithm which exploits the emergent properties of such SOM. Results on synthetic data also in blind studies are convincing. The application of ESOM clustering for a real world problem let to an excellent solution

Self Organized Swarms for cluster preserving Projections of high-dimensional Data

A new approach for topographic mapping, called Swarm-Organized Projection (SOP) is presented. SOP has been inspired by swarm intelligence methods for clustering and is similar to Curvilinear Component Analysis (CCA) and SOM. In contrast to the latter the choice of critical parameters is substituted by self-organization. On several crucial benchmark data sets it is demonstrated that SOP outperforms many other projection methods. SOP produces coherent clusters even for complex entangled high dimensional cluster structures. For a nontrivial dataset on protein DNA sequence Multi Dimensional Scaling (MDS) and CCA fail to represent the clusters in the data, although the clusters are clearly defined. With SOP the correct clusters in the data could be easily detected

Label Propagation for Semi-Supervised Learning in Self-Organizing Maps

Semi-supervised learning aims at discovering spatial structures in high-dimensional input spaces when insufficient background information about clusters is available. A particulary interesting approach is based on propagation of class labels through proximity graphs. The Self-Organizing Map itself can be seen as such a proximity graph that is suitable for label propagation. It turns out that Zhu's popular label propagation method can be regarded as a modification of the SOM's well known batch learning rule. In this paper, an approach for semi-supervised learning is presented. It is based on label propagation in trained Self-Organizing Maps. Furthermore, a simple yet powerful method for crucial parameter estimation is presented. The resulting clustering algorithm is tested on the fundamental clustering problem suite (FCPS)

The architecture of emergent self-organizing maps to reduce projection errors

Abstract. There are mainly two types of Emergent Self-Organizing Maps (ESOM) grid structures in use: hexgrid (honeycomb like) and quadgrid (trellis like) maps. In addition to that, the shape of the maps may be square or rectangular. This work investigates the effects of these different map layouts. Hexgrids were found to have no convincing advantage over quadgrids. Rectangular maps, however, are distinctively superior to square maps. Most surprisingly, rectangular maps outperform square maps for isotropic data, i.e. data sets with no particular primary direction.

Emergence in Self Organizing Feature Maps

This paper sheds some light on the differences between SOM and emergent SOM (ESOM). The discussion in philosophy and epistemology about Emergence is summarized in the form of postulates. The properties of SOM are compared to these postulates. SOM fulfill most of the postulates. The epistemological postulates regarding this issue are hard, if not impossible, to prove. An alternative postulate relying on semiotic concepts, called "semiotic irreducibility" is proposed here. This concept is applied to U-Matrix on SOM with many neurons. This leads to the definition of ESOM as SOM producing a nontrivial U-Matrix on which the terms "watershed" and "catchment basin" are meaningful and which are cluster conform. The usefulness of the approach is demonstrated with an ESOM clustering algorithm which exploits the emergent properties of such SOM. Results on synthetic data also in blind studies are convincing. The application of ESOM clustering for a real world problem let to an excellent solution

Analyzing the Fine Structure of Distributions

One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need to be assessed. Of particular interest is the question of whether the data originate from one process or contain subsets related to different states of the data producing process. Data visualization tools should deliver a clear picture of the univariate probability density distribution (PDF) for each feature. Visualization tools for PDFs typically use kernel density estimates and include both the classical histogram, as well as the modern tools like ridgeline plots, bean plots and violin plots. If density estimation parameters remain in a default setting, conventional methods pose several problems when visualizing the PDF of uniform, multimodal, skewed distributions and distributions with clipped data, For that reason, a new visualization tool called the mirrored density plot (MD plot), which is specifically designed to discover interesting structures in continuous features, is proposed. The MD plot does not require adjusting any parameters of density estimation, which is what may make the use of this plot compelling particularly to non-experts. The visualization tools in question are evaluated against statistical tests with regard to typical challenges of explorative distribution analysis. The results of the evaluation are presented using bimodal Gaussian, skewed distributions and several features with already published PDFs. In an exploratory data analysis of 12 features describing quarterly financial statements, when statistical testing poses a great difficulty, only the MD plots can identify the structure of their PDFs. In sum, the MD plot outperforms the above mentioned methods.Comment: 66 pages, 81 figures, accepted in PLOS ON

Label Propagation for Semi-Supervised Learning in Self-Organizing Maps

Semi-supervised learning aims at discovering spatial structures in high-dimensional input spaces when insufficient background information about clusters is available. A particulary interesting approach is based on propagation of class labels through proximity graphs. The Self-Organizing Map itself can be seen as such a proximity graph that is suitable for label propagation. It turns out that Zhu's popular label propagation method can be regarded as a modification of the SOM's well known batch learning rule. In this paper, an approach for semi-supervised learning is presented. It is based on label propagation in trained Self-Organizing Maps. Furthermore, a simple yet powerful method for crucial parameter estimation is presented. The resulting clustering algorithm is tested on the fundamental clustering problem suite (FCPS)

Techniken zur Dateninspektion am Beispiel der Tagbevölkerungsdichte

Die Reduktion der Flächeninanspruchnahme als auch die standörtliche Lenkung von Bautätigkeiten sind wesentliche Ziele einer nachhaltigen Flächenpolitik. Ein Erkennen und Beurteilen räumlicher Unterschiede in Ausmaß und Lokalität der in Anspruch genommenen Siedlungs- und Verkehrsflächen bedarf der Berücksichtigung standörtlicher Gegebenheiten, welche in einem engen Zusammenhang mit Flächenausweisungen stehen. In diesem Beitrag werden Techniken des Data-Mining vorgestellt, die sich zur Dateninspektion von Messgrößen der Siedlungs- und Freiraumentwicklung auf Ebene der Gemeinden in Deutschland (n = 11 441) eignen. Auf diese Weise lassen sich statistische Eigenschaften der Messgrößen präzisieren und darauf aufbauend räumliche Charakteristika darstellen. Die Ergebnisse der Dateninspektion eignen sich als Grundlage für weiterführende mehrdimensionale Raumbeschreibungen. Perspektivisch können diese Techniken wichtige analytische Beiträge im Zuge eines raumbezogenen Monitoringsystems leisten, welches Messgrößen der Siedlungs- und Freiraumentwicklung beobachtet und bewertet

Visual mining in music collections with Emergent SOM

Different methods of organizing large collections of music with databionic mining techniques are described. The Emergent Self-Organizing Map is used to cluster and visualize similar artists and songs. The first method is the MusicMiner system that utilizes semantic descriptions learned from low level audio features for each song. The second method uses tags that have been assigned to music artists by the users of the social music platform Last.fm. For both methods we demonstrate the visualization capabilities of the U-Map. An intuitive browsing of large music collections is offered based on the paradigm of topographic maps. The semantic concepts behind the features enhance the interpretability of the maps