Visualization of Fuzzy Information in Fuzzy-Classification for Image Segmentation using MDS
Thomas Villmann, Marc Strickert, C. Bayan Bruss, Frank-Michael Schleif, Udo Seiffert · The European Symposium on Artificial Neural Networks · 2007
In this work we introduce a method for visualization of fuzzy label information obtained from prototype based fuzzy labeled self- organizing map (FLSOM) for fuzzy classification. FLSOM returns vectors of fuzyy class labels for the prototypes containing class simlarity informa- tion. This information is used for apropriate visualization by an adequate, similarity preserving color space embedding realized by an advanced MDS- approach. Using this embedding, classification results can be visualized by the similarity-based color representation of the data. The method is ap- plied for image segmentation with uncertain (fuzzy) class membership. 1I ntroduction Real world data are often characterized by uncertain and possibly inconsistent information. In particular in medical and biological applications this problem plays an important role. If data are processed by machine learning approaches, this uncertainty has to be taken into account. Prototype based fuzzy classifica- tion offers a possible solution for learning of labeled data in the context of clas- sification tasks. Respective algorithms are the fuzzy labeled neural gas (FLNG - (1)) or its self-organizing map (SOM) based counterparts FuzzySOM (2) and fuzzy labeled self-organizing map (FLSOM - (3)), which offer better data visual- ization possibilities due to its underlying regular grid structure of self-organizing maps (SOM - (4)). This advantage is caused by the topology preserving mapping realized by unsupervised SOMs under certain conditions. Usually, the supervised variants return a probability vector assigned to each prototype, which reflects the class probabilities for each possible data class. Yet, FuzzySOM does not minimize a predefined cost function because both parts of the adaptation, the SOM learning and the subsequent learning vector quantization are not based on a gradient descent approach. FLSOM, however, is based on the Heskes' variant of SOMs, for which a cost function is given. The SOM adaptation scheme is imposed by a gradient descent on classification accuracy. Further, the topology preservation may be lost by the subsequent learning in FuzzySOM, whereas it is not in FLSOM. Yet, the visualization of fuzzy classification information is difficult. One method is to consider the barplots of the probability vectors as demonstrated for FLSOM (5). However, we can use a special feature of FLSOM. In contrast to FuzzySOM, FLSOM inherently contains the neighborhood cooperativeness also in label adaptation. Therefore, in case of adequate conditions, topological ordering is obtained for both prototype distribution and label vectors. From the