In this paper we have introduced a new method for signature pattern recognition, taking advantage of some image moment transformations combined with fuzzy logic approach. For this purpose first we tried to model the noise embedded in signature patterns inherently and separate it from environmental effects. Based on the first step results, we have performed a mapping into the unit circle using the error least mean square (LMS) error criterion, to get ride of the variations caused by shifting or scaling. Then we derived some orientation invariant moments introduced in former reports and studied their statistical properties in our special input space. Later we defined a fuzzy complex space and also a fuzzy complex similarity measure in this space and constructed a new training algorithm based on fuzzy learning vector quantization (FLVQ) method. A comparison method has also been proposed so that any input pattern could be compared to the learned prototypes through the pre-defined fuzzy similarity measure. Each set of the above image moments were used by the fuzzy classifier separately and the mis-classifications were detected as a measure of error magnitude. The efficiency of the proposed FLVQ model has been numerically shown compared to the conventional FLVQs reported so far. Finally some satisfactory results are derived and also a comparison is made between the above considered image transformations.

In this paper, the LVQ (Learning Vector Quantization) model and its variants are regarded as the clustering tools to discriminate the natural seismic events (earthquakes) from the artificial ones (nuclear explosions). The study is based on the six spectral features of the P-wave spectra computed from the short period teleseismic recordings. The conventional LVQ proposed by Kohenen and also the Fuzzy LVQ (FLVQ) models proposed by Sakuraba and Bezdek are all tested on a set of 26 earthquakes and 24 nuclear explosions using the leave-one-out testing strategy. The primary experimental results have shown that the shapes, the number and also the overlaps of the clusters play an important role in seismic classification. The results also showed how an improper feature space partitioning would strongly weaken both the clustering and recognition phases. To improve the numerical results, a new combined FLVQ algorithm is employed in this paper. The algorithm is composed of two nested sub-algorithms. The inner sub-algorithm tries to generate a well-defined fuzzy partitioning with the fuzzy reference vectors in the feature space. To achieve this goal, a cost function is defined as a function of the number, the shapes and also the overlaps of the fuzzy reference vectors. The update rule tries to minimize this cost function in a stepwise learning algorithm. On the other hand, the outer sub-algorithm tries to find an optimum value for the number of the clusters, in each step. For this optimization in the outer loop, we have used two different criteria. In the first criterion, the newly defined "fuzzy entropy" is used while in the second criterion, a performance index is employed by generalizing the Huntsberger formula for the learning rate, using the concept of fuzzy distance. The experimental results of the new model show a promising improvement in the error rate, an acceptable convergence time, and also more flexibility in boundary decision making.

In this paper we have presented a new method for seismic signal analysis, based on the ARMA modeling and a fuzzy LVQ clustering method. The objective achieved in this work is to sense the changes made naturally or artificially on the seismogram signal, and to detect the sources, which caused these changes (seismic classification). During the study, we have also found out that the model is sometimes capable to alarm the further seismic events just a little time before the onset of those events (seismic prediction). So the application of the proposed method both in seismic classification and seismic prediction are studied through the experimental results. The study is based on the background noise of the teleseismic short period recordings. The ARMA model coefficients are derived for the consecutive overlapped windows. A base model is then generated by clustering the calculated model parameters, using the fuzzy LVQ method proposed by Nassery & Faez in [19]. The time windows, which do not take part in [19] model generation process, are named as the test windows. The model coefficients of the test windows are then compared to the base model coefficients through some pre-defined composition rules. The result of this comparison is a normalized value generated as a measure of similarity. The set of the consecutive similarity measures generate above, produce a curve versus the time windows indices called as the characteristic curves. The numerical results have shown that the characteristic curves often contain much vital seismological information and can be used for source classification and prediction purposes.