Allende , Héctor

In this paper we present a method to detect edges in images. The method consists of using a 3x3 pixel mask to scan the image, moving it from left to right and from top to bottom, one pixel at a time. Each time it is placed on the image, an agglomerative hierarchical cluster analysis is applied to the eight outer pixels. When there is more than one cluster, it means that window is on an edge, and the central pixel is marked as an edge point. After scanning all the image, we obtain a new image showing the marked pixels around the existing edges of the image. Then a thinning algorithm is applied so that the edges are well defined. The method results to be particularly efficient when the image is contaminated. In those cases, a previous restoration method is applied.

In recent years several models for financial high-frequency data have been proposed. One of the most known models for this type of applications is the ACM-ACD model. This model focuses on modelling the underlying joint distribution of both duration and price changes between consecutive transactions. However this model imposes distributional assumptions and its number of parameters increases rapidly (producing a complex and slow adjustment process). Therefore, we propose using two machine learning models, that will work sequentially, based on the ACM-ACD model. The results show a comparable performance, achieving a better performance in some cases. Also the proposal achieves a significatively more rapid convergence. The proposal is validated with a well-known financial data set.

The Neural Gas (NG) is a Vector Quantization technique where a set of prototypes self organize to represent the topology structure of the data. The learning algorithm of the Neural Gas consists in the estimation of the prototypes location in the feature space based in the stochastic gradient descent of an Energy function. In this paper we show that when deviations from idealized distribution function assumptions occur, the behavior of the Neural Gas model can be drastically affected and will not preserve the topology of the feature space as desired. In particular, we show that the learning algorithm of the NG is sensitive to the presence of outliers due to their influence over the adaptation step. We incorporate a robust strategy to the learning algorithm based on M-estimators where the influence of outlying observations are bounded. Finally we make a comparative study of several estimators where we show the superior performance of our proposed method over the original NG, in static data clustering tasks on both synthetic and real data sets.