Recursive Neural Networks and Their Applications to Image Processing

Pattern recognition algorithms and statistical classifiers, such as neural networks or support vector machines (SVMs), can deal with real-life noisy data in an efficient way, so that they can be successfully applied in several different domains. However, the majority of such tools are restricted to process real vectors of a finite and fixed dimensionality. On the other hand, most real-world problems have no natural representation as a single "table," i.e., in several applications, the information that is relevant for solving problems is organized in entities and relationships among entities, so that applying traditional data mining methods implies that an extensive preprocessing has to be performed on the data. For instance, categorical variables are encoded by one-hot encoding, time series are embedded into finite dimensional vector spaces using time windows, preprocessing of images includes edge detection and the exploitation of various filters, sound signals can be represented by spectral vectors, and chemical compounds are characterized by topological indices and physicochemical attributes. However, other data formats and data representations exist, and can be exploited to represent patterns in a more natural way. Sets, without a specified order, can describe objects in a scene or a pool of measurements. Functions, evaluated at specific points, constitute a natural description for time series or spectral data. Sequences of any length also represent time series or spatial data. Tree structures describe terms, logical formulas, parse trees, or document images. Graph structures can be used to encode chemical compounds, images, and, in general, objects composed of atomic elements.