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Principal Component Analysis (PCA) is a well known statistical method that has successfully been applied for reducing data dimensionality. Focusing on a neural network which approximates the results obtained by classical PCA, the main contribution of this work consists in introducing a parallel modeling for such network. A comparative study shows that the proposal presents promising results when a multi-core computer is available.

The problem of recognizing handwritten mathematical expressions includes three important subproblems: symbol segmentation, symbol recognition, and structural analysis of expressions. In order to evaluate recognition methods and techniques, they should be tested on representative sample sets of the application domain. One of the concerns that are being repeatedly pointed recently is the almost non-existence of public representative datasets of mathematical expressions, which makes dicult the development and comparison of distinct approaches. In general, recognition results reported in the literature are restricted to small datasets, not publicly available, and often consisting of data aiming only evaluation of some specic aspects of the recognition. In the case of online expressions, to train and test symbol recognizers, samples are in general obtained asking users to write a series of symbols individually and repeatedly. Such task is boring and tiring. An alternative approach for obtaining samples of symbols would be to ask users to transcribe previously dened model expressions. By doing so, writing would be more natural and less boring, and several symbol samples could be obtained from one transcription. To avoid the task of manually labeling the symbols of the transcribed expressions, in this work a method for handwritten expression matching, in which symbols of a transcribed expression are assigned to the corresponding ones in the model expression, is proposed. The proposed method is based on a formulation that reduces the matching problem to a linear assignment problem, where costs are dened based on symbol features and expression structure. Experimental results using the proposed method show that mean correct assignment rate superior to 99% is achieved.