Fundamental pattern

Abstract: To precisely ablate tumor in radiation therapy, it is important to locate the tumor position in real time during treatment. However, respiration-induced tumor motions are difficult to track. They are semi-periodic and exhibit variations in baseline, frequency and fundamental pattern (oscillatory amplitude and shape). In this study, we try to decompose the above-mentioned components from discrete observations in real time. Baseline drift, frequency (equivalently phase) variation and fundamental pattern change characterize different aspects of respiratory motion and have distinctive clinical indications. Furthermore, smoothness is a valid assumption for each one of these components in their own spaces, and facilitates effective extrapolation for the purpose of estimation and prediction. We call this process 'profiling' to reflect the integration of information extraction, decomposition, processing and recovery. The proposed method has three major ingredients: (1) real-time baseline and phase estimation based on elliptical shape tracking in augmented state space and Poincare sectioning principle; (2) estimation of the fundamental pattern by unwarping the observation with phase estimate from the previous step; (3) filtering of individual components and assembly in the original temporal-displacement signal space. We tested the proposed method with both simulated and clinical data. For the purpose of prediction, the results are comparable to what one would expect from a human operator. The proposed approach is fully unsupervised and data driven, making it ideal for applications requiring economy, efficiency and flexibility.

Abstract: Aim of this paper is to introduce the complex system perspective into retail market analysis. Currently, to understand the retail market means to search for local patterns at the micro level, involving the segmentation, separation and profiling of diverse groups of consumers. In other contexts, however, markets are modelled as complex systems. Such strategy is able to uncover emerging regularities and patterns that make markets more predictable, e.g. enabling to predict how much a country’s GDP will grow. Rather than isolate actors in homogeneous groups, this strategy requires to consider the system as a whole, as the emerging pattern can be detected only as a result of the interaction between its self-organizing parts. This assumption holds also in the retail market: each customer can be seen as an independent unit maximizing its own utility function. As a consequence, the global behaviour of the retail market naturally emerges, enabling a novel description of its properties, complementary to the local pattern approach. Such task demands for a data-driven empirical framework. In this paper, we analyse a unique transaction database, recording the micro-purchases of a million customers observed for several years in the stores of a national supermarket chain. We show the emergence of the fundamental pattern of this complex system, connecting the products’ volumes of sales with the customers’ volumes of purchases. This pattern has a number of applications. We provide three of them. By enabling us to evaluate the sophistication of needs that a customer has and a product satisfies, this pattern has been applied to the task of uncovering the hierarchy of needs of the customers, providing a hint about what is the next product a customer could be interested in buying and predicting in which shop she is likely to go to buy it.

Abstract: One of the most important genomic tasks is the identification of promoters and splice-junction zone, which are essential on deciding whether there is a gene or not in a genome sequence. This problem could be seen as a classification problem, therefore the use of computational algorithms for both, pattern recognition and classification are a natural option to face it. In this chapter we develop a pattern classifier algorithm that works notably with bioinformatics databases. The associative memories model on which the classifier is based is the Alpha-Beta model. In order to achieve a good classification performance it was necessary to develop a new heteroassociative memories algorithm that let us recall the complete fundamental set. The heteroassociative memories property of recalling all the fundamental patterns is not so common; actually, no previous model of heteroassociative memory can guarantee this property. Thus, creating such a model is an important contribution. In addition, an heteroasociative Alpha-Beta multimemory is created, as a fundamental base for the proposed classifier.

Abstract: In a pattern learning method, each of pieces of information representing a plurality of different fundamental patterns is presented to a large number of cells of a neural network, and the cells are thereby caused to learn a large number of feature patterns. The method comprises the steps of causing a cell, which best matches with a fundamental pattern having been presented to the neural network, to learn the fundamental pattern. For neighboring cells that fall within a neighboring region having a predetermined range and neighboring with the cell, which best matches with the fundamental pattern having been presented to the neural network, spatial interpolating operations are carried out from the fundamental pattern, which has been presented to the neural network, and a fundamental pattern, which is other than the fundamental pattern having been presented to the neural network and which has been learned by a cell that is among the large number of the cells of the neural network and that is other than the cell best matching with the fundamental pattern having been presented to the neural network. The neighboring cells are caused to learn the results of the spatial interpolating operations.