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Sossa, Humberto; Barrón, Ricardo; Cuevas, Francisco; Aguilar, Carlos; Cortés, Héctor
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We show how the binary αβ associative memories recently proposed by Yáñez in [1] can be extended to work now in the graylevel case. To get the desired extension we take the operators α and β, foundation of the αβ memories, and propose a more general family of operators among them the original operators α and β are a subset. For this we formulate a set of functional equations, solve this system and find a family of solutions. We show that the α and β originally proposed in [1] are just a particular case of this new family. We give the properties of the new operators. We then use these operators to build the extended memories. We provide the conditions under which the proposed extended memories are able to recall a pattern either from the pattern’s fundamental set or from altered versions of them. We provide real examples with images where the proposed memories show their efficiency.
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Sossa, Humberto; Barrón, Ricardo; Vázquez, Roberto A.
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In this note we describe a new set of associative memories able to recall patterns in the presence of mixed noise. Conditions are given under which the proposed memories are able to recall patterns either from the fundamental set of patterns and from distorted versions of them. Numerical and real examples are also provided to show the efficiency of the proposal.
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Sossa, Humberto; Barrón, Ricardo; Cuevas, Francisco; Aguilar, Carlos; Cortés, Héctor
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In this paper we show how a binary memory can be used to recall graylevel patterns. Given a set of graylevel patterns to be first memorized: 1) Decompose each pattern into a set of binary patterns, and 2) Build a binary associative memory (one matrix for each binary layer) with each training pattern set (by layers). A given pattern or a distorted version of it is recalled in three steps: 1) Decomposition of the pattern by layers into its binary patterns, 2) Recovering of each one of its binary components, layer by layer also, and 3) Reconstruction of the pattern from the binary patterns already recalled in step 2. Conditions for perfect recall of a pattern either from the fundamental set or from a distorted version of one them are also given. Experiments are also provided.
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Cruz, Benjamín; Sossa, Humberto; Barrón, Ricardo
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Associative memories (AM’s) have been extensively used during the last 40 years for pattern classification and pattern restoration. In this paper Conformal Geometric Algebra (CGA) is used to develop a new associative memory (AM). The proposed AM makes use of CGA and quadratic programming to store associations among patterns and their respective classes. An unknown pattern is classified by applying an inner product between the pattern and the build AM. Numerical and real examples are presented to show the potential of the proposal.
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Barrón, Ricardo; Sossa, Humberto; Cruz, Benjamín
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In this work we present an algorithm for training an associative memory based on the socalled multilayered morphological perceptron with maximal support neighborhoods. We compare the proposal with the original one by performing some experiments with real images. We show the superiority of the new one. We also give formal conditions for correct classification. We show that the proposal can be applied to the case of graylevel images and not only binary images.
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By
Sossa, Humberto; Barrón, Ricardo; Vázquez, Roberto A.
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3 Citations
Most results (lemmas and theorems) providing conditions under which associative memories are able to perfectly recall patterns of a fundamental set are very restrictive in most practical applications. In this note we describe a simple but effective procedure to transform a fundamental set of patterns (FSP) to a canonical form that fulfils the propositions. This way pattern recall is strongly improved. We provide numerical and real examples to reinforce the proposal.
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Sossa, Humberto; Barrón, Ricardo; Vázquez, Roberto A.
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1 Citations
In this paper we study how the performance of a median associative memory is influenced when the values of its elements are altered by noise. To our knowledge this kind of research has not been reported until know. We give formal conditions under which the memory is still able to correctly recall a pattern of the fundamental set of patterns either from a nonaltered or a noisy version of it. Experiments are also given to show the efficiency of the proposal.
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Vázquez, Roberto Antonio; Sossa, Humberto; Barrón, Ricardo
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Object recognition under occlusions is an important problem in computer vision, not yet completely solved. In this note we describe a simple but effective technique for the recognition objects under occlusions. The proposal uses the most distinctive parts of the objects for their further detection. During training, the proposal, first detects the distinctive parts of each object. For each of these parts an invariant description in terms of invariants features is next computed. With these invariant descriptions a specially designed set of associative memories (AMs) is trained. During object detection, the proposal, first looks for the important parts of the objects by means of the already trained AM. The proposal is tested with a bank of images of real objects and compared with other similar reported techniques.
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Sossa, Humberto; Barrón, Ricardo
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Median associative memories (MEDMEMs) first described in [1] have proven to be efficient tools for the reconstruction of patterns corrupted with mixed noise. First formal conditions under which these tools are able to reconstruct patterns either from the fundamental set of patterns and from distorted versions of them were given in [1]. In this paper, new more accurate conditions are provided that assure perfect reconstruction. Numerical and real examples are also given.
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Sossa, Humberto; Barrón, Ricardo; Oropeza, José L.
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In this note, we introduce an associative memory useful to recall realvalued patterns altered with mixed noise (additive and subtractive). Numerical and real examples are given to show the effectiveness of the proposal. Conditions under which the proposed memories are able to recall patterns either from the fundamental set of patterns and from distorted versions of them are also given.
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By
Cruz, Benjamín; Barrón, Ricardo; Sossa, Humberto
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1 Citations
Conformal Geometric Algebra (CGA) is a high level language commonly used in mathematical, physics and engineering problems. At a top level, CGA is a free coordinate tool for designing and modeling geometric problems; at a low level CGA provides a new coordinate framework for numeric processing in problem solving. In this paper we show how to use quadratic programming and CGA for, given two sets p and q of points in ℝ^{n}, construct an optimal separation sphere S such that, all points of p are contained inside of it, and all points of q are outside. To classify an unknown pattern x, an inner product must be applied between x and S. Some numerical and real examples to test the proposal are given.
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Sossa, Humberto; Barrón, Ricardo; Vázquez, Roberto A.
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Abstract
In this note we describe a new set of associative memories able to recall patterns in the presence of mixed noise. Conditions are given under which the proposed memories are able to recall patterns either from the fundamental set of patterns and from distorted versions of them. Numerical and real examples are also provided to show the efficiency of the proposal.
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By
Cruz, Benjamín; Barrón, Ricardo; Sossa, Humberto
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2 Citations
Associative memories (AMs) have been extensively used during the last 40 years for pattern classification and pattern restoration. A new type of AMs have been developed recently, the socalled Geometric Associative Memories (GAMs), these make use of Conformal Geometric Algebra (CGA) operators and operations for their working. GAM’s, at the beginning, were developed for supervised classification, getting good results. In this work an algorithm for unsupervised learning with GAMs will be introduced. This new idea is a variation of the kmeans algorithm that takes into account the patterns of the a specific cluster and the patterns of another clusters to generate a separation surface. Numerical examples are presented to show the functioning of the new algorithm.
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By
Sossa, Humberto; Barrón, Ricardo; Cuevas, Francisco; Aguilar, Carlos; Cortés, Héctor
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Abstract
We show how the binary αβ associative memories recently proposed by Yáñez in [1] can be extended to work now in the graylevel case. To get the desired extension we take the operators α and β, foundation of the αβ memories, and propose a more general family of operators among them the original operators α and β are a subset. For this we formulate a set of functional equations, solve this system and find a family of solutions. We show that the α and β originally proposed in [1] are just a particular case of this new family. We give the properties of the new operators. We then use these operators to build the extended memories. We provide the conditions under which the proposed extended memories are able to recall a pattern either from the pattern’s fundamental set or from altered versions of them. We provide real examples with images where the proposed memories show their efficiency.
more …
By
Barrón, Ricardo; Sossa, Humberto; Cortés, Héctor
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1 Citations
Morphological neural networks consider that the information entering a neuron is affected additively by a conductivity factor called synaptic weight. They also suppose that the input channels account with a saturation level mathematically modeled by a MAX or MIN operator. This, from a physiological point of view, appears closer to reality than the classical neural model, where the synaptic weight interacts with the input signal by means of a product; the input channel forms an average of the input signals. In this work we introduce some geometrical aspects of dendrite processing that easily allow visualizing the classification regions, providing also an intuitive perspective of the production and training of the net.
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By
Cruz, Benjamín; Sossa, Humberto; Barrón, Ricardo
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5 Citations
Pattern reconstruction or pattern restoration in the presence of noise is a main problem in pattern recognition. An essential feature of the noise acting on a pattern is its local nature. If a pattern is split into enough subpatterns, a few of them will be less or more affected by noise, others will remain intact. In this paper, we propose a simple but effective methodology that exploits this fact for the efficient restoration of a pattern. A pattern is restored if enough of its subpatterns are also restored. Since several patterns can share the same subpatterns, the final decision is accomplished by means of a voting mechanism. Before deciding if a subpattern belongs to a pattern, subpattern restoration in the presence of noise is done by an associative memory. Numerical and real examples are given to show the effectiveness of the proposal. Formal conditions under which the proposal guaranties perfect restoration of a pattern from an unaltered or and altered version of it are also given.
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By
Sossa, Humberto; Barrón, Ricardo; Cuevas, Francisco; Aguilar, Carlos
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2 Citations
In this note we show how a binary memory can be used to recall graylevel patterns. We take as example the α β associative memories recently proposed in Yáñez, Associative Memories based on order Relations and Binary Operators(In Spanish), PhD Thesis, Center for computing Research, February of 2002, only useful in the binary case. Basically, the idea consists on that given a set of graylevel patterns to be first memorized: (1) Decompose them into their corresponding binary patterns, and (2) Build the corresponding binary associative memory (one memory for each binary layer) with each training pattern set (by layers). A given pattern or a distorted version of it, it is recalled in three steps: (1) Decomposition of the pattern by layers into its binary patterns, (2) Recalling of each one of its binary components, layer by layer also, and (3) Reconstruction of the pattern from the binary patterns already recalled in step 2. The proposed methodology operates at two phases: training and recalling. Conditions for perfect recall of a pattern either from the fundamental set or from a distorted version of one them are also given. Experiments where the efficiency of the proposal is tested are also given.
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