Tunable equivalence fuzzy associative memories

Esmi, Estevão; Sussner, Peter; Sandri, Sandra

doi:10.1016/j.fss.2015.04.004

Cited by 18 publications

(6 citation statements)

References 57 publications

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“…In conclusion, lattice computing, or LC for short, has been proposed as "an evolving collection of tools and mathematical modeling methodologies with the capacity to process lattice-ordered data per se including logic values, numbers, sets, symbols, graphs, etc" [6], [16], [29]. The existence of suitable real functions on lattice-ordered data allows for "fine-tuning" as demonstrated in this work.…”

Section: Introductionmentioning

confidence: 86%

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Kaburlasos

Papakostas

2015

IEEE Comput. Intell. Mag.

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This paper describes the recognition of image patterns based on novel representation learning techniques by considering higher-level (meta-)representations of numerical data in a mathematical lattice. In particular, the interest here focuses on lattices of (Type-1) Inter vals' Numbers (INs), where an IN represents a distribution of image features including orthogonal moments. A neural classif ier, namely fuzzy lattice reasoning (f lr) fuzzy-ART-MAP (FAM), or f lrFAM for short, is described for learning distributions of INs; hence, Type-2 INs emerge. Four benchmark image pattern recognition applications are demonstrated. The results obtained by the proposed techniques compare well with the results obtained by alternative methods from the literature. Furthermore, due to the isomorphism between the lattice of INs and the lattice of fuzzy numbers, the proposed techniques are straightforward applicable to Type-1 and/or Type-2 fuzzy systems. The far-reaching potential for deep learning in big data applications is also discussed.

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Section: Introductionmentioning

confidence: 86%

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Kaburlasos

Papakostas

2015

IEEE Comput. Intell. Mag.

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“…Throughout the paper, we assume that [0, 1], ∨, ∧, D, S is a dual R-clogli. We remark that residual S, derived from D using (12), is a fuzzy co-implication if and only if…”

Section: Fuzzy Sets and Fuzzy Logic Operationsmentioning

confidence: 99%

“…Several associative memory models have been introduced in the literature, and their applications range from optimization [3,4] and prediction [5][6][7] to image processing and analysis [8][9][10]. Associative memory models have also been applied for pattern classification [11][12][13][14], including face recognition [15]. Moreover, the interest in associative memory models increased significantly in the last few years due to their relationship with the attention mechanism used in transformer models [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Apart from the distributed models like the FMAMs with FLA and their variations, non-distributed associative memory models have received considerable attention partly due to their low computational effort and extraordinary successes in pattern recognition and image restoration tasks. Examples of non-distributed associative memories include models based on Hamming distance [35] and kernels [15] as well as subsethood and similarity measures [11,12,14]. In the context of non-distributed models, we introduced max-plus and min-plus projection auto-associative morphological memories (max-plus and min-plus PAMMs), which can be viewed as non-distributed versions of the autoassociative morphological memories of Ritter et al [36].…”

Section: Introductionmentioning

confidence: 99%

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Max-C and Min-D Projection Auto-Associative Fuzzy Morphological Memories: Theory and an Application for Face Recognition

dos Santos,

Valle

2023

AppliedMath

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Max-C and min-D projection auto-associative fuzzy morphological memories (max-C and min-D PAFMMs) are two-layer feedforward fuzzy morphological neural networks designed to store and retrieve finite fuzzy sets. This paper addresses the main features of these auto-associative memories: unlimited absolute storage capacity, fast retrieval of stored items, few spurious memories, and excellent tolerance to either dilative or erosive noise. Particular attention is given to the so-called Zadeh’ PAFMM, which exhibits the most significant noise tolerance among the max-C and min-D PAFMMs besides performing no floating-point arithmetic operations. Computational experiments reveal that Zadeh’s max-C PFAMM, combined with a noise masking strategy, yields a fast and robust classifier with a strong potential for face recognition tasks.

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“…It is worth noting that the morphological associative memories, which emerged in the 1990s, were the first to use this particular algebraic approach [2,3], during the 2000s, a new type of memory called αβ memories was developed [16,18] and another memory model based on minmax algebra was developed in 2021 [6]. The benefits offered by memory models based on minmax algebra have spurred numerous advances in this field [16][17][18][19][37][38][39][40]. One of the main challenges facing associative memories in minmax algebra is the creation of a kernel-a subset of the input pattern x-that remains unaffected by noise.…”

Section: Introductionmentioning

confidence: 99%

Generic Model of Max Heteroassociative Memory Robust to Acquisition Noise

et al. 2023

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Associative memories are a significant topic in pattern recognition, and therefore, throughout history, numerous memory models have been designed due to their usefulness. One such model is the associative memory minmax, which is highly efficient at learning and recalling patterns as well as being tolerant of high levels of additive and subtractive noise. However, it is not efficient when it comes to mixed noise. To solve this issue in the associative memory minmax, we present the generic model of heteroassociative memory max robust to acquisition noise (mixed noise). This solution is based on understanding the behavior of acquisition noise and mapping the location of noise in binary images and gray-scale through a distance transform. By controlling the location of the noise, the associative memories minmax become highly efficient. Furthermore, our proposed model allows patterns to contain mixed noise while still being able to recall the learned patterns completely. Our results show that the proposed model outperforms a model that has already solved this type of problem and has proven to overcome existing methods that show some solution to mixed noise. Additionally, we demonstrate that our model is applicable to all associative minmax memories with excellent results.

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Tunable equivalence fuzzy associative memories

Cited by 18 publications

References 57 publications

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Max-C and Min-D Projection Auto-Associative Fuzzy Morphological Memories: Theory and an Application for Face Recognition

Generic Model of Max Heteroassociative Memory Robust to Acquisition Noise

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