Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
La línea de investigación en sistemas inteligentes se define como un área de investigación de las ciencias computacionales que utiliza modelos y técnicas de inteligencia artificial para realizar pruebas de optimización de procesos computacionales orientados a la resolución de problemas complejos. Actualmente se trabajan temas de: visión por computadora, machine learning, reconocimiento de patrones, cómputo evolutivo orientadas a la optimización computacional mediante el uso de técnicas de inteligencia artificial (redes neuronales, máquinas de soporte vectorial, algoritmos de agrupamiento) para el procesamiento de información, en el reconocimiento de patrones, procesamiento de imágenes aplicados a diferentes problemáticas como el área de la salud, biometría para la seguridad, entre otros. Recientemente se han desarrollado trabajos relacionados con el Deep learning como una rama de machine learning que utiliza principalmente redes neuronal con un mayor número de capas para lograr mejores resultados. Dentro de esta línea se han llevado a cabo trabajos de investigación básica y aplicada que han tenido continuidad en proyectos de nivel doctoral.
La productividad académica de esta línea de investigación ha estado fuertemente apoyada por el trabajo con los estudiantes y las redes de colaboración que se han establecido con otros grupos de investigación entre los que destacan profesores externos de la Universidad de Guanajuato, CIMAT, Instituto Tecnológico de Tijuana, CIC-IPN y la Universidad de Guadalajara. A continuación se enlista la productividad de esta línea de investigación.
En el listado anexo se enlista la productividad académica de la línea de investigación con la participación de estudiantes y alumnos graduados, así como los archivos de las publicaciones.
TeCNM/Instituto Tecnológico de León Maestría en Ciencias la Computación (MCCOM-2011-05)
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
Año de
publicación Generación Apell_pat Apell_mat Nombre Nombre del producto Tipo de producto
2020
2018_2 Rocha Angulo Augusto Rafael
A Novel Set of Moment Invariants for Pattern Recognition Applications Based on Jacobi Polynomials (MCPR Pattern Recogntion)
Capítulo de libro indexado (MCPR 2020)
2020
2018_2 Juárez Santini Carlos Alberto
Single Spiking Neuron Multi-Objective Optimization for
Pattern Classification (JAMRIS 2020) Artículo indexado 2020
2017_1 Aguilar Figueroa Raúl A Study of Highest Perfusion Zones as Biometric
Representation Artículo indexado
2020
2015_2 Acosta Herrera Antonio Gegenbauer-Based Image Descriptors for Visual Scene
Recognition Artículo indexado
2020
2017_2 López Váquez Oscar Gustavo
Comparing evolutionary artificil neural network for second and third generation for solving supervised classification problems
Capítulo de libro indexado
2019
2017_2 Sánchez López Elvi Malitzin
Algortimo de evolución diferencial con reparador
cromosómico aplicado a un problema de secuenciación de vehículos
Artículo indexado
2018
2015_2 Duarte Carrera Daniel Phase Unwrapping for 3D Object Reconstruction by means
of Population-based Metaheuristics Artículo indexado 2018
2015_2 Gódínez Bautista Adán Bio-inspired metaheuristics for hyper-parameter tuning of
support vector machine classifiers Capítulo de libro indexado
PRODUCTOS CON LA PARTICIPACIÓN DE ESTUDIANTES Y GRADUADOS
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
2019
2017_2 López Vázquez Oscar Gustavo
Evolutionary Spiking Neural Networks for Solving
Supervised Classification Problems Artículo indexado 2019
2018_1 Frausto Pérez Oscar Entrenamiento dinámico de redes convolucionales produnddas para clasificación de imáganes
Artículo indexado (mejor artículo del congreso) 2019
2018_1 Zúñiga Núñez Blanca Verónica
Studying Grammatical Evolution’s Mapping Processes for
Symbolic Regression Problems Capitulo de libro indexado 2019
2017_2 Espinosa Susana Evolutionary Training of Deep Belief Networks for
Handwritten Digit Recognition Artículo indexado
2019
2018_1 Zúñiga Núñez Blanca Verónica
Exploring random permutations effects on teh mapping
process for gramatical evolution. Capítulo de libro indexado 2018
2016_1
Cornejo
Acosta Alejandro Un enfoque al problema dinámico de múltiples agentes
viajeros con programación heurística Artículo arbitrado
2018
2016_1 Jiménez Falcón Julio Antonio
Una comparativa de diferentes parámetros en la
construcción evolutiva de descriptores para la clasicación de imágenes de texturas de piezas arqueológicas
Artículo indexado
2018
2016_1 Veloz Javier
Aprendizaje profundo de representaciones robustas para clasificación de multi instancias y multietiquetas de imágenes
Artículo indexado
2018
2017_2 López Jiménez Marlene Parametrización de Índice de Arco Mediante Descriptores
Simples de Región Memoria de Congreso
2016
2015_1 Montesino Guerra Juan Adolfo
Comportamiento Sinérgico en Hiperheurística de selección
para la solución de problemas del agente viajero Artículo indexado
TeCNM/Instituto Tecnológico de León Maestría en Ciencias la Computación (MCCOM-2011-05)
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
Todos los artículos y capítulos de libro de la tabla anterior fueron presentados en coautoría con los profesores del NAB como se puede consultar en los medios de verificación adjuntos.
2016
2015_1 Flores Mendoza Juan Pablo
Segmentación automática de billetes mexicanos basada en
un modelo de color y referencias geométricas Artículo indexado 2016
2015_2 Quiroz Ramírez Olga Judith
Diseño de Redes Neuronales Artificiales usando técnicas
evolutivas Capítulo de libro
2016
2015_2 Avila Uribe Carlos
Gramática evolutiva con estrategia evolutiva como n´ucleo de una hiperheur´ıstica de generaci´on aplicada al problema de empacado
Artículo indexado
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
Año de publicación
Autores Nombre de la revista o
libro Nombre del producto Tipo de producto
2020 Ubaldo Uribe- López,a David Asael Gutiérrez-
Hernández
Optical Engineering 58(9), 092605 (September 2019
Improvement of fringe quality for phase extraction in
double digital fringe projection Artículo indexado JCR
2019 Santiago, R.;
Gutiérrez, D.;
Zamudio, V;
Hernández, I.
Diagnostics 2020, 10(3), 136;
Novel Mathematical Model of Breast Cancer
Diagnostics Using an Associative Pattern Classification Artículo JCR
2019
Carpio, JM;
Puga, H; Rojas, A.
IEEE Access ( Volume:
7 )
Symmetric-Approximation Energy-Based Estimation of Distribution (SEED): A Continuous Optimization Algorithm
Artículo JCR
2019
Rojas, A;
IEEE Access, vol. 7, pp.
120117-120127, 2019,
Modeling the Game of Go by Ising Hamiltonian, Deep
Belief Networks and Common Fate Graphs Artículo indexado 2018
Rojas, A.;
Ornelas, M.
Journal of
Archaeological Science:
Reports
Automated classification of archaeological ceramic
materials by means of texture measures Artículo indexado 2018
Calzada, V.;
Ornelas, M;
Rojas, A.
IEEE Access, vol. 6, pp.
40450-40462,
Evolutionary design of problem-adapted image
descriptors for texture classification Artículo indexado
2017 Luis Carlos
Padierna, Martín Carpio, Alfonso
Rojas, Héctor Puga, Rosario Baltazar and Héctor Fraire
Studies in Computational Intelligence 667
Hyper-Parameter Tuning for Support Vector Machines
by Estimation of Distribution Algorithms Artículo indexado PRODUCTIVIDAD SIN PARTICIPACIÓN DE ESTUDIANTES
TeCNM/Instituto Tecnológico de León Maestría en Ciencias la Computación (MCCOM-2011-05)
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
2016 A. Espinal,1 H.
Rostro- Gonzalez,2 M.
Carpio,1 E
Computational Intelligence and Neuroscience
Quadrupedal Robot Locomotion: A Biologically
Inspired Approach and Its Hardware Implementation Artículo indexado JCR
2015 J. David Terán- Villanueva
• Héctor Joaquín Fraire Huacuja
• Juan Martín Carpio Valadez
Computation Optimization and Applications
A heterogeneous cellular processing algorithm for minimizing the power consumption in wireless communications systems
Artículo indexado JCR
Productividad académica 2016-2020 Línea de investigación Sistemas Inteligentes
ANEXO 2 OFICIO DE AUTORIZACIÓN TECNM.-LÍNEA SISTEMAS INTELIGENTES
A Study of Highest Perfusion Zones as Biometric Representation
Ra ´ul Santiago Montero1, Ra ´ul Aguilar Figueroa2, Agust´ın Sancen Plaza3,
Mar´ıa del Rosario Baltazar Flores1, David Asael Guti ´errez Hern ´andez1, Juan Francisco Mosi ˜no1
1Instituto Tecnol ´ogico de Le ´on,
Division de Estudios de Posgrado e Investigaci ´on, Mexico
2Instituto Tecnol ´ogico de Zit ´acuaro, Mexico
3Instituto Tecnol ´ogico de Celaya, Department of Engineering Sciences,
Mexico
{raul.santiago, david.gutierrez}@itleon.edu.mx, [email protected], {asancenp, jfmosino, rauly.af123}@gmail.com
Abstract. Biometrics focuses on simulate the human ability to associate one or a set of corporal features of a person in a unique way by uses a specific representation, this representation is knows as identity. Visible spectrum face recognition is the identification way more natural which has a higher universality, collectability and acceptability front to the other biometrics modalities, but is weak in the invariance and distinctiveness criterion to be a good biometric. In order to improve the face recognition, the infrared spectrum arises as a good representation to solve these drawbacks in biometric identification. Buddharaju et al., proposed a process by which the vascular net is detected [3] . However, Wu et al. [19, 21], criticized this approach by not take into account the heat transfer between the environment and the person in the time to take the image and proposed a modification of image thermogram and show that it is a better solution to make up for the heat change.
This paper is written intending to know if there is a significant difference between both approaches to be used as biometric representation. We found that the normalization of the thermograms, proposed by Wu et al., do not affect the distinctive zones of high blood perfusion to be used as biometric representation.
Keywords. Face recognition, thermal image, perfusion zones, shape description.
1 Introduction
Biometrics focuses on simulate the human ability to associate one or a set of corporal features of a person in a unique way by uses a specific representation, this representation is knows as identity. The biometric identification has become a real solution for many social, corporate and commercial activities where it is necessary the verification of the identity [11, 1, 16].
In principle, any physiological feature can verify or recognize the biometric identity of a person, these features can be group in several modalities as hands, faces, behavior or medical-chemistry features [17].
Visible spectrum face recognition is the iden- tification way more natural which has a higher universality, collectability and acceptability front to the other biometrics modalities, but is weak in the invariance and distinctiveness criterion to be a good biometric [2, 11].
Although face recognition has more of two decades, many of the research has been over visible spectrum [2, 15, 17]. This approach has difficulties when there are lighting variability, chance of pose or different facial expressions.
Computación y Sistemas, Vol. 24, No. 1, 2020, pp. 325–329 doi: 10.13053/CyS-24-1-2911
In order to improve the face recognition, the in- frared spectrum arises as a good representation to solve this drawbacks in biometric identification [6, 12, 8, 15].
This paper is written with the intention to apply the method of higher intensity region of thermogram of Buddaraju over the propose of Wu and test and contrast the performance of this modification with the original propose of Bud- dharaju [3]. We prove that the perfusion regions with higher intensity are equivalent at the zones of the Buddaraju propose. Our method combines, in first place, the works of Buddaraju and Wu and one simple region shape descriptor is applied to form a nine-dimensional vector feature.
After, it is used the same method over the Buddharaju propose and the performance of both proposes are compared. The UCH image database was employed for this study which has outdoor, indoor and face angle rotations conditions.
In order to highlight the efficiency of the proposed face recognition approach, several classification algorithms were used in our study and we proved that both proposes hold enough information to biometric face representation because of the difference in performance accuracy are not significance. However, the Wu thermogram add more computational work.
2 Related Work
Several approaches and techniques have been proposed for a quantitative description. One of the first work was made by Yoshitomi et al.
They shown that the infrared spectrum is more robust with the lighting variability problem of the visible [22]. After, Friedrich et al., proposed a method based on eigenfaces as face descriptor of thermograms and found that these kinds of images were less affected by the change of pose or facial expressions [7]. The following works have been focused on different ways to describe the thermograms and the frequency domain is one approach widely used [9, 6]. By another hand, an approach derived is the getting of information physiologic contained inside infrared images.
For instance, Prokoski et al., found that it is possible the detection of the face vascular net in
thermograms which could be used as a biometric descriptor [13]. Buddharaju et al., used this idea and proposed a process by which the vascular net is detected. Their hypothesis is based on the existence of zones with high values of intensity in the pixels of the thermogram and that this values they are correlated with the presence of some blood vessel. The method finds the regions with the higher thermogram intensities and they are isolated by morphological transforms. These regions are thinning and its skeleton is formed.
In this skeleton are marked the breaching points, called Thermal Minutia Points (TMP). They are used as minutiae points [4, 5, 3].
The work was criticized because the skeleton did not necessarily show blood vessels and it did not take into account the physics and physiological conditions of the heat transfer [19, 18, 21].
Wu takes into account the heat transfer condition in thermograms and suggests changes the name of the regions detected from the vascular net to the perfusion zones. This approach modifies the pixels values of the thermogram and generates a new image which is more robust to temperature changes in which it is taked. Wu and Zhang tested this representation using cosine transform as descriptor and found that can be used as a good biometric [20].
3 Face Recognition Method
In this section, it is described the methodology following for faces recognition based on simple shape descriptor over maximal perfusion zones.
Figure 1 shows the methodological architecture.
Step 1: Thermogram transformation into an image of blood perfusion. This step is made by the propose of Wu, where each intensity pixel is modified by (1):
W = σ(T4− Te4)
αcb(Ta− T ), (1) where is the skin emissivity, σ is the Stefan-Boltzmann value, α is the tissue/skin countercurrent exchange ratio and cb is the blood specific heat which are constants.
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ISSN 2007-9737
Fig. 1. Diagram of our thermal face recognition process
T is the thermal intensity pixel value, Ta is the artery temperature and Te is the ambient temperature.
Step 2: It is applied the method of the highest intensity blood vessels extraction proposed by Buddharaju: The anisotropic filter was set up under Matlab platform with a gradient modulus threshold value equal to 60, an integration constant equal to 1/5 and the option 1. After, it was implemented a Tophat morphological transform with a disk as structure element of radius equal to 3. Finally, it was used a closed morphological operation for clear the image with a disk with a radius equal to two.
Step 3: The image is segmented in 9 equal dimensional regions, as it is shown in Figure 1.
Step 4: For each sub-image a simple shape descriptor is extracted, in our case it is use the normalize E factor (NEF) [14]. The NEF uses the internal or external border information to give us a measure of the shape porosity. In our approach, each image is taken as an object with holes. After, a nine feature vector is formed with the NEF values.
The example is shown in Figure 1.
Step 5: Finally, the process end with the classification of the database using the NEF description by the following classifiers: Support
Vector Machine, K-Nearest Neighbor (K = 3), Parzen, Normal densities based linear (multi- class), Nearest mean linear, Normal densities based quadratic (multi-class), Minimum least square linear, Logistic Linear, Quadratic, Naive Bayes, LC based on PCA expansion on the joint data.
4 Results
For testing the performance of perfusion zones as biometric identification, we used the UCH Thermal data base [10]. This database is ideal because the thermograms are taken in unconstrained environments, with face rotation, indoor, outdoor session and facial expressions. The images used for these tests were images had a spatial size of 81x150 pixel. To measure the effectiveness of this representation, a 4-folds statistical test done by 5 iterations was implemented in the PrTools library under Matlab platform. Table 1 shows the performance by the average recognition rate which is given for each classification algorithm when it is applied our method indoor and rotation conditions. The best overall performance was for a support vector machine and the worse result was for a normal densities based linear algorithm. A standard deviation (SD) got join to the time process for each algorithm.
Table 1. Performance of higher perfusions zones on UCH image database using our propose method
Algorithm Accuracy SD Speed SVM 89.49% 0.0069 623.162712 s KNN 61.62% 0.0138 2.793641 s Parzen 65.80% 0.0081 2.050866 s NDBL 48.60% 0.0039 7.254782 s NML 63.26% 0.0081 4.507564 s
NDBQ 75.77% 0.01 3.559874 s
MLQL 59.51% 0.0069 31.038115 s
LL 57.84% 0.0677 34.936810 s
Quadratic 78.68% 0.02 41.189440 s
NB 68.03% 0.0107 1.234846 s
LC 47.71% 0.0081 13.115993 s
With the aim to found some difference between the original propose of Buddharaju and the Wu modification, we tested the same extracted
Computación y Sistemas, Vol. 24, No. 1, 2020, pp. 325–329 doi: 10.13053/CyS-24-1-2911
features approach without uses heat transfer equation. The results are described in Table 2. In this case, the support vector machine again got the best classification percentage.
However, the difference between both approach are not significative. There are not an important difference with the classification values of the others algorithms.
Table 2. Performance of classification using NEF descriptor on UCH image database when applying only Buddharaju approach
Algorithm Accuracy SD Speed SVM 89.22% 0.0034 639.940778 s KNN 60.51% 0.0062 2.979696 s Parzen 63.13% 0.0056 2.159387 s NDBL 50.00% 0.0076 7.734073 s NML 62.61% 0.0088 4.526179 s NDBQ 74.72% 0.0126 4.040726 s MLQL 58.06% 0.0065 32.249418 s
LL 54.58% 0.0088 34.873280 s
Quadratic 77.57% 0.0109 41.106188 s
NB 67.84% 0.0102 1.387489 s
LC 49.84% 0.0018 13.063554 s
Finally, we applied our method separately to the Buddharaju and Wu approaches, with the aim to test if there are difference in outdoor condition, using our face descriptor. The results are illustrated in the Table 3, where only the best classification percentage is showed. We could hope that the Wu propose was better than Buddharaju approach. However, we did not find a significative difference in classification rate.
Table 3. Performance of classification using NEF descriptor on UCH image database when applying separately the Buddharaju and Wu approaches
Algorithm Accuracy SD Speed
SVM (Buddharaju) 90.46% 0.0036 583.09 s
SVM (Wu) 90.57% 0.0019 583.46 s
5 Conclusion and Future Work
In this paper, we analyzed how the zones of highest intensity in a modified thermogram can be used as biometric descriptor in combination with the vane
net detection method proposed by Buddharaju. For showing this property, a method was designed by partition the vane net image in nine sub-images.
Our propose showed a robust behavior to change of temperature, environment, face rotation and physiological condition, properties of the well-know UCH Thermal Face data image base. This robustness is evident when a simple shape descriptor is used to conform a characteristic vector and good percentages in classification accuracy is obtained. Unlike the work of Hermosilla et al. [10], where a study of different description algorithms are tested using the totality of the image, we concentrated the work in lower the computational cost in time and spaces by a reduce representation of the thermogram. The result showed that the representation can be uniquely associated. However, it can observed that the modification make by Wu is not had a great impact when the zones of highest blood intensity are extracted and it is used our approach of description. The limitation of our approach is the kind of descriptor, which is weak in affine transformation and can be more sensitive by the image face angle. However, the work is concerned with the representation, not with the its description.
The future work is concerned with applied more complexes descriptor and description methods.
Acknowledgements
We would like to acknowledge the support from Mexican National Science and Technology Council (Consejo Nacional de Ciencia y Tecnolog´ıa, CONACYT) and Tecnol ´ogico Nacional de M ´exico/
Instituto Tecnol ´ogico de Le ´on and Instituto Tec- nol ´ogico de Zit ´acuaro in the develop of this research.
References
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13. Prokoski, F. J. & Riedel, R. B. (1996). Infrared Identification of Faces and Body Parts. Springer US, Boston, MA, pp. 191–212.
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Sossa, J. H. (2014). Digital shape compactness measure by means of perimeter ratios. Electronics Letters, Vol. 50, No. 3, pp. 171–173.
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Blood perfusion models for infrared face recognition.
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Article received on 12/03/2018; accepted on 29/10/2019.
Corresponding author is Ra ´ul Santiago Montero.
Computación y Sistemas, Vol. 24, No. 1, 2020, pp. 325–329 doi: 10.13053/CyS-24-1-2911
Journal of Automation, Mobile Robotics and Intelligent Systems VOLUME 14, N° 1 2020
Single Spiking Neuron Multi-Objective Optimization for Pattern Classification
Carlos Juarez-Santini, Manuel Ornelas-Rodriguez, Jorge Alberto Soria-Alcaraz,
Alfonso Rojas-Domínguez, Hector J. Puga-Soberanes, Andrés Espinal, Horacio Rostro-Gonzalez
Submitted: 20th December 2019; accepted: 30th March 2020
DOI: 10.14313/JAMRIS/1-2020/9
Abstract: As neuron models become more plausible, fewer computing units may be required to solve some problems; such as static pattern classification.
Herein, this problem is solved by using a single spiking neuron with rate coding scheme. The spiking neuron is trained by a variant of Multi-objective Particle Swarm Optimization algorithm known as OMOPSO. There were carried out two kind of experiments: the first one deals with neuron trained by maximizing the inter distance of mean firing rates among classes and minimizing standard deviation of the intra firing rate of each class;
the second one deals with dimension reduction of input vector besides of neuron training. The results of two kind of experiments are statistically analyzed and compared again a Mono-objective optimization version which uses a fitness function as a weighted sum of objectives.
Keywords: Multi-objective Optimization, Spiking Neu- ron, Pattern Classification
1. Introduction
Artificial Neural Networks (ANNs) try to simulate the behavior of the brain when they generate, process or transform information. An ANN is a system formed of simple processing units, which offers the property, and capability of input-output mapping. ANNs learn to solve complex problems in a reasonable amount of time [1]. The ability of learning of ANNs become a powerful tool for wide applications, for instance:
pattern recognition works, classifying, clustering, vi- sion tasks and forecasting [2].
ANNs can be distinguished in three generations ac- cording to their computational units [3]. The first one is based on McCulloch-Pitts neuron as computational units that can handle digital data [3]. The second one is characterized by a multilayer architecture, connec- tivity separating input, intermediate, and output units and applying activation functions with a continuous set of possible output values to a weighted sum of the inputs [4]. The third generation has been developed with the purpose of design neural models more plau-
sible to the biological neurons. These are known as Spiking Neural Networks (SNNs) [5], [6].
ANNs are conformed by neurons organized in in- put, hidden and output layers, which are inter-con- nected by synaptic weights. These simulate the neu- ron synapsis of the human brain. During the training process of an ANN, a set of synaptic weights con- stantly is changing until the knowledge acquired is enough. Once the knowledge process has finished, it is necessary to evaluate the performance of the ANN. It is expected that the ANN can classify with acceptable accuracy the patterns from a particular problem during the testing phase [7]. The training process is an optimization task since it is desired to find the optimal weight set of the ANN. Methods based on gradient-descent have been applied to the training phase [8], but these techniques can be trapped at local minima. Then to overcome this situ- ation, the researchers have proposed different glob- al optimization methods [9] to optimize the ANNs by Evolutionary Algorithms (EAs). These EAs can be used to calibrate the connection weights, optimize the architecture and selecting the input features of ANNs [10].
The present research proposes a method for train- ing full and partially connected SNNs based on the Leaky Integrate and Fire (LIF) model, by using a var- iant of Multi-objective Particle Swarm Optimization known as OMOPSO. This methodology is designed to solve pattern recognition problems. The results are statistically analyzed and compared with a version of mono-objective optimization using the Particle Swarm Optimization algorithm (PSO).
This paper is organized as follows: Section 2 pre- sents the theoretical fundamentals used in this work.
Section 3 explains the implemented methodology.
Section 4 shows the results and statistical analysis.
Finally, in section 5 are presented the conclusions and future work.
2. Background
This section describes the LIF model and the Op- timized Multi-objective Particle Swarm Optimization (OMOPSO), which were used in this work.
this work, we used the OMOPSO algorithm described in [15], which is based on Pareto dominance and an elitist selection through crowding factor. Beside this, the authors incorporated two mutation operators (uniform mutation and non-uniform mutation). The uniform mutation refers to variability range allowed for each decision variable, which is kept constant over generations and the non-uniform mutation has a characteristic variability range allowed for each de- cision variable, which decreases over time. Finally, it was added the e-dominance concept which is the final size of the external file where stores the non-dominat- ed solutions. Algorithm 1 shows the OMOPSO.
Algorithm 1. OMOPSO
Require: Initialize Swarm Pi, Initialize Leaders Li
1: Send Li to e-file 2: crowding(Li), g = 0 3: while g < gmax do 4: for each particle 5: Select leader 6: Fly 7: Mutation 8: Evaluate 9: Update pbest
10: end for 11: Update Li
12: Send Li to e-file 13: crowding(Li), g = g + 1 14: end while
15: Report results in e-file
3. Methodology
This section shows the methodology used in our work. There were proposed two kinds of experi- ments: the first one treats with neuron trained by maximizing the inter distance of mean firing rates among classes and minimizing the standard deviation of the intra firing rate of each class; the second one deals with dimension reduction of input vector be- sides of neuron training.
The LIF neuron model was implemented into jMetal [16], [17] where is available the OMOPSO al- gorithm, which was used for training the LIF neuron.
Furthermore, the OMOPSO algorithm was configured as a mono-objective algorithm (PSO).
The design of the methodology is shown in Fig. 2.
Initially, we set up the parameters of the OMOPSO algo- rithm and the LIF neuron model. Next, it is necessary to initialize the particles and Leaders (Li) with uniformly random numbers to make a swarm. Each particle rep- resents a synaptic weight vector ( )w with the same size as the feature input vector ( )x . Then, whole particles 2.1. Leaky Integrate and Fire Model
The LIF neuron model is one of the most used in the field of computational neuroscience given this model has an easier implementation and a lower computational cost in comparison with other spiking neuron models [11].
The mathematical representation for this model is shown in [11], [12] and it is given by the potential dynamic of the membrane:
τ dvdti = −gleak
(
v Ei− leak)
+I t( )
(1) where gleak and Eleak are the conductance and the re- versal potential of the leak current, t is the membrane time constant and I(t) is a current injected into the neuron.In this work, it was used the representation pro- posed in [11],[13] defined as:
′ = + −
≥ ←
v I a bv
v vthreshold v c
, ,
if then (2)
where I is the input current of the neuron, v denotes the membrane potential, a and b are parameters to configure the behavior of the neuron, c is the rest state voltage and vthreshold is the threshold for the spike (firing) of the neuron. Besides, an initial condition v0
is necessary to solve the differential equation by nu- merical methods.
Since the input patterns cannot be directly pro- cessed by the LIF neuron, they must be transformed to input currents by means of the equation:
I x w= ⋅ ⋅θ (3)
where x∈ is the input pattern vector, wn ∈ is n the set of synaptic weights and θ is a gain factor.
Fig. 1 shows the representation of a LIF neuron.
When I is computed, it continues to solve the equa- tion (2) to obtain the output spike train belonging to the input pattern.
Fig. 1. Representation of a LIF neuron
2.2. Optimized Multi-Objective Particle Swarm Optimization (OMOPSO)
Regarding multi-objective optimization, a con- siderable number of algorithms can be found in the literature. For instance, the Multi-objective Particle Swarm (MOPSO) was proposed by Coello in [14]. In
Journal of Automation, Mobile Robotics and Intelligent Systems VOLUME 14, N° 1 2020
are evaluated into the LIF neuron model, by means of the objective functions. The non-dominated particles in the swarm will be Li, which are sent to e-file. Besides this, it is calculated a crowding factor for each Li as a second discrimination criterion.
Start
After it is initialized an Internal Loop into an External Loop, and each particle is modified into the Internal Loop, updating the position and applying the mutation operators. Then, each particle is evaluated and updated its personal best value ( ). A new particle replaces the if such value is dominated by the new particle or if both are non-dominated concerning each other.
When all particles have been updated, the are modified in the External Loop. Only the particles that overcome their will try to enter to set. Once the have been updated, they are sent to - . Finally, the crowding values of the set of is updated and we eliminate as many leaders as necessary to avoid overflow of the size of the set. The process is repeated until finalizing all iterations.
Fig. 2. Methodology schema
3.1.Objective Functions
Three different objective functions were considered to measure the performance of the solutions (particles):
A. The Euclidean distance between the combination of and , where is the average firing rate of each class and . For this objective function, we looking for maximize the separability between the classes:
( ) (eq.4) B. The Standard Deviation of the firing rate for each pattern class , where and is the total of pattern classes. In this
objective function, we looking for minimize the dispersion of each pattern class:
( ) (eq.5)
C. The dimension of the input feature vector ( ̅).
To avoid redundancies in information, we desire to reduce the dimensionality of the feature vectors, by minimizing the total of of a binary mask ( ̅) with the same size of the input feature vector.
In our proposal, the number of objective functions is related to the number of classes of the dataset.
3.2.Experiments
Four supervised classification datasets from the UCI Machine Learning Repository [18] were employed for experimentation: Iris Plant, Wine, Glass, and SPECT.
Table 1 shows the details of the datasets used.
Each dataset was randomly divided in two subsets with approximately the same size. The first one was employed as training set and the second one as testing set.
Dataset Instances Classes Features
Iris Plant 150 3 4
Wine 178 3 13
Glass 214 6 9
SPECT 267 2 22
Table. 1. Datasets employed for experimentation With the aim to observe the performance of our proposal, four experiments were configurated according to the objective functions seen in section 3.1. The characteristics of each experiment are defined below and summarized in Table 2.
i. Experiment #1 was defined as a multi- objective problem, focusing on the A and B objective functions. The OMOPSO algorithm was used to optimize the synaptic weight vector of the LIF neuron.
ii. Experiment #2 employs the multi-objective approach, considering the A, B and C objective functions. The OMOPSO algorithm was taken to optimize the synaptic weight vector and the dimension of the input vector.
Concerning the optimization of the last parameter, a binary mask ( ̅) was used in equation (3) to calculate a modified input current given by equation (6).
̅ ̅ ̅ (eq.6)
Report results in 𝜀𝜀-𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
Send 𝐿𝐿𝑖𝑖
to 𝜀𝜀-𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Calculate a
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐 for 𝐿𝐿𝑖𝑖
For each particle Initialize
OMOPSO and LIF parameters
Update position (Fly) Initialize
particles and 𝐿𝐿𝑖𝑖
Evaluate particles into LIF
True
Apply mutation operators Update
𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 Update
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐 for 𝐿𝐿𝑖𝑖
Send 𝐿𝐿𝑖𝑖
to 𝜀𝜀-𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Update 𝐿𝐿𝑖𝑖
False Reports
results in 𝜀𝜀-𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
False
End
𝑐𝑐 𝑐𝑐𝑚𝑚𝑚𝑚𝑚𝑚 True
Fig. 2. Methodology schema
After it is initialized an Internal Loop into an Exter- nal Loop, and each particle is modified into the Internal Loop, updating the position and applying the mutation operators. Then, each particle is evaluated and updated its personal best value (pbest). A new particle replaces the pbest if such value is dominated by the new particle or if both are non-dominated concerning each other.
When all particles have been updated, the Li are modified in the External Loop. Only the particles that overcome their pbest will try to enter to Li set. Once the Li have been updated, they are sent to e-file. Finally, the crowding values of the set of Li is updated and we eliminate as many leaders as necessary to avoid over- flow of the size of the Li set. The process is repeated until finalizing all iterations.
3.1. Objective Functions
Three different objective functions were consid- ered to measure the performance of the solutions (particles):
A. The Euclidean distance between the combina- tion of AFRi and AFRj, where AFR is the average firing rate of each class and i ≠ j. For this objective function, we looking for maximize the separability between the classes:
MAXdist AFR AFR
(
i, j)
(4) B. The Standard Deviation of the firing rate for each pattern class SDFRk, where k = 1, ..., K and K is the total of pattern classes. In this objective function, we looking for minimize the dispersion of each pattern class:MIN SDFR
(
k)
(5)C. The dimension of the input feature vector ( )x . To avoid redundancies in information, we desire to reduce the dimensionality of the feature vectors, by minimizing the total of 1's of a binary mask a bina- ry mask ( )r with the same size of the input feature vector.
In our proposal, the number of objective functions is related to the number of classes of the dataset.
3.2. Experiments
Four supervised classification datasets from the UCI Machine Learning Repository [18] were em- ployed for experimentation: Iris Plant, Wine, Glass, and SPECT. Table 1 shows the details of the datasets used.
Each dataset was randomly divided in two subsets with approximately the same size. The first one was employed as training set and the second one as test- ing set.
Tab. 1. Datasets employed for experimentation
Dataset Instances Classes Features
Iris Plant 150 3 4
Wine 178 3 13
Glass 214 6 9
SPECT 267 2 22
With the aim to observe the performance of our proposal, four experiments were configurated ac- cording to the objective functions seen in section 3.1.
The characteristics of each experiment are defined below and summarized in Table 2.
i. Experiment #1 was defined as a multi-objective problem, focusing on the A and B objective functions. The OMOPSO algorithm was used to optimize the synaptic weight vector of the LIF neuron.
ii. Experiment #2 employs the multi-objective approach, considering the A, B and C objective functions. The OMOPSO algorithm was taken to optimize the synaptic weight vector and the dimension of the input vector. Concerning the optimization of the last parameter, a binary mask ( )r was used in equation (3) to calculate a modified input current given by equation (6).
I x w r= ⋅ ⋅ ⋅θ (6) iii. Experiment #3 was designed as a mono-objective
problem. The objective function (eq. 7) was formed by the weighted sum of two objective functions.
The first one is the inverse of the summation of the Euclidean distances among all combinations of AFRi and AFRj and the second objective is the sum of the standard deviation of the firing rate for all classes as shown in equation 7 [11]. PSO algorithm was used to design the synaptic weight vectors.
MIN f
dist SDFR
k K
( )
=(
1)
+∑
= kAFR 1 (7)
iv. Experiment #4 is a mono-objective approach that seeks to optimize the synaptic weight vector and the dimension of the input vector with the PSO algorithm. The objective function (eq. 8) is formed by the weighted sum of the equation (7) and the rate of T and D, where T is total of 1's in the binary mask ( )r and D is the dimension of the input feature vector.
MIN f
dist AFR SDFR
k K
( )
=(
1)
+∑
= k+ 1T
D (8)
Tab. 2. Configuration for experimentation
Algorithm Optimized Parameters Objective Functions Exp
#1 OMOPSO synaptic weight
vector A, B
Exp
#2 OMOPSO synaptic weight vector and dimension of
input vectors
A, B, C
Exp
#3 PSO synaptic weight
vector A, B
Exp
#4 PSO synaptic weight
vector and dimension of input vectors
A, B, C
Table 3 shows a compendium of the number of ob- jective functions by experiment for each dataset.
Tab. 3. Total of Objective Functions by experiment
Objective Functions in Dataset Classes Exp #1 Exp #2 Exp #3 Exp #4
Iris Plant 3 6 7 1 1
Wine 3 6 7 1 1
Glass 6 21 22 1 1
SPECT 2 3 4 1 1
Each experiment consisted of 40 independently executions per each dataset to guarantee statistical significance. The parameter values used in the OMOP- SO algorithm and the LIF neuron model [11] are de- tailed in Table 4 and 5 respectively.
The initial synaptic weights were generated ran- domly θ ∈ [0,1].
4. Results and Statistical Analysis
This section describes the results obtained from the experimentation proposed in section 3. The re- sults are statistically analyzed and discussed below.
Tab. 4. Configuration OMOPSO Parameters
Max particle size: 100
Max iterations: 1000
e-file size: 100
Uniform Mutation
Mutation probability:
1 0. Number of problem variables
Perturbation index: 0.5
Non-uniform Mutation
Mutation probability:
1 0. Number of problem variables
Perturbation index: 0.5
Max iterations: 1000
Tab. 5. Configuration LIF Parameters
a 0.5
b -0.001
c -50 mV
vi -60 mV
vthreshold 50 mV
Time 1000 ms
h 1
θ 0.1
For each execution, at the end of the training phase, the total of particles is evaluated in the LIF neuron model using the training set, and the classification ac- curacy is calculated for each particle. Finally, the par- ticle with the best performance is used in the testing phase for obtaining the accuracy in the testing set.
Tab. 6. Accuracy of training phase over each experiment
OMOPSO PSO
Experiments Experiments
Dataset #1 #2 #3 #4
Iris Plant
0.9817
± 0.0131
0.9793
± 0.0157
0.9
± 0.0232
0.8987 ± 0.0219
Wine
0.7858
± 0.0358
0.8048
± 0.0336
0.6849
± 0.0432
0.6986
± 0.0301
Glass
0.5050
± 0.0441
0.5031
± 0.0405
0.39±
0.0030
0.3638 ± 0.0726
SPECT
0.8592
± 0.0243
0.8286
± 0.0227
0.7276
± 0.0325
0.7273 ± 0.0344
Tables 6 and 7 show the results obtained from the methodology proposed. The accuracy values along with the standard deviations grade the performance of the experiments. The accuracy of the training phase corresponds to the average of the performance of the
