Logical Combinatorial Pattern Recognition

122
J.R. Shulcloper, "Logical Combinatorial Pattern Recognition," Foro Iberoamericano de Reconocimiento de Patrones, pp. 123-138, Barcelona,
Spain, September 2000.
Logical Combinatorial Pattern Recognition
José Ruiz-Shulcloper
IRIS Lab. Electrical and Computer Engineering Department, The University of
Tennessee, Knoxville, USA.
[email protected]
Laboratory of Pattern Recognition, Institute of Cybernetics, Mathematics and Physics,
Havana, Cuba.
[email protected]
Abstract. In this paper we summarize the main results obtained
by the Logical Combinatorial Pattern Recognition (LCPR)
Group. The characteristic features of our approach and the
relationship with the other approaches to Pattern Recognition
(PR) are explained in a framework of a unique science. This
approach was introduced originally in the Soviet Union under
the orientation of the Academic Yuri Ivanovich Zhuravlev from
the Computer Center of the Russian Academy of Sciences.
1. INTRODUCTION
In our point of view, PR is a science with a strong interdisciplinary and applied
character. Dealing with engineering, mathematical and computer processes over physics
(photos; holograms; handwritings; hieroglyphics; symbols; bioelectrical signals;
acoustic signals; etc.) and/or abstract objects (n-tuples of a certain Cartesian product of
sets of several kinds: hard, fuzzy, rough,...) with the purpose (by computer devices
and/or humans) to obtain the information that allows the establishment of properties
and/or relationships of certain subsets or between subsets of the universe of objects.
Based on this, we show in Table 1 a schema of scope of the PR problem. It is not in any
case exhaustive. With this schema we want to underline that PR is an interdisciplinary
science, that it has strong connections with mathematics, engineering and computer
sciences. Also we want to illustrate the relationship between its component parts and its
relative position with respect to those disciplines. Almost all the researches in this field
are applied researches or at least with a big concern with the applications of its results.
That is, PR is essentially an applied science. Nevertheless, that does not mean that there
are not fundamental researches in this field. Perhaps is the time to remember, a
statement by K. Levin “Rien n’est aussi practique qu’une bonne theorie”.
Historically PR had being fractioned in small parts, showed in the schema, which we
believe that is important do not consider as non-communicated areas. We think that we
have an extensive area of researches and this area will increase while more
interconnections we can to establish between all of those component parts.
As we know there are two main forms of representation of objects in the framework of
PR: in terms of certain alphabet of primitive parts of the objects, typical of the syntactic
or structural approach; or in terms of certain set of features (variables), in an indirect
way, typical of statistical and the rest of the approaches to PR. In order to explain what
LCPR means, from here on we assume the latter approach to the representation for
objects.
The representation of objects usually is considered as a sequence of numerical or
exclusively categorical values. Nevertheless, when we actually analyze the real world
PR problems (feature selection, supervised or unsupervised classification problems), we
found that in many cases it is not true that the description of objects taking into account
for the specialists of these areas of knowledge is a flat description in terms of
exclusively numerical or categorical features.
TABLE 1. - Component schema of PR
Mathematics
Engineering
Computer
Mathematics
Image Processing
Signal Processing
Image Analysis and Understanding
Signal Analysis and Understanding
Computer Vision
Remote Sense
Neural Networks for PR
Genetic Algorithms for PR
Artificial Intelligence Techniques for PR
Mathematical Morphology
Statistical PR
Syntactical PR
Logical Combinatorial PR
There are many problems in which the description of the objects is non-classical, that is,
in terms of not exclusively numerical or categorical features, but simultaneously appear
both kinds of values feature and also, sometimes, it is necessary to employ a special
symbol to denote the absence of values (missing values). That is, we could be dealing
with mixed incomplete description of objects. In other words, we are talking about the
process of certain amount of mixed incomplete data.
Why and where was born the logical combinatorial approach to PR?
PR problems with mixed incomplete description of objects frequently appear in Soft
Sciences. For example: the description of geological zones for the establishment of
some prognosis about mineral resources [1, 4]. For many practical problems
geophysicists need to take into account not only measures like magnetic fields,
gravimetric anomaly of Bouguer, intensity of the air magnetic field, an other numerical
variables, but also features like a genetic series of soil, the presence or absence of faults,
level of development of the soil, and others. You can say: well, let us to process all
categorical features and make one decision, then process all numerical variables and
make a second one. Finally, you can arrive at a conclusion over the partial decisions
made before. That is, as any problem of collective decision-making. But the problem is,
as you can see obviously, that non-categorical variable is analyzed together some
numerical variable. For the geophysicists this is a big problem. It is not possible to take
a based solution in these conditions.
Other interesting example appears in Medicine. The knowledge representation in
general, but in particular medical knowledge involved in the process of medical
diagnosis or prognosis of health is a non-trivial problem because of its inherent
subjectivity [5-13]. Normally, a physician evaluates signs and symptoms in the patient
to establish a preventive diagnosis or prognosis of health. Signs are usually numbers.
For example temperature, blood pressure, age, number of children, and so on. But there
are signs that you cannot put in correspondence with a number, but with a code. For
example: pallor, sweating, trembling, and others. Obviously, symptoms are subjective.
What the patient is feeling depends on the person; nevertheless these are very important
data for the physician. It is not too difficult to see the same problem as described above
in the case of Geosciences.
In both of these cases objects (zones, patients or diseases) are just n-ary tuples, elements
of simple Cartesian product without any algebraic, logical or topological properties
assumed on this space. How then, do we select in these cases the most informative
features, classify a new object given a (training) sample of each classes of the problem
or find the relationships between all objects based on a certain measure of similarity?
This is the main problem resolved by LCPR. This approach is a necessary
methodological answer to the fact that in many feature selection and classification
problems, which frequently appear in Soft Sciences, the descriptions of objects are
mixed and incomplete data.
We said that this approach originated in the Soviet Union, with the publication of [see 8
Other references O1] in 1966. The principal task of above paper was to find a solution
to a real problem: the prognosis of mineral resources. For the solution of this problem it
was necessary to take into account, not only the geophysical measure of different
phenomena, but also the type of soil, the present or absence of faults, and other features,
which have only a qualitative character. Actually, in the mentioned paper the authors
consider that all of the features are Boolean and the problem was solved in a qualitative
framework in a very simple way. Later were appearing other works in which was
considered features of different kinds of nature, not only Boolean and not only
qualitative features [14-21]. Any way, it is important to underline that this approach
originated because the practical necessity to modeling real problems in a more adequate
form.
Two important reviews through selected works related on LCPR you can find in
[22,23]. The first textbook in this matter was appearing in Mexico last year [24].
2. COMPOSITION
In this moment 5 persons with the following qualification are in the official staff of our
Group: Dr. José Ruiz-Shulcloper (leader); Dr. Manuel Lazo-Cortés; Dr. Eduardo AlbaCabrera; MS. Ramón Pico-Peña; MS. Ignacio Sánchez-Gutierrez. There are also other
professors and researchers working for other universities and researches centers, in
Cuba and in Mexico, which participate in almost all researches of the Group: MS.
Aurora Pons-Porrata; MS. Fernando Vázquez-Mesa; MS. Damaris Pascual-González;
MS. Roxana Danger-Mercaderes; MS. Aimé Alvarez-Roca at the Oriente University,
Cuba; Dr. Martha R. Ortiz-Posada at the Metropolitan Autonomy University, Mexico;
MS. José F. Martínez-Trinidad; MS. Jesús A. Carrasco-Ochoa; MS. Guillermo SánchezDíaz at the Computer Researches Center, IPN, Mexico; MS. Verónica Jiménez-Jacinto;
Lic. Saturnino J. Morales-Escobar; María E. Guevara-Cruz at the Technological
University of Mexico. Cuban and Mexican undergraduate and postgraduate students are
working too in this area. It is necessary underline that our group has a useful professor
and researcher interchange with several universities and researches centers in Cuba,
Mexico, Portugal, Spain and USA. These relationships allow making more efficient our
scientific work.
3. TEMATICS OF WORK
Starting from the concepts of mixed incomplete data and similarity function our Group
had aboard all related classification and recognition problems. In feature selection
problems the principal tool employed was Testor Theory. This is a branch of
Mathematical Logic that began in the Soviet Union at the end of the 50’s. I. A. Cheguis
and S. V. Yablonskii [O2] were the first researchers that developed this theory. Their
works were motivated by the problem of fault detection in logical schemes, particularly
applied to computer logical circuits. To find a fault in complicated logical circuits is a
very hard task; hence, the natural idea of attempting to simplify this. In the mentioned
paper, authors considered a table of Boolean functions with n Boolean variables. These
functions model all possible faults of a circuit: each function describes the behavior of
the circuit when a certain fault occurs. Values of function arguments are interpreted as
circuit states, and the values the function takes as the circuit response to the states.
For Cheguis and Yablonskii, a testor is a collection of values of arguments (function
inputs), such that, the respective responses (function outputs) for any pair of functions
are different pair wise. In other words a testor is a set of circuit states that allows
identifying the registered fault among all possible faults. The smaller the size of this set,
the more useful the testor is.
In the middle of the 60’s, Y. I. Zhuravlev adapted the testor concept to PR [O1]. It is
worth mentioning that although a fault detection problem can be interpreted as a PR
problem, Yablonskii did not do so.
Suppose that a given training sample, in a framework of a supervised classification
problem, has a (training) matrix representation MI, that is, object descriptions are stored
in a matrix with as many columns as features, as many rows as objects in the sample,
and they are split in groups corresponding with their respective classes. If the complete
set of features R allows us to distinguish between objects (rows of MI) from different
classes, then R is a testor. Furthermore, any non-empty feature subset of R, that satisfies
this property, is a testor (in the Zhuravlev’s way). From the set of all testors of a matrix
MI, there are some testors, which are irreducible. That is: if any feature is eliminated
from them, then they stop being testors. That means, they confuse objects belonging to
different classes. These testors we are called typical testors.
Initially Zhuravlev, in order to simplify, supposed that MI had objects of only 2 disjoint
classes, and features are Boolean, but of course all this is valid for more than two
classes and the extension to non-Boolean feature is not difficult. Obviously, although
the capability for modeling in a more adequate form increases in this last case, also the
complexity of algorithms increase with non-Boolean features.
We can emphasize that, besides Zhuravlev’s concept (and the natural extension
previously exposed), in literature there are many other different testor concepts [O3, O4,
25-37-12]. These concepts were introduced taking into account different characteristics
of real problems, which often appear in soft sciences (fuzzy classes, comparison criteria
of similarity and dissimilarity simultaneously, real comparison criteria, similarity
function different than feature wise total coincidence, etc). These extensions have the
pretension to reach a more adequate model of the reality and this allows reaching better
practical results. Our Group introduced many of these new concepts.
In this field there are three principal tasks: adequate testor concept for the real world
problems; efficient algorithms for the calculus of all typical (also other kinds) testor and
the study of sensitivity of the set of typical testor in presence of changes in the training
matrix; and all of them because the introduction of these concepts and tools in real
world problems. Our Group has worked in all of these problems and has obtained a
body of new results in each one.
As it was mentioned before, different concepts of testor were introduced in order to give
a better answer to different real world situations. Several algorithms for the calculate all
typical testors [38-47] were implemented and employed in the resolution of real
problems like the determination of the influence of the certain social-economic features
in the analysis of young delinquency [14] or the informational weight of the geological
and geophysical characteristics in the Gasopetroliferous forecast in Cuban ophiolitic
association [4], the relevance of symptoms and signs in the evaluation of patients with
clefts of the lip and palate [6,9,10,12], and others applications in Geosciences
[2,4,48,49] or Medicine [13,50] and others [51,52]. The problem of the way to
determinate the relevance of features and objects also was studied by the Group and
interesting results you can find in [43,53-55].
In supervised classification problems the Group has been developed so called partial
precedence algorithms. This is a series of families of parametric algorithms based on
the partial precedence principle meaning that physicians, and other natural scientists on
the base of partial similarities of the objects establish the similarity object wise in real
world problems. An important characteristic of these algorithms is the assumption that
the representation space of objects has not any algebraical, topological or logical
structure. That is, they are only Cartesian products. These families were born in Soviet
Union [O1,O5,O6] and our Group continues their development. As our philosophy is to
make the mathematical and computer tools needed by the practical problems, we
developed several new extensions of these families of partial precedence algorithms
[10,21,56-59].
The classical voting algorithm introduced by Zhuravlev was extended to different real
world situations and were introduced new similarity functions as well as fuzzy set
theory concepts in order to adequately model problems in Geosciences. Our Group
developed other two families of partial precedence algorithms.
The KORA-Ω algorithm [57] is an extension of the known old and very used in
Geosciences algorithm KORA-3 [O5]. This algorithm, was introduced by Bongard in
1963, was devised for the solution of supervised classification problems in Geosciences.
It works with two disjoint classes and objects described in terms of Boolean variables
without missing values. The underlying idea in the initial method is to classify new
objects based on a training sample of objects through the verification of fulfillment of
some complex properties. These properties are a set of three values (complex feature)
corresponding to three features, which appear often enough in one of the classes and do
not appear enough in the other one [O7]. Fuzzy KORA-Ω allows us to solve supervised
classification problems with many classes (hard −disjoint or not− or fuzzy), with any
kind of features and different types of similarity measures. In this model, complex
properties could be of any length grater or equal than one. These complex properties
could be of different representation levels.
Also we developed CR+ algorithm. It is a family of algorithms employing the concept
of representative set. This idea was introduced by Baskakova and Zhuravlev [O6],
based on the concept of partial precedence, they introduced the idea of rating
information in favor of (positive representative set) and against (negative representative
set) the ownership of the objects to the classes, as well as, considering that the
parameters used for the classification should be associated to each class. We extended
the model introducing a more general concept of representative set, which could be
applied in conditions less restrictive, but that conserves like a particular case the original
concept. Also we did some modifications to the algorithm in order to incorporate the
new conditions and concepts, especially the case in which the classes are fuzzy sets,
whereby we introduce a function, in this case lineal, for assigning belongings to new
objects from the total evidence in favor of and against the ownership of the object to the
class.
In both last families we also developed several heuristics for the efficient estimation of
some of parameters of each one, like support sets, similarity thresholds, informational
weights of objects and features among others. All these algorithms were employed in
several real practical researches in Medicine, Geosciences and others soft sciences
[2,4,6,7,10,48-51].
Our Group also using both the partial precedence principle and Cartesian product
representation space assumptions has faced the unsupervised classification problems.
The results in this area are distributed in free unsupervised classification problems, [6064] restricted unsupervised classification problems [65,66], and conceptual clustering
problems [67-72]. In each of these three areas we have been worked in the development
of new concepts, which better allow modeling real world situations; algorithms, which
realizes these new ideas and allow the introduction of them in the practice; and
sensitivity problems, which improve the computational behavior in problems with
changes on the initial information.
In free clustering problems, we most employ clustering criteria as β 0-connected
components, β 0-compact sets, β0-strictly compact sets; and β0-complete maximal sets.
We found the set theoretical relationship between all of these criteria, both in hard and
fuzzy cases. These relationships allow making a better analysis of different data sets in
real problems. Also were developed efficient algorithms for calculating all clusters in
each of criteria mentioned above.
In restricted clustering problems in the framework of LCPR were obtained some
interesting results like an extension of the c-means algorithm for the case of mixed
incomplete data and non-necessarily-distance functions and a series of theorems that
estimate all connected components of the sample.
The conceptual clustering problems introduced by Michalski and his followers, was
aboard since semantic analysis to the development of fuzzy conceptual tools for the
solution of these problems. Connected very hardly with these problems our Group has
continued also in the line of symbolic object theory introduced by Diday. In this last
one, were obtained as new formulations of the concept of symbolic objects as new
algorithms allow us the structuralization of conceptual spaces [73,74].
An important improve in these areas was the introduction of the Fuzzy Set Theory. All
of above-mentioned PR problems were aboard also in fuzzy cases. That is, given the
assumption that the classes were fuzzy sets, or among the feature sets there were some
fuzzy or linguistic variables, or among the similarity comparison criteria of features
were some real functions; and others situations carried on to fuzzy modeling as one of
the best way for object, feature and its relationship representations. In all these cases
were introduced new concepts, and algorithms [75-80].
An important practical problem is created when, in feature selection or any
classification problems, there appear modifications on the initial data set. This fact
could change a solution obtained earlier. In many cases the cost of the re-calculation of
these results is very high and have sense to find heuristics allow obtaining new results to
these problems. This is called sensitivity PR problem. In this sense our Group had
obtained some hopefully results. Actually in this area there are many hard problems yet
not resolved.
As we mentioned above, our objective is to develop mathematical and computer tools
for resolution of real world problems, especially but not exclusively in soft science
areas. Hence, we developed several systems, and software libraries allow introducing
these mathematical tools [3,24,36,38-55,57,60-65,67,69,73,7481-84]. Among of these
programs PROGNOSIS (a Institute of Cybernetics, Mathematics and Physics product)
for the solution of problems in Geosciences and more recently CLASITEX+ (a
Software Pro International product) for the discovering of main theme in textual
documents, are two of the relevant systems in which our group had participated.
Recently the Group starts to aboard the problem of enlargement of amount of data also
in the framework of LCPR assumptions. Hence, were enfaced two related problems:
Data Mining and Data Fusion. That is, we star to develop the called Mixed Incomplete
Data Mining, and Mixed Incomplete Data Fusion as a logical consequence of the
development of the LCPR theory. In the first case were obtained three new clustering
algorithms [81-83] allow dealing with large and very large mixed incomplete data set.
Also some primary results were obtained in Text Mining [84]. At present we are stating
the theoretical bases of the fusion of mixed data hardly connected with the researches of
IRIS Laboratory of Dr. Abidi, the combining classifiers problems developed by Dr.
Kittler, and the schemas for collective decision problems developed by Dr. Kuntcheva.
In the following figure it is shown the relationships between these areas that look like
different appearances, but we think they are a whole consistent entity. In some sense it
show also the future researches, which will be developed by our Group.
PATTERN RECOGNITION
D
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T
A
F
U
S
I
O
N
Logical Combinatorial Pattern Recognition
P
R
A
Mixed Incomplete
Data Fusion
C
T
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Mixed Incomplete Data Mining
E
DATA MINING
4. PROJECTS
In this moment the Group is dealing basically with the following research projects:
Mathematical models and computer tools for the solution of PR problems appearing in
Soft Sciences.
Automatically classification of phyto-pathologic relevant microscopic mushroom based
on exploratory data analysis and advance image processing techniques.
Processing of huge amount of heterogeneous information: Mixed Incomplete Data
Mining
5. FINANCES
Our projects are financed through Science and Technical Agency, which belongs to
Science and Technical Ministry.
6. MORE RELEVANT PAPERS
1. E.N. Cheremesina; José Ruiz-Shulcloper. Cuestiones metodológicas de la
aplicación de modelos matemáticos de Reconocimiento de Patrones en zonas del
conocimiento poco formalizadas. Revista Ciencias Matemáticas, vol. 13; No.2; pp.
93-108, Cuba, (1992).
2. César Alaminos, José‚ Ruiz Shulcloper, Ramón Pico y otros. Aplicación de los
Modelos de Reconocimiento de Patrones Lógico-Combinatorios a la resolución de
tareas geológicas. Memorias de GEOLOGIA'89.
3. José Ruiz-Shulcloper, R. Pico Peña et al. PROGNOSIS y sus aplicaciones a las
Geociencias, Revista Ciencias Matemáticas, Vol. 14, No. 2-3, 1993. pp. 124-144.
Also in: III Congreso Iberoamericano de Inteligencia Artificial. IBERAMIA'92
Proceedings Ed. Limusa, México. pp. 561-586, (1992).
4. Julio Gómez-Herrera; Rodríguez Morán,O.; Valladares Amaro, S.; Ruiz
Shulcloper,J.; Pico Peña, R. y otros. Prognostic of Gas-oil deposits in the Cuban
ophiological association, applying mathematical modeling. Geophysics International
33, 3, pp. 447-467 (1995).
5. Martha R. Ortiz Posadas, José Francisco Martínez-Trinidad, José Ruiz-Shulcloper.
A new approach to differential diagnosis of diseases, International Journal of Biomedical Computing, 40, pp. 179-185 (1996).
6. Martha R. Ortiz Posadas, y M. Lazo Cortés, Evaluación de la rehabilitación de
pacientes con fisuras de paladar utilizando técnicas de reconocimiento de patrones, II
Taller Iberoamericano de Reconocimiento de Patrones. Conferencia Internacional
CIMAF'97. La Habana. Memorias (ISBN 968-29-9892-1), pp. 231-236, 1997.
7. Martha R. Ortiz Posadas, J. Maya Behart y M. Lazo Cortés. Evaluación de la
cirugía de labio y paladar hendido con el enfoque lógico combinatorio de la teoría de
reconocimiento de patrones. Revista Brasileira de Bioengenharia. Caderno de
Engenharia Biomedica, v. 14, n. 1, pp. 7-22, (1998).
8. Martha R. Ortiz Posadas, L. Vega Alvarado, V. Jiménez Jacinto y M. Lazo Cortés.
El concepto de analogía en medicina. Una función de semejanza para pacientes con
fisura de paladar. III Taller Iberoamericano de Reconocimiento de Patrones.
México. Memorias (ISBN 970-18-1081-3), pp. 247-256, 1998.
9. Martha R. Ortiz Posadas, L. Vega Alvarado, V. Jiménez Jacinto y M. Lazo Cortés.
Una herramienta para evaluar la calidad del servicio que ofrece una clínica
multidisciplinaria de labio-paladar hendido. I Congreso Latinoamericano de
Ingeniería Biomédica. Mazatlán, México. pp. 796-799, (1998).
10. Martha R. Ortiz Posadas, L. Vega Alvarado, V. Jiménez Jacinto, M. Lazo Cortés y
J. Maya Behart. Pronóstico de la rehabilitación de pacientes con fisuras de paladar
usando un algoritmo de precedencia parcial. IV Simposio Iberoamericano de
Reconocimiento de Patrones. Conferencia Internacional CIMAF’99. La Habana.
Memorias (ISBN 970-18-2386-9), pp. 411-418, (1999).
11. Martha R. Ortiz-Posadas. Elaboration and application of a new pattern recognition
methodology in Medicine. Ph. D. Thesis, Universidad Autónoma Metropolitana,
Iztapalapa Campus, Mexico City (1999).
12. Martha R. Ortiz-Posadas. Prognosis and evaluation of cleft palate patients
rehabilitation using pattern recognition techniques. World congress on medical
physiscs and Biomedical Engineering 35, 1, 500. Niza, France (1997).
13. Rafael Sánchez Aroche and M. Lazo Cortés. Automatic auditory brainstem response
(ABR) classification using the Convex method for an optimal feature set. International
Journal of Medical Informatics (accepted)
14. José Ruiz Shulcloper y Alberto Fuentes. Un modelo cibernético para el análisis de
la delincuencia juvenil. Revista Ciencias Matemáticas Vol. II(1) pp.141-153. (1981).
Cuba
15. José Ruiz Shulcloper y Orlando Olivera. Algunas perspectivas de la aplicación de
los modelos matemáticos al desarrollo del deporte en Cuba. Revista Control,
Cibernética y Automatización, año XVI(1), enero-marzo pp. 3-7. Cuba. (1982).
16. José Ruiz Shulcloper. Elaboración de la información Biomédica por medio de
modelos de reconocimiento de patrones. Revista Control, Cibernética y
Automatización, año XVI(4), octubre-diciembre pp. 13-21. Cuba. (1982).
17. José Ruiz Shulcloper. Posibilidades del Reconocimiento de Patrones en el
diagnóstico de enfermedades. Revista Control, Cibernética y Automatización, año
XVI(1), enero-marzo pp. 10-13. Cuba. (1982).
18. Alberto Fuentes, José Ruiz Shulcloper y Luis Romero. Algoritmos de clasificación
basados en el peso de los patrones. Revista Ciencias Matemáticas Vol. IV(1) pp.97121. Cuba. (1983).
19. José Ruiz Shulcloper. Problemas de clasificación de objetos y selección de
variables en medios difusos: tres proyectos de tesis. Revista del Seminario de
Enseñanza y Titulación. Año IV No. 21 pp. 41-68. México. (1988).
20. José Ruiz Shulcloper. Problemas actuales en la Teoría Matemática de
Reconocimiento de Patrones. Memorias del Simposium Internacional de
Computación, November 9-11, pp 1-42. México.(1994).
21. José Ruiz-Shucloper. Some questions about Pattern Recognition problems with nondisjoint classes. Editorial Academia, 1-32. (In Spanish). (1995).
22. José Francisco Martínez-Trinidad, Adolfo Guzmán-Arenas. The logical
combinatorial approach to Pattern Recognition, an overview through selected works.
(Accepted to Pattern Recognition).
23. Manuel Lazo-Cortés, José Ruiz-Shulcloper, Eduardo Alba-Cabrera. An overview of
the evolution of the concept of testor in pattern recognition. (Accepted to Pattern
Recognition).
24. José Ruiz-Shulcloper, A. Guzman-Arenas, and J. F. Martínez-Trinidad. Logical
Combinatorial Approach to Pattern Recognition: I. Feature selection and supervised
classification. Editorial Politécnica, Mexico (1999). Also will appear in the Editorial
Fondo de Cultura Económica, Mexico, 150 pp. In Spanish. (2000).
25. José Ruiz-Shulcloper, M. Lazo Cortés. K-testores primos. Revista Ciencias
Técnicas, Físicas y Matemáticas. (Cuba), vol. 9, pp. 17-55, (1991).
26. Manuel Lazo Cortés, and J. Ruiz Shulcloper. Determining the Feature Relevance in
a Pattern Recognition Problem in Fuzzy Environments. Second European Congress on
Intelligent Techniques and Soft Computing. EUFIT 94. Aachen, Germany.
Proceedings, vol. 1, pp. 221-226, (1994).
27. Manuel Lazo Cortés. Una generalización del concepto de testor. Aportaciones
Matemáticas. Serie Comunicaciones (IMATE-UNAM. México), No.14, pp. 283-288,
(1994).
28. José Ruiz Shulcloper, Eduardo Alba Cabrera, et. al. Tópicos acerca de la Teoría de
Testores. Serie Amarilla No 134 (investigaciones), pp. 1-6, CINVESTAV - IPN.
México. (1994).
29. Eduardo Alba Cabrera, Nancy López Reyes, José Ruiz Shulcloper. Extensión del
concepto de testor típico a partir de la función de analogía entre patrones. Algoritmos
para su cálculo. Serie Amarilla No 134 (investigaciones), pp. 7-28, CINVESTAV IPN. México. (1994).
30. Manuel Lazo Cortés. Testores generalizados. Revista Integración. Vol. 14, No. 1,
pp. 31-47, Colombia, (1996).
31. Eduardo Alba Cabrera. Un concepto de testor para cualquier función de analogía
con imagen en un conjunto ordenado totalmente. Revista Integración, Vol. 14, No. 2,
pp. 75-82, UIS, Colombia, (1996).
32. Salvador Godoy Calderón, Manuel Lazo Cortés. ∆-testores. A generalization of the
concept of testor in fuzzy environments. Proceedings of the Second Iberoamerican
Workshop on Pattern Recognition, March 24-28, Havana, Ed. IPN, México, pp. 95103, (In Spanish). (1997).
33. Manuel Lazo Cortés y J. Ruiz Shulcloper. Extensiones Difusas del Concepto de
Testor. I Taller Iberoamericano de Reconocimiento de Patrones. Conferencia
Internacional CIMAF'95. La Habana, 1995. Memorias, edit. Instituto Tecnológico de
Toluca. México. pp. 181-193, (1997).
34. Eduardo Alba Cabrera, Manuel Lazo Cortés. Nueva generalización del concepto de
testor para clases difusas. Resúmenes del III Taller Iberoamericano de
Reconocimiento de Patrones. México, D.F., pp. 237-246, Ed. IPN-México. (1998).
35. Eduardo Alba Cabrera, Manuel Lazo Cortés. Una solución global para la
utilización de los testores en problemas de Reconocimiento de Patrones. Resúmenes
del III Taller Iberoamericano de Reconocimiento de Patrones. México, D.F., pp.
209-218, Ed. IPN-México. (1998).
36. Manuel Lazo-Cortes, Mercedes Douglas de la Peña, Teresita Quintana Gómez.
Testor by class: an application to character recognition. III Taller Iberoamericano de
Reconocimiento de Patrones. México. Memorias (ISBN 970-18-1081-3), pp. 229-236,
(1998).
37. Manuel Lazo Cortés y M. Douglas de la Peña. Extensiones del concepto de testor
por clase. IV Simposio Iberoamericano de Reconocimiento de Patrones.
Conferencia Internacional CIMAF’99. La Habana. Memorias (ISBN 970-18-2386-9),
pp. 209-218, (1999).
38. José Ruiz Shulcloper, Luis Aguila y Adrián Bravo. Algoritmos para el tratamiento
automático de la información relativa a la descripción y clasificación de objetos y
fenómenos. Revista Ciencias Físico-Técnicas y Matemáticas, No.2, pp. 139-149.
(1983).
39. José Ruiz Shulcloper, Luis Aguila y Adrián Bravo. Algoritmo BT y TB para el
cálculo de todos los test típicos. Revista Ciencias Matemáticas Vol. VI(2) pp.11-18.
(1985).
40. José Ruiz-Shulcloper; Pico Peña, R. SELECTOR:sistema herramienta de selección
de variables y objetos. Proceeding INFORMATICA'90, 19-25/2/1990. ICIMAF, pp
86-95. Editorial Academia. Cuba. (1992).
41. Manuel Lazo Cortés y E. E. Barreto Fiu. Testores difusos. Un algoritmo para
determinar los testores difusos típicos de una matriz de aprendizaje. Reporte Técnico
del CINVESTAV-IPN. Serie Amarilla No.134 pp. 29-42. México. (1994).
42. Manuel Lazo Cortés y E. E. Barreto Fiu, Algoritmo TDT para el cálculo de los
testores difusos típicos de una matriz de aprendizaje, Reporte Técnico del
CINVESTAV-IPN. Serie Amarilla No.134 pp. 43-51. México. (1994).
43. Manuel Lazo Cortés and J. Ruiz Shulcloper. Determining the feature relevance for
non-classically described objects and a new algorithm to compute typical fuzzy testors.
Pattern Recognition Letters 16 1259-1265, (1995).
44. Eduardo Alba Cabrera. Cálculo de todos los testores típicos para matrices kvalentes y función de semejanza de un umbral lε. Resúmenes del I Taller
Iberoamericano de Reconocimiento de Patrones. La Habana Cuba, pp. 155-169, Ed.
Tec. de Toluca, México., (1995).
45. Mario Farías Elinos, P. Rayón Villela y M. Lazo Cortés. Programación paralela de
un algoritmo para el cálculo de testores con PVM. II Taller Iberoamericano de
Reconocimiento de Patrones. Conferencia Internacional CIMAF'97. La Habana.
Memorias (ISBN 968-29-9892-1), pp. 149-156, (1997).
46. Guillermo Sánchez Díaz, M. Lazo Cortés y J. García Fernández. Modelos
algorítmicos paralelos y distribuidos para el cálculo de testores típicos. II Taller
Iberoamericano de Reconocimiento de Patrones. Conferencia Internacional
CIMAF'97. La HabanaMemorias (ISBN 968-29-9892-1), pp. 135-140, (1997).
47. Guillermo Sánchez Díaz, M. Lazo Cortés y O. Fuentes Chávez. Algoritmo genético
para calcular testores típicos de costo mínimo. IV Simposio Iberoamericano de
Reconocimiento de Patrones. La Habana. Memorias (ISBN 970-18-2386-9), pp. 207213, (1999).
48. José Ruiz-Shulcloper; Pico Peña, R. et al. Modelación Matemática del pronóstico de
magnitudes máximas sísmicas de los terremotos en la Región del Caribe. In
Reconocimiento de elementos de estructuras espaciales. pp. 81-101. Editorial
Academia. Cuba. (1992).
49. José Ruiz-Shulcloper; Pico Peña, R.; Alaminos Ibarría, C.; Manchado Martín, A. y
Valdés Hernández, Ma. G. Modelación matemática del problema de discriminación de
anomalías AGE perspectiva para rocas fosfóricas de génesis sedimentaria. Revista
Ciencias Matemáticas. Vol. 13, No. 2, (1993).
50. Sergio López Pérez, M. Lazo Cortés y H. M. Estrada García. Electrodiagnóstico
médico utilizando las herramientas de reconocimiento de patrones. II Taller
Iberoamericano de Reconocimiento de Patrones. Conferencia Internacional
CIMAF'97. La Habana. Memorias (ISBN 968-29-9892-1), pp. 237-244, (1997).
51. Ramón Pico Peña, G. Almagro, J. Mena. Aplicación de técnicas de Reconocimiento
de Patrones con enfoque lógico-combinatorio en la clasificación de un complejo de
géneros de hongos patógenos de la Caña de Azúcar. Memorias del III Taller
Iberoamericano de Reconocimiento de Patrones. México. Ed IPN, México. ISBN
970-18-1081-3. (1998).
52. Manuel Lazo-Cortes, Mercedes Douglas de la Peña, Teresita Quintana Gómez.
Testor by class: an application to character recognition. III Taller Iberoamericano de
Reconocimiento de Patrones. México. Memorias (ISBN 970-18-1081-3), pp. 229-236,
(1998).
53. Manuel Lazo Cortés y J. Ruiz Shulcloper. Evaluación de la relevancia de los
rasgos, a partir del concepto de testor, en problemas de clasificación. I Taller
Iberoamericano de Reconocimiento de Patrones. Conferencia Internacional
CIMAF'95. La Habana, 1995. Memorias, edit. Instituto Tecnológico de Toluca. México.
pp. 195-204, (1997).
54. Manuel Lazo Cortés, and J. Ruiz Shulcloper. Determining the Feature Relevance in
a Pattern Recognition Problem in Fuzzy Environments. Second European Congress on
Intelligent Techniques and Soft Computing. EUFIT 94. Aachen, Germany.
Proceedings, vol. 1, pp. 221-226, (1994).
55. Manuel Lazo Cortés, G. Sánchez Díaz y T. Quintana Gómez. Evaluación de la
relevancia de los rasgos en un problema de clasificación supervisada a partir de todos
los testores. IV Simposio Iberoamericano de Reconocimiento de Patrones.
Conferencia Internacional CIMAF’99. La Habana. Memorias (ISBN 970-18-2386-9),
pp. 215-222, (1999).
56. José Ruiz Shulcloper. Modelo de Algoritmos de Reconocimiento con Aprendizaje
Parcial. Memorias del III Congreso Iberoamericano de Inteligencia Artificial,
IBERAMIA’92. February 17-22, La Habana, Cuba pp. 541-559. Editorial Limusa,
México. (1992).
57. Jesús Ariel Carrasco Ochoa, José Ruiz-Shulcloper, Lucía de la Vega Doria. Fuzzy
KORA-Ω algorithm. Proceedings of the Sixth European Congress on Intelligent
Techniques and Soft Computing, EUFIT’98, pp.1190-1194, Aachen, Germany (1998).
58. José Ruiz-Shulcloper and M. Lazo-Cortés. Mathematical Algorithms for the
Supervised Classification Based on Fuzzy Partial Precedence. Mathematical and
Computer Modelling 29, 4, pp. 111-119 (1999).
59. José Ruiz-Shulcloper y M. Lazo Cortés. Herramientas para la clasificación
supervisada basadas en analogías parciales. Revista Mexicana de Ingeniería
Biomédica (ISSN 0188-9532) (México), vol. 16, No. 2, pp. 75-93, (1995).
60. José Fco. Martínez Trinidad, J. Ruiz Shulcloper y M. Lazo Cortés. Criterios
agrupacionales no clásicos para la estructuración de universos. Simposium
Internacional de Computación, México. Memorias (ISBN:968-29-9545-0). pp. 251270, (1996).
61. Leonardo Alvarez; Pico, R.; Cotilla,M. Clasificación no supervisada por métodos
lógico-combinatorios en problemas de zonación Sísmica. Reporte de Investigación.
CEMAFIT. ICIMAF. (1995).
62. Ramón Pico Peña. Determinación del umbral de semejanza β0 para los algoritmos
lógico-combinatorios, mediante el dendrograma de un algoritmo jerárquico. Memorias
del IV Simposio Ibero-americano de Reconocimiento de Patrones (SIARP’99).
Cuba. Ed IPN, México. ISBN 970-18-2386-9. (1999).
63. Ramón Pico Peña; Alvarez,L. y Cotilla,M. Zonación Sísmica de la Isla de Cuba
mediante algoritmos de clasificación lógico-combinatorios. Memorias del II Taller
Iberoamericano de Reconocimiento de Patrones. Ed. IPN, México. ISBN 968-299892-1. (1997).
64. Ramón Pico Peña. Determinación del umbral de semejanza β0 para los algoritmos
lógico-combinatorios, mediante el dendrograma de un algoritmo jerárquico. Memorias
del IV Simposio Ibero-americano de Reconocimiento de Patrones. Cuba. Ed IPN,
México. ISBN 970-18-2386-9. (1999).
65. J.R. García-Serrano, José Francisco Martínez-Trinidad. Extension to C-means
algorithm for the use of similarity functions. Proc. 3rdEuropean Conference on
Principles and Practice of Knowledge Discovery in Databases, pp. 354-359, Prague,
(1999).
66. R. Reyes-González J. Ruiz-Shulcloper. Un algoritmo de estructuración restringida
de espacios. Memorias del IV Simposio Iberoamericano de Reconocimiento de
Patrones, March 22-27, 1999, Ciudad de la Habana. pp. 267-278. Edited by José Ruiz
Shulcloper, José Fco. Martínez Trinidad, Jesús Ariel Carrasco Ochoa, Guillermo
Sánchez Díaz, Stalin Muñoz Gutiérrez, Walterio Mayol Cuevas, pp. 683. Editorial
Politécnico. México. (1999).
67. José Francisco Martínez-Trinidad, José Ruiz-Shulcloper. LC-conceptual algorithm:
characterization using typical testors by class. Proceedings of the Seventh European
Congress on Intelligent Techniques and Soft Computing, EUFIT’99, on CD, Section
FS C, Aachen, Germany (1999).
68. José Francisco Martínez Trinidad, José Ruiz Shulcloper, Aurora Pons Porrata.
Algoritmo LC-Conceptual: Una mejora de la etapa intencional utilizando reglas de
generalización. Memorias del Taller Nacional de Inteligencia Artificial TANIA’99,
ISBN 970-18-3554-9, México, D.F. pp. 179-188, 1999. Also in: Informe Técnico; Serie
Roja No. 70, pp. 1-10, Noviembre ISBN 970-18-3914-5, México. (1999).
69. José Fco. Martínez; J. Ruiz Shulcloper. Algoritmo LC-conceptual para el
agrupamiento de objetos. Simposium Internacional de Computación, CIC’97,
November 12-14, pp. 411-418, México. Also in: Informe Técnico Serie Roja, No. 27;
pp. 1-11, Junio 1998. ISBN 970-18-1551-3, (1997).
70. José Fco. Martínez, J. Ruiz-Shulcloper. Un modelo de estructuración conceptual.
Memorias del II Taller Iberoamericano de Reconocimiento de Patrones, March 2428, 1997, C. de la Habana. pp. 113-123. Edited by Adolfo Guzmán Arenas, José Ruiz
Shulcloper, Humberto Sossa Azuela, Manuel Lazo Cortés, J. Luis Díaz de León
Santiago. Instituto Politécnico Nacional, México. Informe Técnico Serie Roja, No. 29;
pp. 1-8. ISBN 970-18-1553-X, (1998).
71. José Fco. Martínez; J. Ruiz Shulcloper. Estructuración conceptual de espacios I:
Agrupamientos semánticos difusos. Informe Técnico Serie azul, No. 4, August,
Editorial Politécnico, Mexico. (1996)
72. José Fco. Martínez Trinidad, J. Ruiz Shulcloper y M. Lazo Cortés. Criterios
agrupacionales no clásicos para la estructuración de universos. Simposium
Internacional de Computación, México, 1996. Memorias (ISBN:968-29-9545-0). pp.
251-270. Informe Técnico Serie Roja, No. 28, June, Editorial Politécnico; Mexico.
(1998).
73. José Ruiz-Shulcloper, M. Chac, J.F. Martínez. Data analysis between sets of
objects. Proceedings of the 8th International Conference on Systems Research,
Informatics and Cybernetics, August, Baden-Baden, Germany. Edited by G. Lasker.
Advances in Artificial Intelligence and Engineering Cybernetics, Vol. III, pp. 81-85,
(1996).
74. José Ruiz-Shulcloper, M. Chac, J.F. Martínez. Cluster Analysis in Conceptual
Spaces. Proceedings of the 9th International Conference on Systems Research,
Informatics and Cybernetics, August, Baden-Baden, Germany. Edited by G. Lasker.
Advances in Artificial Intelligence and Engineering Cybernetics, Vol. IV, pp., (1997).
75. José Ruiz-Shulcloper and J. J. Montellano-Ballesteros. A new model of fuzzy
clustering algorithms. Proceedings of the European Congress on Intelligent Techniques
and Soft Computing, EUFIT’95, pp. 1484-1488, Aachen, Germany (1995).
76. José Francisco Martínez, José Ruiz-Shulcloper. Fuzzy semantic clustering.
Proceedings of the Fourth European Congress on Intelligent Techniques and Soft
Computing, EUFIT’96, pp. 1397-14101, Aachen, Germany (1996).
77. José Francisco Martínez-Trinidad, José Ruiz-Shulcloper. Fuzzy Conceptual
Clustering, Proceedings of the Fifth European Congress on Intelligent Techniques and
Soft Computing, EUFIT’97, pp. 1852-1857, Aachen, Germany (1997).
78. José Francisco Martínez-Trinidad, José Ruiz-Shulcloper. Fuzzy LC conceptual
algorithm. Proceedings of the Sixth European Congress on Intelligent Techniques and
Soft Computing, EUFIT’98, pp. 20-24, Aachen, Germany (1998).
79. José Francisco Martínez Trinidad, José Ruiz-Shulcloper, Manuel Lazo Cortés.
Structuralization of Universes. Fuzzy Sets and Systems, Vol. 112, No. 3, pp. 485-500,
(2000).
80. José Francisco Martínez Trinidad, José Ruiz-Shulcloper. Fuzzy Clustering of
Semantic Spaces. (Accepted to Pattern Recognition).
81. José Ruiz Shulcloper, Eduardo Alba Cabrera. Mixed Incomplete Data (MID)
MINING for Spatial Databases. CD Memorias de GEOINFO 2000 ISSN 1028-8961.
(2000).
82. José Ruiz Shulcloper, Eduardo Alba Cabrera, Guillermo Sánchez Díaz. Discovering
β0-Density Connected Components from Large Mixed Incomplete Data Sets. CD
Memorias de GEOINFO 2000 ISSN 1028-8961. (2000).
83. José Ruiz Shulcloper, Eduardo Alba Cabrera, Guillermo Sánchez Díaz. DGLC: a
Density-Based Global Logical Combinatorial Clustering Algorithm for Large Mixed
Incomplete Data. Accepted to IGARSS 2000 Honnolulu. (2000).
84. José Fco. Martínez Trinidad, Beatriz Beltrán Martínez, Adolfo Guzmán Arenas,
José Ruiz Shulcloper. CLASITEX+: A tool for Knowledge Discovery from Texts. In:
Principles of Data Mining and Knowledge Discovery. Second European Symposium,
PKDD'98, Nantes, France, Sept. 1998. Edited by Jan M. Zytkow, Mohamed Quafafou.
Lecture Notes in Artificial Intelligence, Vol. 1510. pp. 459-467. Informe Técnico Serie
Verde, No. 19; pp. 1-9, Mayo 1999. ISBN 970-18-3083-0. (1998).
7. ASSOCIATIONS AND GROUPS
Our Group belongs to the:
a) Cuban Association for Pattern Recognition.
b) Cuban Association of Mathematics and Computation.
8. OTHER REFERENCES
There are many other important literature in Russian and in other languages that we are
not cited because the restriction on the length of the paper. We are sorry with those
authors for the omission.
O1.A.N. Dmitriev, Yu. I. Zhuravlev, and F.P Krendelev. About the mathematical
principles of objects and phenomena classification. Sbornik Diskrtnii Analisis 7, pp.
3-15. Novosibirsk . (In Russian). (1966).
O2.I.A. Cheguis, and S.V. Yablonskii. Logical Methods for controlling electrical
systems. Trudy Matematicheskava Instituta imeni V. A. Steklova LI, pp. 270-360.
Moscow. (In Russian). (1958).
O3.N. N. Aizenberg, and A. I. Tsipkin. Prime Tests. Doklady Akademii Nauk 201 (4),
pp. 801-802. (In Russian). (1971).
O4.R. S. Goldman: Problems of Fuzzy Testors Theory. Avtomatika i Telemejanika 10,
pp. 146-153. (In Russian). (1980).
O5.M.N. Bongard, et al. Solving geological problems using recognition programs.
Sovietic Geology, No. 6, Moscow. (In Russian). (1963).
O6.L.V. Baskakova, Yu.I. Zhuravlev. Model of algorithm of recognition with
representative sets and support sets systems. Zhurnal Vichislitielnoi Matemati y
Matematicheskoi Fisiki 21-5, 1264-75. (In Russian). (1981).
O7. V. Keilis-Borok, A. Soloviev. Pattern Recognition in Earthquake Prediction.
Workshop on Non-Linear Dynamics and Earthquake Prediction, ICTP, Trieste,
Italy, pp. 1-14, (1991).