COGMAX+

Cogito, ergo maxplus: ¿es nuestro pensamiento idempotente?

Abstract

Philosopher, mathematician and physicist, his transversal thought turned him into the father of modern philosophy and analytic or cartesian geometry. With his most famous statement “I think, therefore I am”, Descartes laid the foundation of European rationalism whereby the ego is the cornerstone on which our certainty of the world we perceive relies.

In this proposal, we dare to hypothesize that cognition does not obey the cartesian geometry and that our knowledge of the world, shaped by human perception, draws a geometry derived from idempotent algebra. Under this perspective, crucial notions as orthogonality or the combination or accumulation of stimuli should be reconsidered. In sum, we question whether for the emulation of human perception we should use a radically different mathematical setting to program machines.

Strong evidence of the unsuitability of conventional algebra for modeling the acquisition and processing of sensory information can be found, for example, in the employment of maximum operations, oftentimes understood as a lossy simplification that could be, in reality, a way of focalizing attention selecting the most relevant or salient stimuli. We also find examples in the well-known Viterbi optimization method, mathematical morphology based preprocessing tools, max-pooling and winner-take-all strategies in artificial vision and neural networks, log-log representations of cognitive phenomena like speech perception, etc.

This paradigm shift will have important consequences in the processing of most signals like speech, image or video as well as on others not that widespread like haptic, smell or taste.

Methodologically, rather than trying to produce exact models of human perception under the idempotent algebra light, we will take a technological viewpoint and assess the improvements on an automatic determination of visual saliency.

Keywords

idempotency, cognition, perception, saliency, cognitive computing, formal concept, biclustering

Publications

  • F. J. Valverde-Albacete and C. Peláez-Moreno, “The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields,” in Formal Concept Analysis, K. Bertet, D. Borchmann, P. Cellier, and S. Ferré, Eds., Rennes: Springer Berlin Heidelberg, 2017, pp. 211-227.
    [Bibtex]
    @incollection{val:pel:17a,
      Address = {Rennes},
      Author = {Valverde-Albacete, Francisco Jos and Pel\'{a}ez-Moreno, C},
      Booktitle = {Formal Concept Analysis},
      Date-Added = {2017-06-19 08:34:22 +0000},
      Date-Modified = {2017-11-08 18:49:10 +0000},
      Editor = {Bertet, Karell and Borchmann, D. and Cellier, P and Ferr\'e, S.},
      Month = June,
      Pages = {211--227},
      Publisher = {Springer Berlin Heidelberg},
      Title = {{The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields}},
      Year = {2017},
      key = {cogmax}}
  • [DOI] F. J. Valverde-Albacete and C. Peláez-Moreno, “The Evaluation of Data Sources using Multivariate Entropy Tools,” Expert Systems with Applications, vol. 78, pp. 145-157, 2017.
    [Bibtex]
    @article{val:pel:17b,
      Author = {Valverde-Albacete, Francisco J and Pel\'aez-Moreno, C},
      Date-Added = {2017-01-13 13:55:34 +0000},
      Date-Modified = {2017-03-02 10:56:57 +0000},
      Doi = {10.1016/j.eswa.2017.02.010},
      Journal = {Expert Systems with Applications},
      Pages = {145-157},
      Title = {The Evaluation of Data Sources using Multivariate Entropy Tools},
      Volume = {78},
      Year = {2017},
      Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.eswa.2017.02.010},
      key = {cogmax}}
  • F. J. Valverde Albacete and C. Peláez-Moreno, “Entropy operates in Non-Linear Semifields,” Arxiv, iss. 1710.04728 [cs.IT], 2017.
    [Bibtex]
    @article{val:pel:17c,
      Author = {Valverde Albacete, Francisco Jos\'e and Carmen Pel\'aez-Moreno},
      Date-Added = {2017-11-04 20:13:49 +0000},
      Date-Modified = {2017-12-14 09:49:54 +0000},
      Journal = {Arxiv},
      Number = {1710.04728 [cs.IT]},
      Title = {Entropy operates in Non-Linear Semifields},
      Year = {2017},
      key = {cogmax}}
  • [DOI] F. J. Valverde-Albacete and C. Peláez-Moreno, “The spectra of reducible matrices over complete commutative idempotent semifields and their spectral lattices,” International Journal of General Systems, vol. 45, iss. 2, pp. 86-115, 2016.
    [Bibtex]
    @article{val:pel:16,
      Author = {Francisco Jos{\'e} Valverde-Albacete and Carmen Pel{\'a}ez-Moreno},
      Date-Added = {2017-11-05 12:20:30 +0000},
      Date-Modified = {2017-11-05 12:22:07 +0000},
      Doi = {10.1080/03081079.2015.1072923},
      Eprint = {http://dx.doi.org/10.1080/03081079.2015.1072923},
      Journal = {International Journal of General Systems},
      Number = {2},
      Pages = {86-115},
      Publisher = {Taylor & Francis},
      Title = {The spectra of reducible matrices over complete commutative idempotent semifields and their spectral lattices},
      Url = {http://dx.doi.org/10.1080/03081079.2015.1072923},
      Volume = {45},
      Year = {2016},
      Bdsk-Url-1 = {http://dx.doi.org/10.1080/03081079.2015.1072923},
      key = {cogmax}}
  • [DOI] I. González-Díaz, M. Birinci, F. Díaz-de-María, and E. J. Delp, “Neighborhood Matching for Image Retrieval,” IEEE Transactions on Multimedia, vol. 19, iss. 3, pp. 544-558, 2017.
    [Bibtex]
    @article{Gonzalez17a,
    author={I. González-Díaz and M. Birinci and F. Díaz-de-María and E. J. Delp},
    journal={IEEE Transactions on Multimedia},
    title={Neighborhood Matching for Image Retrieval},
    year={2017},
    volume={19},
    number={3},
    pages={544-558},
    keywords={computational complexity;formal verification;geometry;image matching;image retrieval;Oxford 105 k dataset;Oxford 5 k dataset;computational complexity;computational efficiency;fast approximations;geometric verification step;image geometric layout;initial reference image ranking;keypoint matching process;large-scale image retrieval framework;multimedia community;neighborhood matching;Computational complexity;Computational modeling;Feature extraction;Histograms;Image retrieval;Visualization;Vocabulary;Geometric verification;image retrieval;neighborhood matching (NM);robust estimation},
    doi={10.1109/TMM.2016.2616298},
    ISSN={1520-9210},
    month={March},
    key= {cogmax}}
  • I. González-D’iaz, “Incorporating the Knowledge of Dermatologists to Convolutional Neural Networks for the Diagnosis of Skin Lesions,” CoRR, vol. abs/1703.01976, 2017.
    [Bibtex]
    @article{Gonzalez17b,
      author    = {Iv{\'{a}}n Gonz{\'{a}}lez{-}D{\'{\i}}az},
      title     = {Incorporating the Knowledge of Dermatologists to Convolutional Neural
                   Networks for the Diagnosis of Skin Lesions},
      journal   = {CoRR},
      volume    = {abs/1703.01976},
      year      = {2017},
      url       = {http://arxiv.org/abs/1703.01976},
      archivePrefix = {arXiv},
      eprint    = {1703.01976},
      timestamp = {Wed, 07 Jun 2017 14:41:22 +0200},
      biburl    = {https://dblp.org/rec/bib/journals/corr/González-Díaz17},
      bibsource = {dblp computer science bibliography, https://dblp.org},
      key= {cogmax}
    }
  • [DOI] G. I. Díaz, “DermaKNet: Incorporating the knowledge of dermatologists to Convolutional Neural Networks for skin lesion diagnosis,” IEEE Journal of Biomedical and Health Informatics, iss. 99, pp. 1-1, 2018.
    [Bibtex]
    @article{Gonzalez18,
    author={I. González Díaz},
    journal={IEEE Journal of Biomedical and Health Informatics},
    title={DermaKNet: Incorporating the knowledge of dermatologists to Convolutional Neural Networks for skin lesion diagnosis},
    year={2018},
    volume={},
    number={99},
    pages={1-1},
    keywords={Image segmentation;Informatics;Lesions;Malignant tumors;Skin;Solid modeling;Task analysis;CAD;Convolutional Neural Networks;Dermoscopy;Melanoma;Skin lesion analysis},
    doi={10.1109/JBHI.2018.2806962},
    ISSN={2168-2194},
    month={},
    key= {cogmax}}
  • [DOI] F. José Valverde-Albacete and C. Peláez-Moreno, “The Multivariate Entropy Triangle and Applications,” in Hybrid Artificial Intelligent Systems, F. MartinezAlvarez, A. Troncoso, H. Quintian, and E. Corchado, Eds., , 2016, vol. 9648, pp. 647-658.
    [Bibtex]
    @inbook{RN408,
       author = {José Valverde-Albacete, Francisco and Peláez-Moreno, Carmen},
       title = {The Multivariate Entropy Triangle and Applications},
       booktitle = {Hybrid Artificial Intelligent Systems},
       editor = {MartinezAlvarez, F. and Troncoso, A. and Quintian, H. and Corchado, E.},
       series = {Lecture Notes in Artificial Intelligence},
       volume = {9648},
       pages = {647-658},
       ISBN = {978-3-319-32034-2; 978-3-319-32033-5},
       DOI = {10.1007/978-3-319-32034-2_54},
       url = {<Go to ISI>://WOS:000389499600054},
       year = {2016},
       type = {Book Section},
       key = {cogmax}
    }
  • [DOI] F. J. Valverde-Albacete and C. Peláez-Moreno, “Towards Galois Connections over Positive Semifields,” in Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, Pt Ii, J. P. Carvalho, M. J. Lesot, U. Kaymak, S. Vieira, B. BouchonMeunier, and R. R. Yager, Eds., , 2016, vol. 611, pp. 81-92.
    [Bibtex]
    @inbook{RN409,
       author = {Valverde-Albacete, Francisco J. and Peláez-Moreno, Carmen},
       title = {Towards Galois Connections over Positive Semifields},
       booktitle = {Information Processing and Management of Uncertainty in Knowledge-Based Systems, {IPMU} 2016, Pt Ii},
       editor = {Carvalho, J. P. and Lesot, M. J. and Kaymak, U. and Vieira, S. and BouchonMeunier, B. and Yager, R. R.},
       series = {Communications in Computer and Information Science},
       volume = {611},
       pages = {81-92},
       ISBN = {978-3-319-40581-0; 978-3-319-40580-3},
       DOI = {10.1007/978-3-319-40581-0_8},
       url = {<Go to ISI>://WOS:000387430000008},
       year = {2016},
       type = {Book Section},
       key ={cogmax}
    }

Funded by

MINECO (Ministry of Economy and Competitiveness)

TEC2014-61729-EXP (Convocatoria 2014 de Proyectos de I+D del Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia). Sep. 2015 – Ago. 2017.

Contact Persons
Carmen Peláez-Moreno (carmen at tsc.uc3m.es)

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