Abstract

This paper analyzes the necessity of using many information representations simultaneously in image-processing and -analysis systems. The difference between Kolmogorov-complexity and algorithmic-probability criteria when solving induction problems and making decisions is investigated. It is shown that making the optimum decisions (for example, in recognition or prediction problems) requires the use of many representations of information, in terms of which alternative descriptions of the images are constructed. A representational algorithmic-probability criterion is derived for determining the optimum set of representations from a given selection of images.

© 2012 OSA

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  1. D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (W. H. Freeman, San Francisco, 1982; Radio i Svyaz’, Moscow, 1987).
  2. A. S. Potapov, “Choosing image representations by minimizing their representational description length,” Izv. Vyssh. Uchebn. Zaved. Prib. 51, No. 7, 3 (2008).
  3. V. A. Kovalevski?, “Local versus global decisions in image recognition,” Proc. IEEE 67, 745 (1979).
    [CrossRef]
  4. R. J. Solomonoff, Does Algorithmic Probability Solve the Problem of Induction? (Oxbridge Research, Cambridge, Mass., 1997).
  5. R. J. Solomonoff, “Algorithmic probability, heuristic programming and AGI,” in Proceedings of the 3rd Conference on Artificial General Intelligence (AGI-2010), Lugano, Switzerland, March 5–8, 2010, pp. 151–157.
  6. J. Poland and M. Hutter, “MDL convergence speed for Bernoulli sequences,” Stat. Comp. 16, 161 (2006).
    [CrossRef]
  7. E. Bauer and R. Kohavi, “An empirical comparison of voting classification algorithms: bagging, boosting, and variants,” Mach. Learn. 36, 105 (1999).
    [CrossRef]
  8. A. S. Potapov, “Synthetic pattern-recognition methods based on the representational minimum description length principle,” in Proceedings OSAV’2008, The 2nd International Topical Meeting on Optical Sensing and Artificial Vision, St. Petersburg, Russia, 12–15 May, 2008, pp. 354–362.
  9. R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
    [CrossRef]

2008 (1)

A. S. Potapov, “Choosing image representations by minimizing their representational description length,” Izv. Vyssh. Uchebn. Zaved. Prib. 51, No. 7, 3 (2008).

2006 (1)

J. Poland and M. Hutter, “MDL convergence speed for Bernoulli sequences,” Stat. Comp. 16, 161 (2006).
[CrossRef]

1999 (1)

E. Bauer and R. Kohavi, “An empirical comparison of voting classification algorithms: bagging, boosting, and variants,” Mach. Learn. 36, 105 (1999).
[CrossRef]

1998 (1)

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

1979 (1)

V. A. Kovalevski?, “Local versus global decisions in image recognition,” Proc. IEEE 67, 745 (1979).
[CrossRef]

Bartlett, P.

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

Bauer, E.

E. Bauer and R. Kohavi, “An empirical comparison of voting classification algorithms: bagging, boosting, and variants,” Mach. Learn. 36, 105 (1999).
[CrossRef]

Freund, Y.

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

Hutter, M.

J. Poland and M. Hutter, “MDL convergence speed for Bernoulli sequences,” Stat. Comp. 16, 161 (2006).
[CrossRef]

Kohavi, R.

E. Bauer and R. Kohavi, “An empirical comparison of voting classification algorithms: bagging, boosting, and variants,” Mach. Learn. 36, 105 (1999).
[CrossRef]

Kovalevskii, V. A.

V. A. Kovalevski?, “Local versus global decisions in image recognition,” Proc. IEEE 67, 745 (1979).
[CrossRef]

Lee, W. S.

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

Marr, D.

D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (W. H. Freeman, San Francisco, 1982; Radio i Svyaz’, Moscow, 1987).

Poland, J.

J. Poland and M. Hutter, “MDL convergence speed for Bernoulli sequences,” Stat. Comp. 16, 161 (2006).
[CrossRef]

Potapov, A. S.

A. S. Potapov, “Choosing image representations by minimizing their representational description length,” Izv. Vyssh. Uchebn. Zaved. Prib. 51, No. 7, 3 (2008).

A. S. Potapov, “Synthetic pattern-recognition methods based on the representational minimum description length principle,” in Proceedings OSAV’2008, The 2nd International Topical Meeting on Optical Sensing and Artificial Vision, St. Petersburg, Russia, 12–15 May, 2008, pp. 354–362.

Schapire, R. E.

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

Solomonoff, R. J.

R. J. Solomonoff, “Algorithmic probability, heuristic programming and AGI,” in Proceedings of the 3rd Conference on Artificial General Intelligence (AGI-2010), Lugano, Switzerland, March 5–8, 2010, pp. 151–157.

R. J. Solomonoff, Does Algorithmic Probability Solve the Problem of Induction? (Oxbridge Research, Cambridge, Mass., 1997).

Ann. Stat. (1)

R. E. Schapire, Y. Freund, P. Bartlett, and W. S. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26, 1651 (1998).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Prib. (1)

A. S. Potapov, “Choosing image representations by minimizing their representational description length,” Izv. Vyssh. Uchebn. Zaved. Prib. 51, No. 7, 3 (2008).

Mach. Learn. (1)

E. Bauer and R. Kohavi, “An empirical comparison of voting classification algorithms: bagging, boosting, and variants,” Mach. Learn. 36, 105 (1999).
[CrossRef]

Proc. IEEE (1)

V. A. Kovalevski?, “Local versus global decisions in image recognition,” Proc. IEEE 67, 745 (1979).
[CrossRef]

Stat. Comp. (1)

J. Poland and M. Hutter, “MDL convergence speed for Bernoulli sequences,” Stat. Comp. 16, 161 (2006).
[CrossRef]

Other (4)

D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (W. H. Freeman, San Francisco, 1982; Radio i Svyaz’, Moscow, 1987).

A. S. Potapov, “Synthetic pattern-recognition methods based on the representational minimum description length principle,” in Proceedings OSAV’2008, The 2nd International Topical Meeting on Optical Sensing and Artificial Vision, St. Petersburg, Russia, 12–15 May, 2008, pp. 354–362.

R. J. Solomonoff, Does Algorithmic Probability Solve the Problem of Induction? (Oxbridge Research, Cambridge, Mass., 1997).

R. J. Solomonoff, “Algorithmic probability, heuristic programming and AGI,” in Proceedings of the 3rd Conference on Artificial General Intelligence (AGI-2010), Lugano, Switzerland, March 5–8, 2010, pp. 151–157.

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