P. Foldi'ak and M. P. Young. Sparse coding in the primate cortex. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 895--898. The MIT Press, Cambridge, Massachusetts, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... have previously shown that nonnegativity is a useful constraint for matrix factorization that can learn a parts representation of the data [4, 5] The nonnegative basis vectors that are learned are used in distributed, yet still sparse combinations to generate expressiveness in the reconstructions [6, 7]. In this submission, we analyze in detail two numerical algorithms for learning the optimal nonnegative factors from data. 2 Non negative matrix factorization We formally consider algorithms for solving the following problem: Non negative matrix factorization (NMF) Given a non negative matrix ....

Foldiak, P & Young, M (1995). Sparse coding in the primate cortex. The Handbook of Brain Theory and Neural Networks, 895--898. (MIT Press, Cambridge, MA).

....of the Gabor like kernel can be found for any image location, one can safely assume that the V1 representation is overcomplete. The idea that sparse coding plays an essential role in sensory perception, and particularly visual perception, has a long history in psychophysics and brain research [3, 6, 69, 71, 20, 22]. It seems likely that a sparse coding principle is used by V1: Cortical cells are much less active than their retinal inputs, i.e. the distribution of their activity is super gaussian [71, 20] Simple cells in V1 are nonlinearly tuned to their optimal stimuli. Examples of the latter ....

P. Foldiak, M Young, \Sparse coding in the primate cortex", in The Handbook of Brain Theory and Neural Networks, ed. Michael A. Arbib, pp. 895-898, 1995. 32

.... experimental and theoretical work indicates that patterns are likely to be encoded in a sparse way that is, for a given pattern the fraction of neurons that are simultaneously active will be much less than a half (there will be fewer ones than zeros in the binary representations of patterns) (Foldiak and Young, 1995). With this 12 Bogacz, et al. Figure 6. Comparison of the simulated familiarity discrimination capacities of the perirhinal network for different degrees of sparseness of connectivity, with the corresponding theoretical predictions. Method of simulation as in Fig. 5. constraint, the inverted ....

Foldiak P, Young M (1995) Sparse coding in the primate cortex. In: Arbib MA, ed. Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge, MA.

.... have previously shown that nonnegativity is a useful constraint for matrix factorization that can learn a parts representation of the data [4, 5] The nonnegative basis vectors that are learned are used in distributed, yet still sparse combinations to generate expressiveness in the reconstructions [6, 7]. In this submission, we analyze in detail two numerical algorithms for learning the optimal nonnegative factors from data. Non negative matrix factorization We formally consider algorithms for solving the following problem: Non negative matrix factorization (NMF) Given a non negative matrix V ....

Foldiak, P & Young, M (1995). Sparse coding in the primate cortex. The Handbook of Brain Theory and Neural Networks, 895--898. (MIT Press, Cambridge, MA).

....( for the fractal contour image shown at left. Note that these reasons for desiring sparseness are separate from those that have been written about elsewhere, such as increasing capacity in associative memory (Baum et al. 1988) minimizing wiring length and ease of forming associations (Foldiak, 1995), or metabolic efficiency (Baddeley, 1996) While these are obvious advantages of a sparse code, they are independent from the criteria we are considering here. If the data were actually composed from causes with multimodal distributions with heavy peaks around non zero values, then seeking a ....

....parameter or attribute such as color or stimulus velocity. However, it should be noted that the code being utilized here is a sparse, distributed code, which actually occupies a middle ground between dense population codes at one end and local represenations (i.e. grandmother cells) at the other (Foldiak, 1995). In a sparse distributed code, units both share in the representation of different images and also minimize the total number active per image. Thus, such a code combines the advantages (as well as disadvantages) of both coding schemes. There are situations where dense population codes are ....

Foldiak P (1995) "Sparse coding in the primate cortex," In: The Handbook of Brain Theory and Neural Networks, Arbib MA, ed, MIT Press, pp. 895-989.

....among the first #(n) then we will obtain an adaptive representation obeying a polynomial depth search constraint, as well as the embedding ### p # C p , for all p 2 3, which is optimal. The polynomial depth search constraint can also be motivated by appeal to the concept of sparse coding [15, 16]. We allow sparse decomposition, where most atoms in the original dictionary are not used in any given decomposition; but we allow only rules in which the sparsity (propensity to use elements near position n) scales like a power law in n rather than like a decaying exponential in n. 7 Lower ....

....The coe#cients at fine levels are therefore in a sense controlled by the square root of the boundary curvature. 11.1.4 Comparisons Now we make a few remarks comparing the decomposition developed here and ongoing work in vision. Such comparisons are necessarily hazardous. Field [15] and Foldiak [16] have emphasized the potential benefit that sparse coding could play in the design of the visual cortex. Field, in particular, has pointed to the sparsity of wavelet expansions as providing inspiring examples. In this paper we have another example of a system which uses sparse codes. It achieves ....

Foldiak, P. (1995) Sparse coding in the primate cortex. in The Handbook of Brain Theory and Neural Networks, M.A. Arbib, ed. MIT Press, pp. 895-899.

....rise to a distribution such as depicted in Figure 1b. Note that these reasons for desiring sparseness are separate from those that have been written about elsewhere, such as increasing capacity in associative memory (Baum et al. 1988) minimizing wiring length and ease of forming associations (Foldiak, 1995), or metabolic efficiency (Baddeley, 1996) While these are obvious advantages of a sparse code, they are independent from the criteria we are considering here. If the data were actually composed from causes with multimodal distributions with heavy peaks around non zero values, then seeking a ....

....parameter or attribute such as color or stimulus velocity. However, it should be noted that the code being utilized here is a sparse, distributed code, which actually occupies a middle ground between dense population codes at one end and local representations (i.e. grandmother cells) at the other (Foldiak 1995; Hinton Ghahramani 1997) Note for example that the learned basis functions are broadly tuned to some stimulus dimensions (e.g. spatial frequency) as would be expected of a coarse code, while narrowly tuned to others (e.g. position) as in a local code. In a sparse distributed code, units ....

Foldiak P (1995) "Sparse coding in the primate cortex," In: The Handbook of Brain Theory and Neural Networks, Arbib MA, ed, MIT Press, pp. 895-989.

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P. Foldi'ak and M. P. Young. Sparse coding in the primate cortex. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 895--898. The MIT Press, Cambridge, Massachusetts, 1995.

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P. Foldi'ak and M. P. Young. Sparse coding in the primate cortex. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 895-- 898. The MIT Press, Cambridge, Massachusetts, 1995.

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P. Foldiak and M. P. Young. Sparse coding in the primate cortex. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 895--898. The MIT Press, Cambridge, Massachusetts, 1995.

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