A bigradient optimization approach for robust PCA, MCA, and source separation

Wang, L.; Karhunen, Juha; Oja, Erkki

doi:10.1109/icnn.1995.488872

Cited by 33 publications

(22 citation statements)

References 15 publications

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“…The pseudoinverse activity optimisation, and thus the decision making is not formulated in terms of neural activities nor in terms of similarities (or closeness) between inputs and memory vectors, but rather in terms of the reconstruction error. The pseudoinverse procedure can be important, for example, for nets coding independent components [26][27][28][29][30], since these components are generally not orthogonal.…”

Section: Discussionmentioning

confidence: 99%

Winner-Take-All Network Utilising Pseudoinverse Reconstruction Subnets Demonstrates Robustness on the Handprinted Character Recognition Problem

Körmendy-Rácz

Szabó

Lörincz

et al. 1999

Neural Computing & Applications

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Wittmeyer's pseudoinverse iterative algorithm is formulated as a dynamic connectionist Data Compression and Reconstruction (DCR) network, and subnets of this type are supplemented by the winnertake-all paradigm. The winner is selected upon the goodness-of-fit of the input reconstruction. The network can be characterised as a competitive-cooperative-competitive architecture by virtue of the contrast enhancing properties of the pseudoinverse subnets. The network is capable of fast learning. The adopted learning method gives rise to increased sampling in the vicinity of dubious boundary regions that resembles the phenomenon of categorical perception. The generalising abilities of the scheme allow one to utilise single bit connection strengths. The network is robust against input noise and contrast levels, shows little sensitivity to imprecise connection strengths, and is promising for mixed VLSI implementation with on-chip learning properties. The features of the DCR network are demonstrated on the NIST database of handprinted characters.

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Section: Discussionmentioning

confidence: 99%

Winner-Take-All Network Utilising Pseudoinverse Reconstruction Subnets Demonstrates Robustness on the Handprinted Character Recognition Problem

Körmendy-Rácz

Szabó

Lörincz

et al. 1999

Neural Computing & Applications

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show abstract

“…This equation is the so-called bigradient separating algorithm working on whitened inputs (Wang et al 1995;Karhunen et al 1997) and thus the model CA1 sub®eld separates. We note that non-linear operation is assumed during the theta phase and linear operation is assumed during the sharp wave phase.…”

Section: Separation With Reconstruction Architecturementioning

confidence: 99%

“…There is a ®rst stage that whitens, i.e., decorrelates and rescales the input, giving rise to outputs of equal variance. The second stage makes use of the whitened information and does`blind source separation' (Jutten and Herault 1991;Comon 1994;Bell and Sejnowski 1995;Wang et al 1995). Upon training, the outputs of this stage become statistically independent.…”

Section: Associative Stagementioning

confidence: 99%

“…Association that leads to independent components (IC) can be built up from three stages (Wang et al 1995;Karhunen et al 1997). There is a ®rst stage that whitens, i.e., decorrelates and rescales the input, giving rise to outputs of equal variance.…”

Section: Associative Stagementioning

confidence: 99%

“…We require that the associative stage develops statistically independent, i.e. separated, outputs (Jutten and Herault 1991;Comon 1994;Bell and Sejnowski 1995;Wang et al 1995).…”

Section: Associative Stagementioning

confidence: 99%

See 2 more Smart Citations

Forming independent components via temporal locking of reconstruction architectures: a functional model of the hippocampus

Lörincz

1998

Biological Cybernetics

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The assumption is made that the formulation of relations as independent components (IC) is a main feature of computations accomplished by the brain. Further, it is assumed that memory traces made of non-orthonormal ICs make use of feedback architectures to form internal representations. Feedback then leads to delays, and delays in cortical processing form an obstacle to this relational processing. The problem of delay compensation is formulated as a speed-field tracking task and is solved by a novel control architecture. It is shown that in addition to delay compensation the control architecture can also shape long-term memories to hold independent components if a two-phase operation mode is assumed. Features such as a trisynaptic loop and a recurrent collateral structure at the second stage of that loop emerge in a natural fashion. Based on these properties a functional model of the hippocampal loop is constructed.

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A new blind source separation method based on fractional lower‐order statistics

Zha

Qiu

2006

Adaptive Control & Signal

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We proposed neural network structures related to multilayer feed-forward networks for performing blind source separation (BSS) based on fractional lower-order statistics. As alpha stable distribution process has no its second-or higher-order statistics, we modified conventional BSS algorithms so that their capabilities are greatly improved under both Gaussian and lower-order alpha stable distribution noise environments. We analysed the performances of the new algorithm, including the stability and convergence performance. The analysis is based on the assumption that the additive noise can be modelled as alpha stable process.The simulation experiments and analysis show that the proposed class of networks and algorithms is more robust than second-order-statistics-based algorithm.

show abstract

A bigradient optimization approach for robust PCA, MCA, and source separation

Cited by 33 publications

References 15 publications

Winner-Take-All Network Utilising Pseudoinverse Reconstruction Subnets Demonstrates Robustness on the Handprinted Character Recognition Problem

Winner-Take-All Network Utilising Pseudoinverse Reconstruction Subnets Demonstrates Robustness on the Handprinted Character Recognition Problem

Forming independent components via temporal locking of reconstruction architectures: a functional model of the hippocampus

A new blind source separation method based on fractional lower‐order statistics

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