Performance analysis of LVQ algorithms: A statistical physics approach

Ghosh, Anarta; Biehl, Michael; Hammer, Barbara

doi:10.1016/j.neunet.2006.05.010

Cited by 26 publications

(49 citation statements)

References 14 publications

(16 reference statements)

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“…Also for N → ∞ the rescaled quantity t ≡ µ/N can be conceived as a continuous time variable. Accordingly, the dynamics can be described by a set of coupled ODE [3,10] after performing an average over the sequence of input data:…”

Section: Analysis Of Learning Dynamicsmentioning

confidence: 99%

Learning dynamics and robustness of vector quantization and neural gas

et al. 2008

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Various alternatives have been developed to improve the Winner-Takes-All (WTA) mechanism in vector quantization, including the Neural Gas (NG). However, the behavior of these algorithms including their learning dynamics, robustness with respect to initialization, asymptotic results, etc. has only partially been studied in a rigorous mathematical analysis. The theory of on-line learning allows for an exact mathematical description of the training dynamics in model situations. We demonstrate using a system of three competing prototypes trained from a mixture of Gaussian clusters that the Neural Gas can improve convergence speed and achieves robustness to initial conditions. However, depending on the structure of the data, the Neural Gas does not always obtain the best asymptotic quantization error.

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Section: Analysis Of Learning Dynamicsmentioning

confidence: 99%

Learning dynamics and robustness of vector quantization and neural gas

et al. 2008

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“…Also for N → ∞, the rescaled quantity α ≡ μ/N can be conceived as a continuous time variable. Accordingly, the dynamics can be described by a set of coupled ordinary differential equations (ODE) (Ghosh, Biehl, & Hammer, 2006) after performing an average over the sequence of input data:…”

Section: Discussionmentioning

confidence: 99%

Window-Based Example Selection in Learning Vector Quantization

et al. 2010

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A variety of modifications have been employed to learning vector quantization (LVQ) algorithms using either crisp or soft windows for selection of data. Although these schemes have been shown in practice to improve performance, a theoretical study on the influence of windows has so far been limited. Here we rigorously analyze the influence of windows in a controlled environment of gaussian mixtures in high dimensions. Concepts from statistical physics and the theory of online learning allow an exact description of the training dynamics, yielding typical learning curves, convergence properties, and achievable generalization abilities. We compare the performance and demonstrate the advantages of various algorithms, including LVQ 2.1, generalized LVQ (GLVQ), Learning from Mistakes (LFM) and Robust Soft LVQ (RSLVQ). We find that the selection of the window parameter highly influences the learning curves but not, surprisingly, the asymptotic performances of LVQ 2.1 and RSLVQ. Although the prototypes of LVQ 2.1 exhibit divergent behavior, the resulting decision boundary coincides with the optimal decision boundary, thus yielding optimal generalization ability.

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“…Ghosh Biehl and Hammer 2006 studied five LVQ algorithms in detail: Kohonen's original LVQ1, unsupervised vector quantization (VQ), a mixture of VQ and LVQ, LVQ2.1, and a variant of LVQ which is based on a cost function. Surprisingly, basic LVQ1 showed very good performance in terms of stability, asymptotic generalization ability, and robustness to initializations and model parameters which, in many cases, was superior to recent alternative proposals [8] . Sanchez and Marques 2006 introduced an adaptive algorithm for competitive training of a nearest neighbor (NN) classifier when using a very small codebook, which was based on the well-known LVQ method, and used an alternative neighborhood concept to estimate optimal locations of the codebook vectors [9] .…”

Section: Introductionmentioning

confidence: 92%

Research on credit risk evaluation model based on LVQ neural network

Wong

Xiao

et al. 2008

2008 IEEE International Conference on Automation and Logistics

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In this paper, we have established one credit risk evaluation model based on Learning Vector Quantization respectively. This model is used to identify two patterns samples of Chinese listed companies, including training samples of 285 listed companies 59 companies with special treatment and 226 normal companies and test samples of 117 listed companies(29 companies with special treatment and 88 normal companies). The two patterns indicate that the listed companies are divided into two groups in terms of their business conditions: credit default group (ST and *ST listed companies) and credit non-default group (normal listed companies). 4 main financial indexes are considered: earning per share, net asset per share, return on equity, cash flow per share. The simulating results showed that, after 20 training steps, LVQ neural network becomes steady after 300 training epochs and the overall discriminant accuracy rate is 92.79%. Therefore this indicates that the credit risk evaluation model based on Learning Vector Quantization neural network is able to result in good classification and has research value to the reality.

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Performance analysis of LVQ algorithms: A statistical physics approach

Cited by 26 publications

References 14 publications

Learning dynamics and robustness of vector quantization and neural gas

Learning dynamics and robustness of vector quantization and neural gas

Window-Based Example Selection in Learning Vector Quantization

Research on credit risk evaluation model based on LVQ neural network

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