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Invariant object recognition based on combination of sparse DBN and SOM with temporal trace rule

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Abstract

This paper proposes a trace rule based self-organized map (SOM) model built upon a sparse 2-stage deep belief network (DBN). The combination of SOM and sparse DBN forms a hierarchical network where DBN serves as a V2 features detector while SOM layer learns to extract transformation invariant features guided by trace learning rule during training phase. The performance of our proposed method is evaluated by stimulus specific information (SSI) measuring and comparison with classic algorithms. It is demonstrated that trace rule based SOM model can generate more neurons with high SSI value which is beneficial to convey more useful and discriminative information for further object recognition.

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Acknowledgments

This work was supported in part by the Project of National Natural Science Foundation of China (Grant Nos. 61076097, 61473257).

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Authors and Affiliations

  1. School of Microelectronics, Xidian University, Xi’an, Shaanxi, 710071, China

    Huimin Cai, Shulong Wang & Hongxia Liu

  2. College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    Eryun Liu

Authors
  1. Huimin Cai
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  2. Shulong Wang
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  3. Eryun Liu
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  4. Hongxia Liu
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Corresponding author

Correspondence to Shulong Wang.

Appendix

Appendix

Assume that P(t) = 1/S, where S is the number of objects, we can derive the possible maximum SSI of a neuron by:

$$ P(r)=\sum\limits_{t\in S}P(t)P(r\mid t)=\frac{1}{S}\sum\limits_{t\in S}P(r\mid t) $$
(11)
$$\begin{array}{@{}rcl@{}} I(s,R)&=&\sum\limits_{r\in R}P(r\mid s)\log_{2}\frac{P(r\mid s)}{P(r)} \end{array} $$
(12)
$$\begin{array}{@{}rcl@{}} &=&\sum\limits_{r\in R}P(r\mid s)\log_{2}\frac{S\cdot P(r\mid s)}{\sum\limits_{t\in S}P(r\mid t)} \end{array} $$
(13)
$$\begin{array}{@{}rcl@{}} &=&\sum\limits_{r\in R}P(r\mid s)\left[ \log_{2}S+\log_{2}\frac{P(r\mid s)}{\sum\limits_{t\in S}P(r\mid t)} \right] \end{array} $$
(14)
$$\begin{array}{@{}rcl@{}} &=&\log_{2}S+\sum\limits_{r\in R}P(r\mid s)\log_{2}\frac{P(r\mid s)}{\sum\limits_{t\in S}P(r\mid t)} \end{array} $$
(15)
$$\begin{array}{@{}rcl@{}} &\because& 0\leq P(r\mid s)\leq \sum\limits_{t\in S}P(r\mid t) \end{array} $$
(16)
$$\begin{array}{@{}rcl@{}} &\therefore& \log_{2}\frac{P(r\mid s)}{{\sum}_{t\in S}P(r\mid t)}\leq 0 \end{array} $$
(17)
$$\begin{array}{@{}rcl@{}} &\therefore& \sum\limits_{r\in R}P(r\mid s)\log_{2}\frac{P(r\mid s)}{{\sum}_{t\in S}P(r\mid t)}\leq 0 \end{array} $$
(18)
$$\begin{array}{@{}rcl@{}} &\therefore& I(s,R)\leq \log_{2}S \end{array} $$
(19)

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Cai, H., Wang, S., Liu, E. et al. Invariant object recognition based on combination of sparse DBN and SOM with temporal trace rule. Multimed Tools Appl 76, 12017–12034 (2017). https://doi.org/10.1007/s11042-016-3956-3

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