# An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications

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## Abstract

**:**

## 1. Introduction

## 2. Weakly Coupled Oscillatory Neural Network and Pattern Recognition

## 3. Topology of the Proposed ONN System

#### 3.1. Network Initialization

^{−1}s, the convergence frequency is 17.5 Hz.

#### 3.2. Pattern Recognition

^{−1}s and the convergence frequency appears to be 17.3 Hz. Figure 5 shows a detective pattern with lack of recognition. When changing the ninth oscillator’s frequency with coordinate (1, 5) to a more than twice the average value of those ten oscillators in the stored pattern, the coupled oscillators of the ONN are not able to synchronize.

## 4. Hierarchical Clustering of Impedance Sensing Grid

#### 4.1. Hierarchical Associative Memory Model

#### 4.2. Sensing Device

#### 4.3. Comparison with Other Algorithms

## 5. Validation of the Proposed Approach

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ONN | Oscillator neural network |

AM | Associative memory |

## Appendix A

## References

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**Figure 7.**Sensor based unit cell of the proposed ONN for clustering applications. Oscillator i and oscillator j are connected with sensor i and sensor j, respectively. Oscillator i and oscillator j are coupled with ${K}_{ij}$, which is one in this system.

**Figure 8.**The detected pattern on the second layer and the similarity measure with the first stored pattern. The similarity measurement is based on network synchronization time and frequency.

**Figure 9.**The detected pattern on the second layer and the similarity measure with the second stored pattern. The similarity measurement is based on network synchronization time and frequency.

**Figure 10.**The simulation results are shown as a particular stable 2-cluster partitions, where each curve represents the phase difference ${\varphi}_{i}-{\varphi}_{j}$, for i = 1, 2, …, 16, j = 1, when ${a}_{1}=5,{a}_{2}=11$.

**Figure 11.**The simulation results are shown as a particular stable 2-cluster partitions, where each curve represents the phase difference ${\varphi}_{i}-{\varphi}_{j}$, for i = 1, 2, …, 16, j = 1, when ${a}_{1}=13,{a}_{2}=3$,

**Figure 12.**Three sample images for each individuals. In each row, the first and the second are storage patterns, the third is the recognition pattern.

**Figure 13.**The simulation results are shown for the first individual’s third image using the first individual’s ${H}_{ij}$ function, which is a particular stable 2-cluster partition. Each curve represents the phase difference ${\varphi}_{i}-{\varphi}_{1}$.

**Figure 14.**The simulation results are shown for the first individual’s third image using the second individual’s ${H}_{ij}$ function, which is a unstable cluster partition. Each curve represents the phase difference ${\varphi}_{i}-{\varphi}_{1}$.

Synchronization Pattern | Convergence Time (s) | Convergence Frequency (Hz) |
---|---|---|

Stored | 1.576800 × 10^{−1} | 17.5 |

Recognition | 1.731000 × 10^{−1} | 17 |

Recognition upper threshold | 2.742600 × 10^{−1} | 19.3 |

Recognition lower threshold | 1.841300 × 10^{−1} | 16.5 |

Lack of Recognition | No Convergence | No Convergence |

ONN Characteristics | Hierarchical AM Model | Single AM Model |
---|---|---|

No. of layers | 2 | 1 |

No. of oscillators | ${n}^{2}$ | ${n}^{2}$ |

No. of oscillators in each layer | n | ${n}^{2}$ |

Connections (Number of weights) | ${C}_{n+1}^{2}$ | ${C}_{{n}^{2}}^{2}$ |

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**MDPI and ACS Style**

Zhang, T.; Haider, M.R.; Massoud, Y.; Alexander, J.I.D. An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications. *Electronics* **2019**, *8*, 64.
https://doi.org/10.3390/electronics8010064

**AMA Style**

Zhang T, Haider MR, Massoud Y, Alexander JID. An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications. *Electronics*. 2019; 8(1):64.
https://doi.org/10.3390/electronics8010064

**Chicago/Turabian Style**

Zhang, Ting, Mohammad R. Haider, Yehia Massoud, and J. Iwan D. Alexander. 2019. "An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications" *Electronics* 8, no. 1: 64.
https://doi.org/10.3390/electronics8010064