# Machine Learning Algorithms for Prediction of the Quality of Transmission in Optical Networks

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Machine Learning Challenges

#### 1.3. Article Organization

## 2. Data and DWDM Network Description

- The first network consists of 187 nodes, in which a mixture of non-coherent and coherent transponders were installed. Such a network is quite representative of DWDM networks used by operators nowadays whereby legacy non-coherent transponders are still in use whilst modern coherent transponders are gradually introduced. The non-coherent transponders belong to Nokia 1626 family whilst the coherent ones are from Nokia PSS 1830 family. The non-coherent transponders have 2.5G and 10G transmission rate and use NRZ modulation. The coherent transponders operate at either 100G or 200G transmission rate and use three types of modulation: QPSK, 8QAM and 16QAM. In the remainder of the article the dataset corresponding to the 187-node network will be referred to as dataset 1.
- The second network consists of 83 nodes with coherent transponders only. This is a typical representative of a new network established by an operator. In this instance the coherent transponders belong to Ciena’s 6500 family of equipment, with transmission rate of 100G, 200G and 400G and four types of modulation: QPSK, 16QAM, 32QAM and 64QAM. In the remainder of this article the dataset corresponding to the 83-node network will be referred to as dataset 2.

#### 2.1. Channel Attributes

`hop_lenghts`(a natural number describing the length of the edge, expressed in kilometres, e.g., 67 km);`number_of_paths_in_hops`(a natural number representing the number of channels in the edge, e.g., 17);`hop_losses`(a real number describing edge suppression, expressed in decibels e.g., 17.7 dB);`number_of_hops`(a natural number representing the number of edges of which the path (channel) consists, e.g., 9);`transponder_modulation`(description of the transponder modulation that is installed at the beginning and the end of the path (channel), e.g., QAM);`transponder_bitrate`(a natural number describing the transmission rate of the transponder, e.g., 100 Gbps.).

#### 2.2. Vector Representation

`hop_lengths`,

`num_of_paths_in_hops`,

`hop_losses`) over all hops in a path (i.e., an optical channel) by applying the following set of aggregation functions:

- mean and standard deviation (assuming 0 for one-hop channels),
- minimum and maximum,
- median, the first quartile, and the third quartile,
- linear correlation coefficient with the ordinal number of the hop in the optical channel.

`number_of_hops`,

`transponder_modulation`, and

`transponder_bitrate`).

## 3. Algorithms

#### 3.1. Logistic Regression

#### 3.2. Support Vector Machines

**margin****maximization:**- the location of the decision boundary (separating hyperplane) is optimized with respect to the classification margin,
**soft****margin:**- incorrectly separated instances are permitted,
**kernel****trick:**- complex nonlinear relationships can be represented by representation transformation using kernel functions.

#### 3.3. Decision Trees

#### 3.4. Random Forest

#### 3.5. Extreme Gradient Boosting

#### 3.6. Increasing Sensitivity to the Minority Class

#### 3.7. Classification Model Evaluation

## 4. Experiments

#### 4.1. Attribute Subsets

**subset****0:**`number_of_hops`,`transponder_modulation`, and`transponder_bitrate`,**subset****1:**- subset 0 plus all attributes obtained by applying the mean and standard deviation aggregation functions to hop properties,
**subset****2:**- subset 1 plus all attributes obtained by applying the minimum and maximum aggregation functions to hop properties,
**subset****3:**- subset 2 plus all attributes obtained by applying the median, first quartile, and third quartile aggregation functions to hop properties,
**subset****4:**- subset 3 plus all attributes obtained by applying the correlation aggregation function to hop properties (i.e., the full attribute set).

#### 4.2. Algorithm Implementations and Setup

**logistic****regression:**- the implementation provided by the standard
`glm`R function [56], **SVM:**- the implementation provided by the
`e1071`R package [57], **decision****trees:**- the implementation provided by the
`rpart`R package [58], **random****forest:**- the implementation provided by the
`ranger`R package [59], **extreme gradient****boosting:**- the implementation provided by the
`xgboost`R package [60].

`cost`:- the cost of constraint violation,
`gamma`:- the kernel parameter,
`class.weights`:- class weight for the minority class in constraint violation penalty (a weight of 1 was used for the dominating class).

`prior`parameter. Parameters specifying the stop criteria were tuned by grid search:

`minsplit`:- the minimum number of instances required for a split,
`cp`:- the complexity parameter,
`maxdepth`:- the maximum tree depth.

`num.trees`:- the number of trees,
`mtry`:- the number of attributes for split selection at each node,
`case.weights`:- weights for instances of the minority class (weights of 1 were used for instances of the dominating class).

`nrounds`:- the number of boosting iterations,
`weight`:- weights for instances of the minority class class (weights of 1 were used for instances of the dominating class).

- apply each algorithm with all attribute subsets and all grid search parameter setups,
- select the attribute subset with the highest maximum PR AUC over all parameter setups,
- select the parameter setup with both a near-maximum PR AUC and a near-maximum ROC AUC for the previously selected attribute subset, where ‘near-maximum’ was technically interpreted as ‘at least $0.99$ of the maximum’.

#### 4.3. Results

**for dataset****1:**- the prediction quality achieved by all the algorithms appears to be very good, with AUC values between $0.86$ and $0.89$,
- reasonable model operating points are possible, with the true positive rate of $0.9$ or more and the false positive rate of $0.2$ or less,
- the random forest, xgboost, and logistic regression algorithms achieve the best predictive performance, followed by SVM and decision trees,

**for dataset****2:**- all algorithms appear to achieve nearly perfect predictions, with AUC values of 0.97–0.98,
- nearly perfect model operating points are possible, with the true positive rate of 1 and the false positive rate of $0.05$ or less,
- the logistic regression, decision trees, random forest, and xgboost peform on roughly the same level, and SVM is only marginally worse.

**for dataset****1:**- the logistic regression, decision trees, and SVM algorithms fail to achieve an acceptable level of precision, with the PR AUC below $0.1$,
- the random forest and xgboost algorithms produce much more useful models, with the average precision above $0.4$,
- even for the best random forest models there is the precision drops quickly when recall exceeds $0.4$,

**for dataset****2:**- all algorithms manage to achieve average precision of about $0.4$ or more,
- a reasonable level of precision can be maintained over a wide range of recall values,
- the xgboost and random forest algorithms achieve the best predictive power, and decision tree models are the worst.

`nround`parameter, so we arbitrarily used 50 as the default). It is easy to see that parameter tuning improved the results substantially for all algorithms. Even for the random forest algorithm, which is not overly sensitive to parameter settings, it was beneficial (particularly on dataset 2), and it turned out absolutely necessary for SVM to deliver acceptable results.

**for dataset****1:**- the most useful attributes are
`number_of_hops`, the minimum of`num_of_paths_hops`, as well as attributes derived by aggregating`hop_lengths`and`hop_losses`, whereas`transponder_modulation`and`transponder_bitrate`have little or no predictive utility, **for dataset****2:**`transponder_modulation`and`transponder_bitrate`are the most useful attributes by far.

#### 4.4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ML | Machine Learning |

DWDM | Dense Wavelength Division Multiplexing |

QoT | Quality of Transmission |

SDN | Software Defined Networking |

IoT | Internet of Things |

5G | 5G Network Technology |

KDN | Knowledge-based Network |

Gbps | Giga bit per second |

Tbps | Tera bit per second |

ROC | Receiver Operating Characteristic |

AUC | Area Under the ROC Curve |

PR | Precision-recall |

SVM | Support Vector Machines |

QPSK | Quadrature Phase Shift Keying |

QAM | Quadrature amplitude modulation. |

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Dataset 1 | |

Optical Channel Type | #Channel |

“good” non-coherent optical channels | 1046 |

“good” coherent optical channels | 87 |

“bad” non-coherent optical channels | 13 |

“bad” coherent optical channels | 2 |

Dataset 2 | |

Optical Channel Type | #Channel |

“good” coherent optical channels | 103 |

“bad” coherent optical channels | 3 |

Dataset 1 | ||

Algorithm | Attribute Subset | Parameter Settings |

Logistic regression | subset 0 | — |

Decision trees | subset 0 | minsplit=10, cp=0.001, maxdepth=2 |

SVM | subset 2 | cost=10, gamma=0.15, class.weights=5 |

Random forest | subset 4 | num.trees=500, mtry=10, case.weights=2 |

xgboost | subset 2 | nrounds=5, weight=5 |

Dataset 2 | ||

Algorithm | Attribute subset | Parameter settings |

Logistic regression | subset 0 | — |

Decision trees | subset 0 | minsplit=15, cp=0.0002, maxdepth=4 |

SVM | subset 0 | cost=5, gamma=0.15, class.weights=20 |

Random forest | subset 1 | num.trees=1000, mtry=2, case.weights=20 |

xgboost | subset 0 | nrounds=15, weight=20 |

Dataset 1 | ||||

Algorithm | Default Parameters | Tuned Parameters | ||

AUC | PR AUC | AUC | PR AUC | |

Decision trees | $0.77$ | $0.05$ | $0.86$ | $0.06$ |

SVM | $0.74$ | $0.06$ | $0.87$ | $0.09$ |

Random forest | $0.90$ | $0.43$ | $0.89$ | $0.46$ |

xgboost | $0.88$ | $0.20$ | $0.88$ | $0.42$ |

Dataset 2 | ||||

Algorithm | Default Parameters | Tuned Parameters | ||

AUC | PR AUC | AUC | PR AUC | |

Decision trees | $0.94$ | $0.31$ | $0.98$ | $0.37$ |

SVM | $0.58$ | $0.09$ | $0.97$ | $0.39$ |

Random forest | $0.97$ | $0.29$ | $0.98$ | $0.42$ |

xgboost | $0.97$ | $0.30$ | $0.98$ | $0.46$ |

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**MDPI and ACS Style**

Kozdrowski, S.; Cichosz, P.; Paziewski, P.; Sujecki, S.
Machine Learning Algorithms for Prediction of the Quality of Transmission in Optical Networks. *Entropy* **2021**, *23*, 7.
https://doi.org/10.3390/e23010007

**AMA Style**

Kozdrowski S, Cichosz P, Paziewski P, Sujecki S.
Machine Learning Algorithms for Prediction of the Quality of Transmission in Optical Networks. *Entropy*. 2021; 23(1):7.
https://doi.org/10.3390/e23010007

**Chicago/Turabian Style**

Kozdrowski, Stanisław, Paweł Cichosz, Piotr Paziewski, and Sławomir Sujecki.
2021. "Machine Learning Algorithms for Prediction of the Quality of Transmission in Optical Networks" *Entropy* 23, no. 1: 7.
https://doi.org/10.3390/e23010007