A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem. <s> BIB001 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> The M-ary support vector machine (SVM) is introduced as a nonparameter nonlinear phase noise (NLPN) mitigation approach for the coherent optical systems. The NLPN tolerance of the system can be improved by using the M-ary SVM to conduct nonlinear detection. In this scheme, SVMs with different classification strategies are utilized to execute binary classification for signals impaired by fiber NLPN. Since the separating hyperplane of each SVM is constructed by training data, this scheme is independent from the knowledge of the transmission link. In numerical simulation, the M-ary SVM performs better than the method of amplitude-dependent phase rotation at the transmitter and receiver, as well as the maximum likelihood detection with back rotation. <s> BIB002 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Kernel-based learning (KBL) methods have recently become prevalent in many engineering applications, notably in signal processing and communications. The increased interest is mainly driven by the practical need of being able to develop efficient nonlinear algorithms, which can obtain significant performance improvements over their linear counterparts at the price of generally higher computational complexity. In this article, an overview of applying various KBL methods to statistical signal processing-related open issues in cognitive radio networks (CRNs) is presented. It is demonstrated that KBL methods provide a powerful set of tools for CRNs and enable rigorous formulation and effective solutions to both long-standing and emerging design problems. <s> BIB003 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A support vector machine (SVM)-based data detection is proposed for coherent optical fiber amplitude phase-shift keying (APSK) communication systems where the nonlinear phase noise is the main system impairment. The performances of the detection with SVMs are investigated for three different 16-APSK modulation formats. In addition, three transmission scenarios with dispersion being considered or not are adopted to simulate and analyze the performances. Compared with the traditional two-stage maximum-likelihood detection, the SVM conducts detection without the need to know the information of transmission link, and it gains a relatively large improvement in the nonlinear system tolerance, particularly in the high nonlinear regime. Compared with quadrature amplitude modulation (QAM), the 16-APSK system can increase the nonlinear system tolerance by 4.88 dB at BER 1/4 1E - 3. <s> BIB004 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> The distribution range of fiber-optical is wide, and the alarm information is scattered, the managers cannot monitor on the line fault in real time. The fiber-optical fault diagnosis is difficult, and the traditional diagnosis cannot form an effective fault diagnosis mechanism, the fault diagnosis effect is not satisfying. Large number of fiber-optical data can be used for the fiber-optical fault nodes localization, the fiber-optical fault nodes can be predicted based on the sampled data. For improving the fault diagnosis efficient and effectiveness, an improved fiber-optical fault diagnosis method is proposed based on the support vector machine (SVM) fault feature extraction and data mining. The fault feature of fiber-optical is extracted, and the fault feature matrix is established. With the SVM filter, the redundant data of features are deleted, the computing cost and complexity of fiber-optical fault diagnosis is reduced. According to the relevant principle of SVM, the fiber-optical fault feature classification problem is transformed into a nonlinear programming problem, and the solution is obtained. Finally, the fiber optical fault diagnosis is realized. Simulation result shows that, the improved algorithm is applied in the fiber-optical diagnosis, the fault diagnosis accuracy is improved greatly, and it has strong stability and practicability in application. <s> BIB005 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A machine learning-based classifier, namely SVM, is introduced to create the nonlinear decision boundary in M-ary PSK-based coherent optical system to mitigate NLPN. The maximum transmission distance and LPRD tolerance are improved by 480 km and 3.3 dBm for 8PSK. <s> BIB006 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> In this paper, we propose a novel block-wise detection technique using support vector machine (SVM) to overcome the scintillation noise in free-space optical (FSO) links. Considering that the turbulence fading is of millisecond level and the signalling rates can typically be hundreds of Mbps, the SVM method provides an extremely large data block which is proportional to the bit rates. At the bit rate of 100 Mbps, for example, a block length of 105 bits is reached. Moreover, the calculation of SVM scheme is independent of the channel's turbulence conditions and the received signal models, and requires no knowledge of prior information or heuristic assumptions. Numerical simulations show that the SVM-based detector can mitigate the fading-channel impairments effectively. With the application of the 4-fold cross validation and grid-search, the best SVM parameters can be acquired and adapted to the channel condition dynamically. <s> BIB007 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Abstract An effective machine learning algorithm, the support vector machine (SVM), is presented in the context of a coherent optical transmission system. As a classifier, the SVM can create nonlinear decision boundaries to mitigate the distortions caused by nonlinear phase noise (NLPN). Without any prior information or heuristic assumptions, the SVM can learn and capture the link properties from only a few training data. Compared with the maximum likelihood estimation (MLE) algorithm, a lower bit-error rate (BER) is achieved by the SVM for a given launch power; moreover, the launch power dynamic range (LPDR) is increased by 3.3 dBm for 8 phase-shift keying (8 PSK), 1.2 dBm for QPSK, and 0.3 dBm for BPSK. The maximum transmission distance corresponding to a BER of 1 × 10 − 3 is increased by 480 km for the case of 8 PSK. The larger launch power range and longer transmission distance improve the tolerance to amplitude and phase noise, which demonstrates the feasibility of the SVM in digital signal processing for M -PSK formats. Meanwhile, in order to apply the SVM method to 16 quadratic amplitude modulation (16 QAM) detection, we propose a parameter optimization scheme. By utilizing a cross-validation and grid-search techniques, the optimal parameters of SVM can be selected, thus leading to the LPDR improvement by 2.8 dBm. Additionally, we demonstrate that the SVM is also effective in combating the laser phase noise combined with the inphase and quadrature (I/Q) modulator imperfections, but the improvement is insignificant for the linear noise and separate I/Q imbalance. The computational complexity of SVM is also discussed. The relatively low complexity makes it possible for SVM to implement the real-time processing. <s> BIB008 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A support vector machine (SVM)-based data detection for 8-superposed pulse amplitude modulation in visible light communication is proposed and experimentally demonstrated. In this work, the SVM detector contains three binary classifiers with different classification strategies. And the separating hyperplane of each SVM is constructed by training data. The experiment results show that the SVM detection offers 35% higher data rates when compared with the traditional direct decision method. <s> BIB009 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A novel blind nonlinear equalizer (BNLE) based on support vector machines is experimentally demonstrated for ~41-Gb/s 16-QAM CO-OFDM at 2000 km. For 2 dBm launched optical power, BNLE reduces the fiber nonlinearity penalty by ~1 dB compared to Volterra-based NLE. <s> BIB010 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A support vector machine (SVM)-based classification nonlinear equalizer (NLE) is demonstrated, for the first time, in coherent optical orthogonal frequency-division multiplexing (CO-OFDM). For a 40-Gb/s 16 quadrature amplitude modulated (16QAM) CO-OFDM system at 400 km of transmission, SVM-NLE reduces the fiber-induced nonlinearity penalty by about 1 dB in comparison to the benchmark artificial-neural-network (ANN)-based and inverse-Volterra-series-transfer-function-based NLEs. <s> BIB011 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> It is a key requirement for any perimeter intrusion detection system to distinguish the intrusion from environmental events without reducing the efficiency. We implement and demonstrate a fiber optic perimeter detection system, which screens the event signal by its features in frequency domain. These features are extracted by method of principal component analysis (PCA) and then identified by support vector machine (SVM). Experimental results show that the combination of PCA and SVM improve evidently the anti-disturbance ability. <s> BIB012 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> We demonstrate the applications of machine-learning based DSP methods in short reach optical interconnection system. The machine-learning algorithms including mainly support vector machine (SVM) provides an effective recipe for distorted signal in PAM and CAP optical interconnect systems. <s> BIB013 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Linear signal processing algorithms are effective in dealing with linear transmission channel and linear signal detection, whereas the nonlinear signal processing algorithms, from the machine learning community, are effective in dealing with nonlinear transmission channel and nonlinear signal detection. In this paper, a brief overview of the various machine learning methods and their application in optical communication is presented and discussed. Moreover, supervised machine learning methods, such as neural networks and support vector machine, are experimentally demonstrated for in-band optical signal to noise ratio estimation and modulation format classification, respectively. The proposed methods accurately evaluate optical signals employing up to 64 quadrature amplitude modulation, at 32 Gbd, using only directly detected data. <s> BIB014 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> An effective bit-based support vector machine (SVM) is proposed as a non-parameter nonlinear mitigation approach in the millimeter-wave radio-over-fiber (RoF) mobile fronthaul (MFH) system for various modulation formats. First, we analyze the impairments originated from nonlinearities in the millimeter-wave RoF system. Then we introduce the operation principle of the bit-based SVM detector. As a classifier, the SVM can create nonlinear decision boundaries by kernel function to mitigate the distortions caused by both linear and nonlinear noise. In our design, SVM can learn and capture the link characteristics from only a few training data without requiring the prior estimation of the system link. The bit-based SVM only needs log2M SVMs to detect the signal of M-order modulation format. Experimental results have been obtained to verify the feasibility of the proposed method. The sensitivities are improved by 1.2-dB for 16-QAM, 1.3-dB for 64-QAM, 1.8-dB for 16-APSK and 1.3-dB for 32-APSK at BER = 1E-3 with SVM detector, respectively. The proposed bit-based SVM gains a large improvement in the nonlinear system tolerance and outperforms the system employing k-means algorithm. <s> BIB015 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> In this work, we firstly apply support vector machine (SVM) detector in 122-Gbps Multi-CAP system. It can de-map the rotated constellations directly without any correction. The concrete simulations indicate such a machine-learning based detector provides considerable BER reduction for high-density CAPs in low-frequency band, compared with hard decision. <s> BIB016 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> An equalization algorithm is proposed for carrier-less amplitude and phase (CAP) modulation system, which is regarded as a good candidate for short range optical communications, like electrical power optical fiber communication, optical access network. The constant module algorithm (CMA) combined with support vector machine (SVM) performs the equalization function. The simulation system was setup for both single-band 16-CAP signal at 10Gbps and multi-band M-CAP (4-CAP, 16-CAP, 64-CAP) signal at 100Gbps. After the CMA-SVM equalization, the impaired CAP signals are compensated effectively. The phase rotation is recovered and the centralization of each constellation points is improved obviously, which demonstrate the feasibility of the proposed equalization algorithm. <s> BIB017 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A support vector machine (SVM)-based data detection for 8-superposed pulse amplitude modulation and direct-current-biased optical orthogonal frequency division multiplexing in visible light communication is proposed and experimentally demonstrated. In this work, the SVM detector contains multiple binary classifiers with different classification strategies. The separating hyperplane of each SVM is constructed by means of the training data. The experiment results presented that the SVM detection offers improved bit error rate performance compared with the traditional direct decision method. <s> BIB018 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> We applied genetic algorithm to optimize the parameters of support vector machine for improving prediction accuracy. The proposed method is measured experimentally in 16-QAM coherent communication system for mitigating the fiber-nonlinearity-induced impairments. <s> BIB019 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> The $\nu $ -support vector classification has the advantage of using a regularization parameter $\nu $ to control the number of support vectors and margin errors. Recently, a regularization path algorithm for $\nu $ -support vector classification ( $\nu $ -SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for $\nu $ -SVC and, then, propose a robust $\nu $ -SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does. <s> BIB020 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A novel quality of transmission (QoT) estimator based on support vector machines (SVM) is proposed for classifying optical connections (lightpaths) into high or low quality categories in impairment-aware wavelength-routed optical networks (WRONs). The performance of the SVM-based estimator is evaluated in a long haul communications network and compared to previous semi-analytical and cognitive proposals. Results show that the SVM approach significantly reduces the necessary computing time to estimate the QoT of a given lightpath, critical aspect of design in these networks, and even slightly improves accuracy. <s> BIB021 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> In this paper, we propose a performance monitoring and failure prediction method in optical networks based on machine learning. The primary algorithms of this method are the support vector machine (SVM) and double exponential smoothing (DES). With a focus on risk-aware models in optical networks, the proposed protection plan primarily investigates how to predict the risk of an equipment failure. To the best of our knowledge, this important problem has not yet been fully considered. Experimental results showed that the average prediction accuracy of our method was 95% when predicting the optical equipment failure state. This finding means that our method can forecast an equipment failure risk with high accuracy. Therefore, our proposed DES-SVM method can effectively improve traditional risk-aware models to protect services from possible failures and enhance the optical network stability. <s> BIB022 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Abstract Vertical cavity surface emitting lasers (VCSELs) based optical interconnect is evolving to 100 Gb/s and beyond. Penalties due to relative intensity noise and mode partition noise become significant and cannot be compensated or equalized by conventional equalizer. As one of the machine learning based DSP algorithms, support vector machine based nonlinear equalizer (SVM-NLE) has been proposed for VCSEL based optical interconnect links recently and was proved having an excellent capability of mitigating the modulation nonlinearity. In this paper, we propose a feature enhancement method for SVM-NLE by means of sinc interpolation and the performance of the new SVM-NLE in the VCSEL based optical link transmission experiment is evaluated under different parameter settings and training strategies at 60 Gb/s transmission rate. At least 3.5 dB performance improvements can be derived by our proposal compared with the conventional method. In addition, error free 40 Gb/s transmission is realized with the aid of the new SVM-NLE. Its complexity is also theoretically analyzed from the perspective of AISC design, which is shown controllable and acceptable for an appropriate optical link bandwidth design. <s> BIB023 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> A novel blind nonlinear equalization (BNLE) technique based on the iterative re-weighted least square is experimentally demonstrated for single- and multi-channel coherent optical orthogonal frequency-division multiplexing. The adopted BNLE combines, for the first time, a support vector machine-learning cost function with the classical Sato or Godard error functions and maximum likelihood recursive least-squares. At optimum launched optical power, BNLE reduces the fiber nonlinearity penalty by ~1 (16-QAM single-channel at 2000 km) and ~1.7 dB (QPSK multi-channel at 3200 km) compared to a Volterra-based NLE. The proposed BNLE is more effective for multi-channel configuration: 1) it outperforms the “gold-standard” digital-back propagation and 2) for a high number of subcarriers the performance is better due to its capability of tackling inter-subcarrier four-wave mixing. <s> BIB024 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Fiber-induced intra- and interchannel nonlinearities are experimentally tackled using blind nonlinear equalization (NLE) by unsupervised machine-learning-based clustering (MLC) in ∼46-Gb/s single-channel and ∼20-Gb/s (middle-channel) multichannel coherent multicarrier signals (orthogonal frequency-division multiplexing (OFDM) based). To that end, we introduce, for the first time, hierarchical and fuzzy-logic C -means (FLC)-based clustering in optical communications. It is shown that among the two proposed MLC algorithms, FLC reveals the highest performance at optimum launched optical powers (LOPs), while at very high LOPs, hierarchical can compensate more effectively nonlinearities only for low-level modulation formats. When employing binary phase-shift keying and quaternary phase-shift keying, FLC outperforms K-means, fast-Newton support vector machines, supervised artificial neural networks, and NLE with deterministic Volterra analysis. In particular, for the middle channel of a QPSK wavelength-division multiplexing coherent optical OFDM system at optimum −5 dBm of LOP and 3200 km of transmission, FLC outperforms Volterra-NLE by 2.5 dB in Q-factor. However, for a 16-QAM single-channel system at 2000 km, the performance benefit of FLC over inverse Volterra-series transfer function reduces to ∼0.4 dB at a LOP of 2 dBm (optimum). Even when using novel sophisticated clustering designs in 16 clusters, no more than additional ∼0.3-dB Q-factor enhancement is observed. Finally, in contrast to the deterministic Volterra-NLE, MLC algorithms can partially tackle the stochastic parametric noise amplification . <s> BIB025 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Abstract High-order modulation signals are suited for high-capacity communication systems because of their high spectral efficiency, but they are more vulnerable to various impairments. For the signals that experience degradation, when symbol points overlap on the constellation diagram, the original linear decision boundary cannot be used to distinguish the classification of symbol. Therefore, it is advantageous to create an optimum symbol decision boundary for the degraded signals. In this work, we experimentally demonstrated the 64-quadrature-amplitude modulation (64-QAM) coherent optical communication system using support-vector machine (SVM) decision boundary algorithm to create the optimum symbol decision boundary for improving the system performance. We investigated the influence of various impairments on the 64-QAM coherent optical communication systems, such as the impairments caused by modulator nonlinearity, phase skew between in-phase (I) arm and quadrature-phase (Q) arm of the modulator, fiber Kerr nonlinearity and amplified spontaneous emission (ASE) noise. We measured the bit-error-ratio (BER) performance of 75-Gb/s 64-QAM signals in the back-to-back and 50-km transmission. By using SVM to optimize symbol decision boundary, the impairments caused by I/Q phase skew of the modulator, fiber Kerr nonlinearity and ASE noise are greatly mitigated. <s> BIB026 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Filter cascading effects are identified and compensated in flexible coherent multi-carrier optical networks using, for the first time, a complex-valued support vector machine (C-SVM) non-linear equaliser which is compared to phase-conjugated subcarrier-coding (PC-SC)-based non-linearity compensation. The transmission performance of super-channel-based dual-polarisation coherent multi-band optical OFDM (DP-MB-OFDM) is analysed in a flexible network with two-stage wavelength selective-switch reconfigurable optical add-drop multiplexer for coarse and fine switching granularity. It is shown that filter cascading effects have significant impact only on edge OFDM sub-bands. On the other hand, C-SVM outperforms PC-SC resulting in an extension of the transmission-reach, for instance, by 420 km when employing 32-quadrature amplitude modulation at a targeted bit-error-rate of 10−3. This occurs since C-SVM can compensate more effectively stochastic-induced nonlinear cross-talk effects. Moreover, the interplay between polarisation-mode dispersion (PMD) and fibre non-linearity is also investigated in DP-MB-OFDM, revealing that a high PMD causes time fluctuation on the non-linear interaction affecting the balance of the ‘twin-subcarriers’ in PS-SC. <s> BIB027 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Abstract This paper proposes a method of blind modulation format identification using decision tree twin support vector machine classifier trained with the features extracted from the high-order cumulant and cyclic spectrum after compressed sensing in order to solve the problem of identification efficiency and computing speed and reduce the performance requirements of the sampling system in low optical signal to noise ratio. By reconstructing the feature parameters of fourth-order, eighth-order cumulants and cyclic spectrum under the theory of compressed sensing, and introducing the decision tree twin support vector machine classifier to achieve high-precision classification, the different modulation formats of amplitude shift keying, multiple phase-shift keying and multiple quadrature amplitude modulation are effectively identified. Simulation analysis of the influence of identification accuracy and identification time improves the identification performance and achieves the purpose of identifying more signals with fewer feature parameters. The results indicate that the average identification accuracy of the optical modulation format signals can be achieved over 94% when the OSNR is -5dB, and the identification time is 4.3 times higher than the standard SVM. Owing to its excellent performance, this method can be employed in the next generation optical transport network for auto-adaption real-time modulation format identification. <s> BIB028 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> A. Support Vector Machine <s> Abstract High-order quadrature amplitude modulation (QAM) formats are very effective for increasing the transmission capacity due to the highly increased spectral efficiency. However, the signal-to-noise-ratio (SNR) hungry and dense constellation of QAM make it very sensitive to nonlinear distortion. The nonlinear decision boundary adaptively generated by machine learning method of support vector machine (SVM) can be effectively used for the classification of the symbols. The different classification methods have different performance in terms of classification complexity. We experimentally investigated five SVM multi-classification methods for machine learning assisted adaptive nonlinear mitigation, including the one versus rest (OvR), the symbol encoding (SE), the binary encoding (BE), the constellation rows and columns (RC), and the in-phase and quadrature components (IQC). The comprehensive results with comparisons are demonstrated, indicating significant nonlinear mitigation with BER reductions. The SVM multi-classifier based on the in-phase and quadrature components is relatively optimal, considering the calculation and storage. <s> BIB029
Definition: A Support Vector Machine (SVM) is a discriminative classifier, which based on the input labeled data generates an optimal separating hyperplane that divides input data in two classes ( Fig.1.a) . There is no separating hyperplane for nonlinear combination of input data classes ( Fig.1.b) , so, the data should be mapped to higher dimensions to find the separating hyperplane ( Fig.1.c) . This technique is called kernel that acts as a nonlinear SVM (Fig.1.d) . Depending on the input data type, there are various kernels that could be used (e.g., linear, polynomial, exponential, etc.). Linear kernel calculate separating hyperplane in lower dimensions, while polynomial and exponential kernels calculate separating hyperplane. These three kernels are in the following form: ( , ) = (− ∑ ( -)). where 0 and are defined based on training data, <. > is dot production, is new input, and is support vector. Increasing dimension is only useful for nonlinear data structures; but for situations that two data sets have overlap, the degree of SVM model should be increased. So, two options are available; tolerating some outlier points ( Fig. 2 .a) or perfect partitioning ( Fig. 2.b) . The second one is called regularization trick, which uses a regularization parameter to tell the amount of avoided misclassification of each training example. Large regularization parameter ( Fig. 2 .c) has a smaller-margin hyperplane if that hyperplane does a better job of getting all the training points classified correctly, and an inverse will be held for small regularization parameters ( Fig. 2.d) . Selecting a good margin (separating line), which could separate classes better, is very important. A good margin allows the points to be in their respective classes without crossing to other class ( Fig.3.a) , and a bad margin is reverse ( Fig.3.b) [1]. Fiber OC: The SVM, due to its simplicity, is one of the most widely used algorithms in ML for OC. SVM is shown to be powerful for combatting NLPN BIB006 BIB004 BIB002 , laser phase noise BIB008 , modulator nonlinearity BIB013 , phase skew and modulator imperfections between in-phase and quadrature BIB008 , fiber Kerr effect, Amplified Spontaneous Emission (ASE) noise, and dealing with linear/non-linear channel/signal detection BIB014 . SVM could be used anywhere that exist two or multiple distinct groups of data. For example for classification of the received bit sequences to 0 and 1, or classification of normal fiber and fault encountered fiber BIB005 . Its procedure is simple, it collects data from the distinct categories and learns how to classify them from extracted features. Generally speaking, SVM has lower complexity BIB009 , because it does not consider the hole data, it just searches for hyperplane based on marginal data. Furthermore, with SVM, the redundant features could be deleted, so, the computing cost and complexity would be reduced. Although, SVM leads to the transmission delay due to use of the training data, it has low delay in the testing phase (when separating hyperplane is defined). In addition to complexity reduction, SVM could do well some applications, in which traditional techniques are not effective, e.g. forming an effective fault diagnosis, but, SVM solves it properly by transforming the classification problem into a nonlinear programming problem BIB005 . Fortunately, despite other ML algorithms, there are many SVM based investigations in ML for OC, so these works could be classified in a better way. One of the most widely used applications of SVM in OC is detection, which has mostly shielded on Fiber OC, and there are few implementations in WOC applications. Actually, SVM is a binary classifier, which can only be used for binary signaling not M-ary signaling. In order to solve this issue, should construct hyperplane (instead of one hyperplane), one of the efficient M-ary SVM solutions is the bit-based SVM, which only needs log 2 ( ) SVMs (hyperplane) for M-ary signaling detection BIB015 . Another M-ary SVM technique is decision tree, which transforms an M-ary and complex multi-class classification problem into binary and multi-layer classification problem (Fig.4 .a, b) BIB028 . SVM does not require information about the transmission link and has a relatively large improvement especially in high nonlinearity BIB004 , and it is shown that M-ary SVM can perform better than ML detection with back rotation BIB002 . The higher order modulations (dense constellations) have high capacity, and spectral efficiency, but are sensitive to various faults, and cannot be classified by linear decision boundary (binary classification). Noisy signals have always worse constellations, because they are widely scattered and their boundaries are ambiguous. SVM is able to directly de-map the rotated constellation and has low complexity for making decision. For noisy constellations which are highly overlapped, the standard SVM could hardly create proper decision boundaries, the available extended SVMs are somehow complex and require simplification. Carrier less amplitude phase (CAP) modulation is good for short-range communication links. Results indicate that SVM based detector BIB016 , and equalizer (based on constant module algorithm (CMA)) BIB013 BIB017 in highdensity CAP OC, has performance improvement over traditional techniques BIB016 . In addition to detection, SVM is widely used for equalizing linear and nonlinear effects of fiber propagation media BIB023 . Convolutional equalizers could not compensate these issues because of relative intensity noise and mode partition noise of vertical cavity surface emitting laser (VCSEL) based optical interconnect links. This caused especially that higher order modulations be practically limited. However, this problem solved by M-ary SVM methods such as one versus rest ( Fig.  5.a) , symbol encoding, binary encoding ( Fig. 5.b) , and in-phase and quadrature components (Fig.5.c) BIB029 . The SVM based nonlinear equalizers (NLE)s are only implemented in Fiber OC BIB023 ; however, they could be considered for the same task in WOC systems in future researches. The blind spot of SVM is the insufficiency of features; this issue could be solved by feature enhancement methods such as sync interpolation. However, feature enhancement decreases SVM speed; this issue could be solved using Newton based SVM, which reduces classifier complexity, and computational load [16] . An SVMbased NLE could be applied to single/multi-channel WDM and OFDM BIB010 systems for increasing nonlinearity tolerance in long-range communication BIB011 . It could tackle deterministic fiber nonlinearity and the interaction between nonlinear effects and stochastic noises, as well as inter-subcarrier nonlinear crosstalk effects. The fiber effects are really hard to be modeled, therefore, the detection and equalization should be done blindly or approximately. NLE/Blind NLE reduces the fiber nonlinearity penalty and increases data rate compared with inverse Volterra series transfer function (IVSTF) NLE. Combining the SVM cost function with Sato and Godard error functions and then minimizing the obtained cost function using iterative algorithms, e.g. least squares (LS) BIB010 or weighted least square (WLS) BIB024 , releases a new version of SVM which could be used for Blind NLE. This technique better reduces nonlinearity compared to IVSTF NLE, and is a bbeter choice for multi-channel configuration. The investigated SVM based detection, and equalization techniques used binary or M-ary SVMs. SVM is a linear classifier, and is not suitable for nonlinear input features (e.g. in classifying filter cascading effects); for solving this issue, a mapping should be done from the feature space to the so called kernel space, in which features could be separated linearly BIB025 . Kernel based SVM has recently become more popular, because it helps linear algorithm to be deployed non-linearly, and obtain significant performance improvements with higher complexity. It has a flexible decision boundary, because any desired boundary shapes can be created utilizing Gaussian radial basis function (RBF) BIB026 . Besides SVM, other kernel methods include kernel linear discriminant analysis (Fig.6 .a.), kernel K-means clustering (Fig.6 .b.), kernel PCA (Fig.6.c) , and kernel online learning (Fig.6 .d.) BIB003 . However, due to the youth of the subject kernel based SVM is only investigated in combating filter cascading effects. Filter cascading leads to enhance stop band rejection and steepness of transition band. However, they affect edge sub-channels of the OFDM super-channel. It is important to identify and compensate them; previously, these were done by phase-conjugated subcarrier coding based nonlinearity compensation technique, now, these could be done using a complex-valued kernel based SVM BIB027 . In addition to compensation of filter cascading effects, complex-valued SVM could also be used in order to compensate stochastic induced nonlinear cross-talk effects BIB018 . The same as SVM, kernel based SVM has better performance than traditional direct decision method. In addition to use of techniques such as bit based or kernel based SVM, which are related to the data structure, some other techniques could be used (for improving performance) that are related to the structure of SVM. Actually SVM has some hyperparameters, which tuning them would result in better performance for the same data. One of the well-known techniques is Genetic algorithm (GA) (Fig.7 .a), which despite its performance, has high computational load, and dependent on the situation (e.g. time demanding applications), might not be preferable BIB019 . Furthermore, for improper fiber nonlinearity, in which the fiber nonlinear interaction and ASE noise expand considerably, the effect of SVM and GA-SVM are similar. Other tuning techniques such as manual search, grid-search, and random search (Fig.7 .c) in cross-validation ( Fig.7.b) phase, the optimal parameters of SVM could be selected. The bit, kernel, PCA, tuning based SVM, all have one important barrier, and that is un-flexibility on number of support vectors. Regularized SVM controls number of support vectors and margin errors by adding a regularization parameter to the cost function BIB020 . The same as SVM, this could be solved using the dual problem; first an equivalent dual formulation for regularized SVM should be constructed, then solved by a robust regularized SVM based on lower-upper decomposition with partial pivoting. The discussed SVMs all assumed input vectors to be independent, so, they are not appropriate for dealing with inter symbol interference (ISI) applications. For considering this issue, decision feedback based SVM could be used, which considers the temporal correlation between input vectors in the presence of ISI. Further the pattern space viewpoint of the problem illustrates benefit of a bank of SVM. This technique could robustly address nonlinearities in the presence of ISI BIB001 . Network: After detection and equalization, the third important application of SVM is optical link failures prediction/ detection, as well as quality of transmission (QoT) estimation BIB021 . Because SVM could learn optical link properties with a few training data, and without any prior information or heuristic assumptions. The results indicated efficiency of SVM in reducing the computation time. Detection the intrusion of environmental events while keeping the efficiency is important in perimeter intrusion detection in optical links. In this situation, common extracted features might not be so helpful, because they might be contaminated with noise. Usually, in this situations PCA could be a better choice for extracting features. PCA reorders the features based on their variance, and removes the low variance features assuming them as noise. The PCA based SVM could be applied in perimeter intrusion detection BIB012 . In addition, an accurate equipment failure risk prediction effectively improves the optical network stability. In addition to traditional methods, such as double exponential smoothing, ML algorithms, such as SVM could be effectively used to improve the accuracy of models for failure prediction, in an optical network BIB022 . WOC: ML techniques are at the beginning of deployment over WOC systems; this is simply because of lack of joint experts on WOC and ML. SVM is mostly shielded on Fiber OC, and there are few implementations in WOC applications such as VLC BIB009 , and FSO BIB007 . The WOC signaling rates are typically Gb/s, and duration of link atmospheric turbulence is on the order of millisecond. The SVM detection could provide a large data block and proportionally a high bit rate BIB009 BIB007 . 