A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> C. Principle Component Analysis <s> We propose a novel technique for simultaneous multi-impairment monitoring and autonomous bit-rate and modulation format identification (BR-MFI) in next-generation heterogeneous fiber-optic communication networks by using principal component analysis-based pattern recognition on asynchronous delay-tap plots. The results of numerical simulations performed for three commonly used modulation formats at two different bit-rates each demonstrate simultaneous and independent monitoring of optical signal-to-noise ratio, chromatic dispersion, and differential group delay with mean errors of 1 dB, 4 ps/nm, and 1.6 ps, respectively, without knowing the signal's bit-rate and modulation format. Similarly, the results for joint BR-MFI validate accurate identification of all the bit-rates and modulation formats despite the presence of various network impairments. The effects of fiber nonli-nearity and transmitter variations on the performance of the proposed technique are also investigated. <s> BIB001 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> C. Principle Component Analysis <s> In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be used to further understand the method, formulate possible extensions, and properly address them. As an example, a new convex optimization problem for semisupervised classification is proposed, which seems particularly well suited whenever the number of known labels is small. Our formulation resembles a least squares support vector machine problem with a regularization parameter multiplied by a negative sign, combined with a variational principle for KPCA. Our primal optimization principle for semisupervised learning is solved in terms of the Lagrange multipliers. Numerical experiments in several classification tasks illustrate the performance of the proposed model in problems with only a few labeled data. <s> BIB002 </s> A Survey on Machine Learning for Optical Communication [Machine Learning View] <s> C. Principle Component Analysis <s> Optical spectrum (OS) is a vital characteristic of optical signals. Ultra-high resolution (UHR) OS can provide more detailed and accurate information for optical performance monitoring and optical link quality diagnosis. By comparing actual signal UHR-OS observed at in-line monitoring points with the theoretical ideal ones, various signal distortions can be readily identified and more accurately estimated. But in the future flexible heterogeneous optical networks optical signals with different symbol rates, modulation formats and pulse shaping schemes may coexist in the same system. Hence the ideal reference OS of the channel to be monitored can’t be assumed to be fixed or known in advance. It may also be impossible to undertake a reference OS measurement at or near the transmitter as the route path may be dynamically generated. To solve this problem we proposed an automatic ideal reference optical spectrum retrieval (OSR) method according to the actually observed ones. The OSR method can tolerate large OS distortions due to non-ideal optical links or transmitters by the integration of two machine learning techniques, namely unsupervised principle component analysis (PCA) and supervised multiclass support vector machines (SVMs) for feature extraction and UHR-OS classification, respectively. Extensive simulations conducted for nine types of optical signals commonly used show that this method performs very well in the presence of various significant distortions caused by non-ideal optical links or transmitters. <s> BIB003
Definition: PCA is an orthogonal transformation of possibly correlated data into a linearly uncorrelated data entitled principal components. The first component of PCA has higher variance, and each succeeding component in turn has the higher variance and is orthogonal to the preceding components. This transformation could be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix. Considering a set of input data as { 1 , 2 , … , }, vector of dimensions, the mean and covariance vectors will be calculates as: where ∑ has eigenvalue ( ) and eigenvectors ( ). PCA sorts eigenvalues, and selects the first eigenvalue ( ≪ ). Fiber OC: PCA is mostly suitable for feature extraction; (considering discussions of previous sections) its main application is in joint monitoring of OSNR, CD, and PMD of different modulation formats and data rates BIB001 . It is proven that PCA could accurately identify the data rates and modulation formats of the signals in the presence of noise, CD, and PMD. Fig.16.a. Lasso, b . Ridge, and c. Bayesian Regression Network: The PCA could be used for arranging priority, and recognizing abnormal or attack flow  . The abnormal attack flow changes the correlation between the flows; PCA extracts the correlation between potential abnormal parts of multiple flows and uses the degree of correlation changes as a measure BIB002 . Optical spectrum (OS) has an important role in optical signal processing, such that ultra-high resolution (UHR)-OS provides more and accurate information about optical link quality. Comparing experimental and theoretical UHR-OS is one way for detecting signal distortions. However, the monitored UHR-OS of the channel might not be fixed or known. Also measuring the ideal UHR-OS at or near the transmitter might be impossible. It is shown that use of PCA for feature extraction from observed OS, and use of SVM for classification, could combat these issues and retrieve UHR-OS BIB003 .