In a cognitive, heterogeneous, optical network, it would be important to identify physical layer information, especially the modulation formats of transmitted signals. The modulation format information is also indispensable for carrier-phase-recovery in a coherent optical receiver. Because constellation diagrams of modulation signals are susceptible to various noises, we utilize a convolutional neural network to process the amplitude data after the modulation-format-agnostic clock recovery. Furthermore, for the carrier-phase-recovered data, we use the clustering method based on a fast search and find the density peaks to classify the constellation clusters and use the k-nearest-neighbor method to label the samples. The proposed receiver system has a simple architecture to identify the modulation format based on the amplitude information and can track fast changes of the signals to improve the accuracy of the symbol decision. We have demonstrated this experimentally and have achieved remarkable BER improvement.