What are the equations involved in calculation of the parameters of embedding layer?

Like all hidden layers in a neural network, an embedding layer can be thought of as a feature extractor with parameters that are automatically learned during training. So, like any other layer, the parameters are adjusted during training by the backpropagation algorithm.

The specific equations used to compute error gradients and update weights are likely to depend on the optimizer used to train the network. The classic optimizer is stochastic gradient descent, but more sophisticated optimizers like Adagrad, RMSProp, and ADAM are commonly used nowadays.