We are currently developing our own machine learning platform with an emphasis on text mining and we are looking for a reproducible methodology to implement backpropagation.
I'd recommend, for easier implementation, you outline the problem you need to solve, use a flowchart if possible or any diagramming tool to draw the flow you wish to attain, afterwards you put down the pseudocode of the implementation.. By so doing, you'll have a firm understanding of the final implementation when writing the program on any language.. I believe the routine can be done with any programming language you're very familiar with and not just learning a new one..
Note: The final implementation must follow the back propagation principle for artificial neural network...
Thanks.
For further reading: http://ieeexplore.ieee.org/abstract/document/298623/
I am sharing a PDF with this answer. This is the best way to implement backpropagation in a vectorized manner. Make sure you know how to use inbuilt libraries for optimization algorithms.