We present a novel technique for pruning called activation-based pruning to effectively prune fully connected feedforward neural networks for multi-object classification. Our technique is based on the number of times each neuron is activated during model training. We compare the performance of activation-based pruning with a popular pruning method: magnitude-based pruning. Further analysis demonstrated that activation-based pruning can be considered a dimensionality reduction technique, as it leads to a sparse low-rank matrix approximation for each hidden layer of the neural network. We also demonstrate that the rank-reduced neural network generated using activation-based pruning has better accuracy than a rank-reduced network using principal component analysis. We provide empirical results to show that, after each successive pruning, the amount of reduction in the magnitude of singular values of each matrix representing the hidden layers of the network is equivalent to introducing the sum of singular values of the hidden layers as a regularization parameter to the objective function.