We propose an adaptation of a convolutional neural network (CNN) scheme proposed for segmenting brain lesions with considerable mass-effect, to segment white matter hyperintensities (WMH) characteristic of brains with none or mild vascular pathology in routine clinical brain magnetic resonance images (MRI). This is a rather difficult segmentation problem because of the small area (i.e., volume) of the WMH and their similarity to non-pathological brain tissue. We investigate the effectiveness of the 2D CNN scheme by comparing its performance against those obtained from another deep learning approach: Deep Boltzmann Machine (DBM), two conventional machine learning approaches: Support Vector Machine (SVM) and Random Forest (RF), and a public toolbox: Lesion Segmentation Tool (LST), all reported to be useful for segmenting WMH in MRI. We also introduce a way to incorporate spatial information in convolution level of CNN for WMH segmentation named global spatial information (GSI). Analysis of covariance corroborated known associations between WMH progression, as assessed by all methods evaluated, and demographic and clinical data. Deep learning algorithms outperform conventional machine learning algorithms by excluding MRI artefacts and pathologies that appear similar to WMH. Our proposed approach of incorporating GSI also successfully helped CNN to achieve better automatic WMH segmentation regardless of network's settings tested. The mean Dice Similarity Coefficient (DSC) values for LST-LGA, SVM, RF, DBM, CNN and CNN-GSI were 0.2963, 0.1194, 0.1633, 0.3264, 0.5359 and 5389 respectively.