This article presents a machine learning methodology for diagnosing Parkinson's disease (PD) based on the use of vertical Ground Reaction Forces (vGRFs) data collected from the gait cycle. A classification engine assigns subjects to healthy or Parkinsonian classes. The diagnosis process involves four steps: data pre-processing, feature extraction and selection, data classification and performance evaluation. The selected features are used as inputs of each classifier. Feature selection is achieved through a wrapper approach established using the random forest algorithm. The proposed methodology uses both supervised classification methods including K-nearest neighbour (K-NN), decision tree (CART), random forest (RF), Naïve Bayes (NB), support vector machine (SVM) and unsupervised classification methods such as K-means and the Gaussian mixture model (GMM). To evaluate the effectiveness of the proposed methodology, an online dataset collected within three different studies is used. This data set includes vGRFs measurements collected from eight force sensors placed under each foot of the subjects. 93 patients suffering from Parkinson's disease and 72 healthy subjects participated in the experiments. The obtained performances are compared with respect to various metrics including accuracy, precision, recall and F-measure. The classification performance evaluation is performed using the Leave-one-out cross validation. The results demonstrate the ability of the proposed methodology to accurately differentiate between PD subjects and healthy subjects. For the purpose of validation, the proposed methodology is also evaluated with an additional dataset including subjects with neurodegenerative diseases (Amyotrophic Lateral Sclerosis (ALS) and Huntington's disease (HD)). The obtained results show the effectiveness of the proposed methodology to discriminate PD subjects from subjects with other neurodegenerative diseases with a relatively high accuracy.