In this paper, we propose a semi-supervised classifier termed as Fast Laplacian Twin Support Vector Machine (FLap−TWSVM) with an objective to reduce the requirement of labeled data and simultaneously lessen the training time complexity of a traditional Laplacian Twin Support Vector Machine semi-supervised classifier. FLap−TWSVM is faster than existing Laplacian twin support vector machine as it solves a smaller size Quadratic Programming Problem (QPP) along with an Unconstrained Minimization Problem (UMP) to obtain decision hyperplanes which can also handle heteroscedastic noise present in the training data. Traditional semi-supervised classifiers generally have no explicit control over the choice of labeled data available for training, hence to overcome this limitation, we propose a pool-based active learning framework which identifies most informative examples to train the learning model. Moreover, the aforementioned framework has been extended to deal with multi-category classification scenarios. Several experiments have been performed on machine learning benchmark datasets which proves the utility of the proposed classifier over traditional Laplacian Twin Support Vector Machine (Lap−TWSVM) and active learning based Support Vector Machine (SVMAL). The efficacy of the proposed framework has also been tested on human activity recognition problem and content based image retrieval system.