Given the challenge of gathering labelled training data for machine learning tasks, active learning has become popular. This paper focuses on the beginning of unsupervised active learning, where there are no labelled data at all. The aim of this zero initialised unsupervised active learning is to select the most informative examples - even from an imbalanced dataset - to be labelled manually. Our solution with proposed selection strategy, called Optimally Balanced Entropy-Based Sampling (OBEBS) reaches a balanced training set at each step to avoid imbalanced problems. Two theorems of the optimal solution for selection strategy are also presented and proved in the paper. At the beginning of the active learning, there is not enough information for supervised machine learning method, thus our selection strategy is based on unsupervised learning (clustering). The cluster membership likelihoods of the items are essential for the algorithm to connect the clusters and the classes, i.e., to find assignment between them. For the best assignment, the Hungarian algorithm is used, and single, multi, and adaptive assignment variants of OBEBS method are developed. Based on generated and real images datasets of handwritten digits, the experimental results show that our method surpasses the state-of-the-art methods.