A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest points for each point inside a database. Their main usage resonates in spatial databases and they consist the backbone of many location-based applications and not only (i.e. $k$NN joins in databases, classification in data mining). So, it is very crucial to develop methods that answer them efficiently. In this work, we propose a novel method for classifying multidimensional data using an A$k$NN algorithm in the MapReduce framework. Our approach exploits space decomposition techniques for processing the classification procedure in a parallel and distributed manner. To our knowledge, we are the first to study the classification of multidimensional objects under this perspective. Through an extensive experimental evaluation we prove that our solution is efficient and scalable in processing the given queries. We investigate many different perspectives that can affect the total computational cost, such as different dataset distributions, number of dimensions, growth of $k$ value and granularity of space decomposition and prove that our system is efficient, robust and scalable.