The Self-Organizing Map algorithm has been proven and demonstrated to be a useful paradigm for unsupervised machine learning of two-dimensional projections of multidimensional data. The tri-state Self-Organizing Maps have been proposed as an accelerated resource-efficient alternative to the Self-Organizing Maps for implementation on field-programmable gate array (FPGA) hardware. This paper presents a generalization of the tri-state Self-Organizing Maps. The proposed generalization, which we call integer Self-Organizing Maps, requires only integer operations for weight updates. The presented experiments demonstrated that the integer Self-Organizing Maps achieve better accuracy in a classification task when compared to the original tri-state Self-Organizing Maps.