The accumulation and use of data are rapidly expanding. With it, new kinds of interactions emerge that go beyond traditional data analytics, to the point at which a whole new research area of human-data interaction is has been suggested. Our study reconsiders cluster analysis from this point of view. We aim to redesign the process to be more interactive and transparent for purposes beyond conventional data analysis. We address the core issue of cluster analysis, namely what criteria are to determine the homogeneity of a cluster by means of breaking the algorithm into a sequence of explorative subdivisions proceeding as a human-data dialogue. The system provides the human agent with a heuristic. It is formed by sorting the variables of the data set by descending orthogonality against the variable that was applied as the subdivision criterion of the previous iteration. This allows minimizing redundancy of the analysis while securing distinctions relevant for the analytic intention and contextuality, which go beyond the reach of algorithmic decision. The proposed method constitutes a quick and intuitive access to data mining, facilitating new insights and identifying actionable generalizations.