Clustering algorithms have been shown to be useful to explore large-scale gene expression profiles. Visualization and objective evaluation of clusters are two important considerations when users are selecting different clustering algorithms, but they are often overlooked. The developments of a framework and software tools that implement comprehensive data visualization and objective measures of cluster quality are crucial. In this paper, we describe a theoretical framework and formalizations for consistently developing clustering algorithms. A new clustering algorithm was developed within the proposed framework. We demonstrate that a theoretically sound principle can be uniformly applied to the developments of cluster-optimization function, comprehensive data-visualization strategy, and objective cluster-evaluation measures as well as actual implementation of the principle. Cluster consistency and quality measures of the algorithm are rigorously evaluated against those of popular clustering algorithms for gene expression data analysis (K-means and self-organizing maps), in four data sets, yielding promising results.