Cluster structure of gene expression data obtained from DNA microarrays is analyzed and visualized with the Self-Organizing Map (SOM) algorithm. The SOM forms a non-linear mapping of the data to a two-dimensional map grid that can be used as an exploratory data analysis tool for generating hypotheses on the relationships, and ultimately of the function of the genes. Similarity relationships within the data and cluster structures can be visualized and interpreted. The methods are demonstrated by computing a SOM of a set of yeast genes of known functional classes. The cluster structure is visualized and the clusters are characterized in terms of the properties of the expression profiles of the genes. Additionally, relationships of the functional classes and division of the classes into subclasses are visualized.