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 yeast genes. The relationships of known functional classes of genes are investigated by analyzing their distribution on the SOM, the cluster structure is visualized by the U-matrix method, and the clusters are characterized in terms of the properties of the expression profiles of the genes. Finally, it is shown that the SOM visualizes the similarity of genes in a more trustworthy way than two alternative methods, multidimensional scaling and hierarchical clustering.