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Visualization techniques often use color to present categorical differences to a user. When selecting a color palette, the perceptual qualities of color need careful consideration. Large coherent groups visually suppress smaller groups and are often visually dominant in images. This paper introduces the concept of class visibility used to quantitatively measure the utility of a color palette to present coherent categorical structure to the user. We present a color optimization algorithm based on our class visibility metric to make categorical differences clearly visible to the user. We performed two user experiments on user preference and visual search to validate our visibility measure over a range of color palettes. The results indicate that visibility is a robust measure, and our color optimization can increase the effectiveness of categorical data visualizations.