Selecting an optimal set of icons is a crucial step in the pipeline of visual design to structure and navigate through content. However, designing the icons sets is usually a difficult task for which expert knowledge is required. In this work, to ease the process of icon set selection to the users, we propose a similarity metric which captures the properties of style and visual identity. We train a Siamese Neural Network with an online dataset of icons organized in visually coherent collections that are used to adaptively sample training data and optimize the training process. As the dataset contains noise, we further collect human-rated information on the perception of icon's similarity which will be used for evaluating and testing the proposed model. We present several results and applications based on searches, kernel visualizations and optimized set proposals that can be helpful for designers and non-expert users while exploring large collections of icons.