We define a “good image cluster” as one in which images can be easily composed (like a puzzle) using pieces from each other, while are difficult to compose from images outside the cluster. The larger and more statistically significant the pieces are, the stronger the affinity between the images. This gives rise to unsupervised discovery of very challenging image categories. We further show how multiple images can be composed from each other simultaneously and efficiently using a collaborative randomized search algorithm. This collaborative process exploits the “wisdom of crowds of images”, to obtain a sparse yet meaningful set of image affinities, and in time which is almost linear in the size of the image collection. “Clustering-by-Composition” yields state-of-the-art results on current benchmark data sets. It further yields promising results on new challenging data sets, such as data sets with very few images (where a `cluster model' cannot be `learned' by current methods), and a subset of the PASCAL VOC data set (with huge variability in scale and appearance).