Odors can be defined categorically by their membership in one of 10 perceptual dimensions identified by non-negative matrix factorization (NMF). Left: Matrix of odor weights (H). Each column corresponds to a single monomolecular odorant. Rows are the 10 perceptual dimensions discovered by NMF. Prominent block—diagonal structure suggests that a given odorant is best defined by its membership in one perceptual dimension. Right: two-dimensional embedding of the matrix H, using stochastic neighbor embedding. Each point corresponds to a column of H. Colors indicate clusters identified by eye.