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Hidden Markov models (HMMs) and their variants are capable to classify complex and structured objects. However, one of their major restrictions is their inability to cope with shape or conformation intrinsically: HMM-based techniques have difficulty predicting the n-dimensional shape formed by the symbols of the visible observation (VO) sequence. In order to fulfill this crucial need, we propose a novel paradigm that we named conformation-based hidden Markov models (COHMMs). This new formalism classifies VO sequences by embedding the nodes of an HMM state transition graph in a Euclidean vector space. This is accomplished by modeling the noise contained in the shape composed by the VO sequence. We cover the one-level as well as the multilevel COHMMs. Five problems are assigned to a multilevel COHMM: 1) sequence probability evaluation, 2) statistical decoding, 3) structural decoding, 4) shape decoding, and 5) learning. We have applied the COHMMs formalism to human face identification tested on different benchmarked face databases. The results show that the multilevel COHMMs outperform the embedded HMMs as well as some standard HMM-based models.