Ivectors

i-vectors, short for identity vectors, are compact fixed-length representations of speech utterances designed to capture both speaker characteristics and channel or recording variability. They provide a single vector that summarizes an utterance, enabling standard statistical methods to be applied for speaker recognition tasks such as verification and identification.

The core idea is to model all variability in speech with a total variability space. A large speaker- and condition-dependent Gaussian mixture model (GMM) called a universal background model (UBM) is trained on a diverse dataset. For each utterance, sufficient statistics are computed from the acoustic features (often MFCCs), and these statistics are used to estimate a low-dimensional vector, the i-vector, that locates the utterance within the total variability space spanned by a matrix T. The resulting i-vector w is typically obtained by maximum likelihood or MAP estimation in this factor analysis framework.

Typical i-vector dimensions are a few hundred, commonly in the 400–600 range. Training requires substantial data to estimate the UBM and the total variability matrix T. After extraction, i-vectors often undergo whitening and length normalization, and may be reduced with Linear Discriminant Analysis (LDA). Scoring between utterances commonly uses cosine similarity or probabilistic linear discriminant analysis (PLDA) to improve discrimination.

Applications include speaker verification, speaker identification, and diarization. The approach played a dominant role in speaker recognition from the mid-2000s through the 2010s and remains a reference method, though neural network–based embeddings such as x-vectors have become popular in newer systems.