Dirichlet process mixture model based on topologically augmented signal representation for clustering infant vocalizations

• Bonafos Guillem
• Bourot Clara
• Pudlo Pierre
• Freyermuth Jean-Marc
• Reboul Laurence
• Tronçon Samuel
• Rey Arnaud

• Clustering
• Bayesian non-parametric
• Dirichlet process
• Mixture model
• Topologically-augmented machine learning
• TDA
• Babbling
• Language development
• Vocalizations

Based on audio recordings made once a month during the first 12 months of a child's life, we propose a new method for clustering this set of vocalizations. We use a topologically augmented representation of the vocalizations, employing two persistence diagrams for each vocalization: one computed on the surface of its spectrogram and one on the Takens' embeddings of the vocalization. A synthetic persistent variable is derived for each diagram and added to the MFCCs (Mel-frequency cepstral coefficients). Using this representation, we fit a non-parametric Bayesian mixture model with a Dirichlet process prior to model the number of components. This procedure leads to a novel data-driven categorization of vocal productions. Our findings reveal the presence of 8 clusters of vocalizations, allowing us to compare their temporal distribution and acoustic profiles in the first 12 months of life.