Obtaining psychological embeddings through joint kernel and metric learning

Psychological embeddings provide a powerful formalism for characterizing human-perceived similarity among members of a stimulus set. Obtaining high-quality embeddings can be costly due to algorithm design, software deployment, and participant compensation. This work aims to advance state-of-the-art embedding techniques and provide a comprehensive software package that makes obtaining high-quality psychological embeddings both easy and relatively efficient. Contributions are made on four fronts. First, the embedding procedure allows multiple trial configurations (e.g., triplets) to be used for collecting similarity judgments from participants. For example, trials can be configured to collect triplet comparisons or to sort items into groups. Second, a likelihood model is provided for three classes of similarity kernels allowing users to easily infer the parameters of their preferred model using gradient descent. Third, an active selection algorithm is provided that makes data collection more efficient by proposing comparisons that provide the strongest constraints on the embedding. Fourth, the likelihood model allows the specification of group-specific attention weight parameters. A series of experiments are included to highlight each of these contributions and their impact on converging to a high-quality embedding. Collectively, these incremental improvements provide a powerful and complete set of tools for inferring psychological embeddings. The relevant tools are available as the Python package PsiZ, which can be cloned from GitHub (https://github.com/roads/psiz).