[Paper Review] Inferring and Learning from Neuronal Correspondences

Ashish Kapoor, E. Paxon Frady+3 more|arXiv (Cornell University)|Jan 23, 2015

Cell Image Analysis Techniques39 references3 citations

TL;DR

This paper proposes a machine learning framework to infer neuronal correspondences across multiple leech nervous systems, enabling joint analysis of neural data from distinct animals. By combining metric learning, probabilistic PCA, and graph matching, the method aligns neurons across animals despite variability in cell counts and properties, significantly improving behavioral state prediction from pooled data.

ABSTRACT

We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences combine data effectively from cross-animal studies to make joint inferences about behavioral decision making that are not possible with the data from a single animal. We focus on data collection, machine learning, and prediction in the representative and long-studied invertebrate nervous system of the European medicinal leech. Acknowledging the computational intractability of the general problem of identifying correspondences among neurons, we introduce efficient computational procedures for matching neurons across animals. The methods include techniques that adjust for missing cells or additional cells in the different data sets that may reflect biological or experimental variation. The methods highlight the value harnessing inference and learning in new kinds of computational microscopes for multiunit neurobiological studies.

Motivation & Objective

• Address the challenge of matching neurons across multiple animals despite biological and experimental variability in neuronal counts and properties.
• Enable joint inference about neural circuits and behavior by pooling data from multiple leech preparations.
• Develop a scalable, computationally efficient method for correspondence matching across more than two animals, overcoming NP-hard complexity.
• Improve the accuracy and timeliness of behavioral state discrimination (e.g., swim vs. crawl) by leveraging aligned data from multiple animals.
• Provide a generalizable framework applicable to other invertebrate and vertebrate nervous systems for data integration and analysis.

Proposed method

• Formulate neuronal correspondence as a bipartite graph-matching problem using a learned compatibility function based on physical and functional neuron features.
• Learn a Mahalanobis-style metric via metric learning to define similarity between neuron pairs across animals, using user-provided match/non-match pairs as supervision.
• Iteratively recover a correspondence map by solving a constrained optimization problem (equation 3) that maximizes total compatibility while ensuring one-to-one matching.
• Use probabilistic PCA (pPCA) on a permuted data matrix Y, constructed from aligned neurons across animals, to infer missing or unobserved neuronal activity.
• Integrate data from six leech preparations, with each animal’s ganglion data represented as a set of time-series voltage-sensitive dye signals.
• Apply ISOMAP for non-linear dimensionality reduction on pooled, aligned data to visualize and compare behavioral states across animals consistently.

Experimental results

Research questions

• RQ1 Can neuronal correspondence across multiple leech preparations be reliably inferred despite variations in cell counts and experimental artifacts?
• RQ2 Does pooling neural data from multiple animals using inferred correspondences improve the accuracy and speed of behavioral state prediction compared to single-animal analysis?
• RQ3 Can a learned compatibility metric effectively identify functional and structural correspondences between neurons across different animals?
• RQ4 To what extent does the use of probabilistic PCA on aligned data improve the recovery of missing or unobserved neuronal activity?
• RQ5 Can the framework be extended to enable real-time guidance of ongoing experiments using a learned model of neuronal correspondence?

Key findings

• The method successfully infers one-to-one correspondences between neurons across six leech preparations, even with missing or extra cells, by combining metric learning and graph matching.
• Pooled data from aligned neurons enabled earlier and more significant discrimination between swim and crawl behavioral states than possible with data from a single animal.
• Non-linear projections using ISOMAP on aligned data revealed consistent trajectories across all animals, whereas individual-animal projections were inconsistent.
• The use of probabilistic PCA on the aligned data matrix Y allowed for effective inference of missing neuronal activity, improving data completeness.
• The framework demonstrated that joint analysis of multiple animals via correspondence inference leads to more robust and generalizable insights into neural circuit function.
• The approach enables consistent visualization and analysis of behavioral dynamics across animals, overcoming variability in individual preparations.