Source-linked AI summary
Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations
Gaute Johannessen, Geert Roelof van der Ploeg, Evrim Acar
TL;DR
Tensor factorizations have largely analyzed complex, noisy data without exploiting computational-model knowledge for unsupervised pattern discovery. The paper jointly analyzes real and simulated tensors with linearly coupled factorizations, finding consistently cleaner patterns and potential mismatches between data and models.
Problem
Existing tensor-factorization approaches are mainly data-driven, limiting use of computational models as prior information for unsupervised pattern discovery in noisy complex data.
Method
The approach jointly factorizes real tensor X and simulated tensor Y, coupling their metabolites-mode factors through linear relations.
Results
Coupling consistently improves recovery of cleaner, biologically meaningful patterns in real metabolomics data, including insulin/glucose components with stronger correlations to BMI-related variables.
Takeaways & Limitations
Coupled tensor factorizations can bring computational models into interpretable pattern discovery while revealing potential mismatches between simulated and real dynamics.
Abstract
from arXiv · showhide
In order to understand complex systems such as the human metabolome or human brain, different sensing technologies are used, generating complex data. These datasets are often multiway, i.e., with more than two axes of variation such as a subjects by metabolites by time array. While tensor factorizations have successfully revealed interpretable patterns from such complex data, they have so far been mainly data-driven. On the other hand, there is more to data -- there are computational models (of these systems), which are rich sources of prior information. In this paper, we introduce a knowledge-guided approach that brings together data and computational models by jointly analyzing real data and simulated data (generated using a computational model) using coupled tensor factorizations with linear coupling. Our experiments on real metabolomics measurements demonstrate that guiding the analysis of such noisy data with simulated data improves the pattern discovery performance while also revealing potential discrepancies between data and computational models.
1. INTRODUCTION
The paper addresses the limited use of computational-model knowledge in data-driven tensor factorizations for unsupervised pattern discovery. It proposes jointly analyzing noisy real data with cleaner simulated data through linearly coupled tensor factorizations, improving pattern discovery.
- Motivation: Existing tensor-factorization approaches are predominantly data-driven and do not exploit prior information encoded in computational models.Such models can encode biochemistry- and physiology-grounded dynamics that are difficult to infer from noisy observations.
- Approach: The proposed approach jointly analyzes real tensor X and simulated tensor Y generated by a computational model.The tensors are coupled in the metabolites mode so simulated data can guide analysis of noisy real data.
- Approach: The coupled CP model links the real and simulated metabolites-mode factor matrices through a coupling relation.The linked matrices are Areal and Avirtual.
- Contribution: Coupled models consistently improve pattern discovery when real data analysis is guided by simulated data.The experiments include coupled CP and PARAFAC2-based approaches.
2. METHODS
The methods combine CP or PARAFAC2 tensor models with coupled factorizations that jointly fit real and simulated datasets. Linear coupling matches shared metabolites through transformation matrices and a consensus matrix.
- Tensor models: The CP model approximates a higher-order tensor as a sum of rank-one tensors with factor matrices for each mode.For metabolomics tensors, components can represent metabolite groups, temporal profiles, and subject stratification.
- Tensor models: PARAFAC2 allows time-profile factors to vary across subject-specific slices instead of using one shared time-profile matrix.Its factors can reveal metabolite groups, subject stratifications, and subject-specific temporal differences.
- Coupled models: Coupled tensor factorizations jointly analyze real tensor X and simulated tensor Y by coupling their metabolites modes.The coupled setup uses tensor models for multiple datasets.
- Coupled models: Transformation matrices Hr and Hv define matching metabolites, while consensus matrix Δ links the corresponding factor matrices.When simulated data contain only a metabolite subset, the transformations select shared metabolites and ignore unmatched entries.
- Coupled models: The coupled PARAFAC2-CP model uses PARAFAC2 for real data and CP for simulated data.This preserves subject-specific time profiles in the real-data analysis while coupling the datasets through the metabolites mode.
3. EXPERIMENTS
Experiments use real meal-challenge metabolomics and simulated data from a human metabolic model to evaluate whether joint analysis improves pattern discovery. Models are compared using correlations between subject factors and body-composition or insulin-resistance measures.
- Data: The study combines meal-challenge metabolomics from male COPSAC2000 participants with simulated data generated by a human metabolic model.Both datasets are organized as metabolites-by-time-points-by-subjects tensors.
- Data: The analysis targets metabolic-response patterns and their ability to stratify subjects by body composition and insulin resistance.Real measurements include fasting and seven post-meal time points, with insulin and C-peptide measurements.
- Evaluation: The evaluation compares coupled real-and-simulated models with individual analysis of real data.Comparisons include T0-corrected and uncorrected CP settings, with linear coupling in the metabolites mode.
- Evaluation: Performance is assessed through correlations between subject-mode factors and body-composition or insulin-resistance measures.Measures include HOMA-IR, BMI, waist circumference, fat mass, muscle mass, and related indices.
- Evaluation: Figure 2 compares uncoupled dark models with linearly coupled light models for each model pair.It displays correlations for the component with the highest correlations in each model.
4. RESULTS
Jointly analyzing noisy real and simulated data improves recovery of a biologically meaningful insulin/glucose component and produces cleaner patterns with stronger correlations to BMI-related measures. The coupled analysis also exposes discrepancies between simulated and observed temporal and individual-variation patterns.
- Joint analysis with simulated data improves recovery of a biologically meaningful insulin/glucose component from noisy real data.In uncoupled real-data models, the component is either missed because other metabolites dominate or is noisier.
- CP versus coupled CP-CP: Coupled CP-CP produces a purer insulin/glucose component with stronger correlations with variables of interest than the uncoupled CP model.The uncoupled model captures a BMI-associated pattern, but it is mainly dominated by metabolites other than insulin and glucose.
- PARAFAC2 versus coupled PARAFAC2-CP: Coupled PARAFAC2-CP captures a cleaner insulin/glucose pattern with stronger correlations with BMI-related variables than PARAFAC2 alone.The uncoupled PARAFAC2 model recovers an insulin-dominated factor with only a small glucose coefficient.
- The simulated insulin/glucose time profile has a sharper peak around 1 hour post-meal, whereas observed real-data profiles are broader or show greater individual variation.This contrast indicates a potential discrepancy between the real data and the computational model.
- Coupled subject-mode factors show substantially less individual variation in simulated data than in real data.
5. CONCLUSION
The paper introduces a knowledge-guided approach that jointly analyzes real and simulated data with linearly coupled tensor factorizations for interpretable pattern discovery. Metabolomics experiments produce cleaner patterns than real-data-only analysis and reveal potential mismatches between observations and computational models.
- Linearly coupled tensor factorizations jointly bring together real data and computational models for interpretable pattern discovery.
- Metabolomics experiments show that the coupled approach consistently provides cleaner patterns than analysis using only real data.
- The coupled framework can reveal potential mismatches between real data and computational models.
- Future work: Future work will examine whether conflicting information can be reliably extracted through coupled tensor factorizations, including via unshared factors.