PHyCLIP: Unified Phylogenetic Clustering & Inference

• PHyCLIP is a unified framework that integrates hierarchical clustering, metric geometry, and probabilistic inference to analyze evolutionary, semantic, and compositional relationships.
• It employs methodologies such as Maximum Parsimony, Bayesian MCMC with split–merge moves, and ℓ1-product hyperbolic embeddings to accurately resolve complex clustering challenges.
• Its practical applications span astrophysics, molecular epidemiology, and vision–language tasks, providing interpretable clusters and enhanced scalability for large-scale data analysis.

PHyCLIP refers to a set of methodologies, algorithms, and software architectures for phylogenetic clustering and inference across divergent domains, notably astrophysics, infectious disease epidemiology, classical phylogenetic analysis, and vision–language representation learning. Central to PHyCLIP is the unified treatment of hierarchical and compositional relations, often leveraging advances in metric geometry, clustering algorithms, and probabilistic inference.

1. Theoretical Foundations: Hierarchy, Clustering, and Compositionality

In all domains addressed by PHyCLIP, the primary challenge is to reconcile classification with evolutionary, semantic, or compositional relationships. In astrophysical applications (Fraix-Burnet, 2017), multivariate clustering historically evolved from low-dimensional moralities to high-dimensional parameterizations of galaxies, stellar populations, and globular clusters, necessitating techniques that aggregate similar objects and infer evolutionary relationships. The phylogenetic approach employs Maximum Parsimony (cladistics) for tree inference, minimizing a global evolutionary cost:

$$C(T) = \sum_{\text{branches}} d(\text{state}_i, \text{state}_j)$$

where $d$ is a discrete distance function, often optimized via the $l_1$-norm (Wagner criterion).

In molecular epidemiology (Villandré et al., 2017), hierarchical clustering is foundational for tracing transmission dynamics among sequences, necessitating probabilistic models that jointly infer topology and cluster membership, with distinct priors for within- and between-cluster branch lengths.

In vision–LLMs (Yoshikawa et al., 10 Oct 2025), hierarchy refers to intra-family taxonomies (e.g., "dog ⪯ mammal ⪯ animal"), whereas compositionality models cross-family interactions (e.g., "a dog in a car")—an interaction not amenable to single-space geometric models.

2. PHyCLIP Methodologies in Bioinformatics and Epidemiology

The DM-PhyClus algorithm (Villandré et al., 2017), representative of PHyCLIP philosophies, integrates phylogenetic clustering with a Bayesian Markov chain Monte Carlo (MCMC) framework:

• Cluster definitions are embedded in the model using branch length priors: within-cluster (exponential, short mean) vs. between-cluster (log-normal).
• The likelihood for data $y$ under topology $\tau$ and cluster configuration $c$ is:

$$P(c_1, \ldots, c_n | y, \tau, \alpha, \lambda) \propto \zeta(\tau, ... | c_1, ..., c_n) \cdot P(c_1, ..., c_n | \tau, \alpha, \lambda)$$

where $\zeta$ is computed recursively (Felsenstein’s pruning), integrating over random branch lengths conditioned on cluster membership.

• The MCMC proposals (split–merge moves) are topology-constrained, avoiding arbitrary thresholds.
• Performance is evaluated against conventional post hoc cutpoint-based methods (Bootstrap-70, Gap), with mean cluster recovery quantified via adjusted Rand Index (ARI). DM-PhyClus consistently demonstrates higher ARI.
• PHyCLIP-style clustering informs public health strategies by providing interpretable clusters derived from principled probabilistic inference.

3. Computational Architecture: The PHyCLIP Library

The PHyCLIP software library (Silva, 2020) formalizes four essential workflow steps:

Step	Description	Algorithmic Options
Distance Calculation	Computes pairwise distances (e.g., Hamming)	Eager/lazy; MLST, SNP formats
Distance Correction	Adjusts for multiple substitutions (e.g., Jukes–Cantor)	Correction models included
Inference Algorithm	Constructs trees via clustering (NJ, GCP, MST)	Saitou–Nei-NJ, goeBURST
Local Optimization	Refines trees (e.g., Local Branch Recrafting)	Harmonic/tie-breaking

• Algorithms conform to theoretical complexity: NJ ($O(n^3)$), MST/GCP ($O(n^2)$) for time; NJ algorithms optimize toward linear memory.
• Modularity and extensibility are central: a reflection-based API allows stepwise workflow execution, continuous extension, and porting across platforms.
• The command-line interface supports stepwise workflow interruption/resumption, facilitating comparative algorithmic experiments and large-scale genomic pipelines.

4. PHyCLIP in Vision–Language Representation Learning

The PHyCLIP model (Yoshikawa et al., 10 Oct 2025) innovates by embedding multimodal data into an $\ell_1$-product of hyperbolic spaces:

$$\mathbf{X} = (\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, ..., \mathbf{x}^{(k)}),\quad \mathbf{x}^{(i)} \in \mathbb{H}^{d_i}$$

The $\ell_1$-product metric is defined as:

$$d_{\mathbb{H}^d}^k(\mathbf{X}, \mathbf{Y}) = \sum_{i=1}^k d_{\mathbb{H}^{d_i}}(\mathbf{x}^{(i)}, \mathbf{y}^{(i)})$$

• Hierarchical relations (entailment cones) are encoded in individual hyperbolic factors.
• Compositionality is modeled by the additive $\ell_1$ metric, paralleling Boolean algebra union.
• Empirical evaluation demonstrates superior performance over single-space baselines (CLIP, MERU, HyCoCLIP) on zero-shot classification, retrieval, hierarchical classification (Tree Induced Error, LCA error, Jaccard similarity), and compositional tasks (VL-CheckList, SugarCrepe).
• Factor-wise analysis (norm distribution, HoroPCA projections) reveals automatic specialization per concept family, mirroring theoretical expectations.

5. Practical Implementation and Applications

PHyCLIP, across its variants, is implemented to facilitate both research and operational use:

• In astrophysics, discretization schemes (20–30 bins) for continuous observables and cost matrices (Wagner optimization) enable robust unsupervised classification and evolutionary inference from sky surveys (Fraix-Burnet, 2017).
• In molecular epidemiology, applications to HIV-1 transmission clusters demonstrate interpretable outputs directly informing targeted intervention strategies (Villandré et al., 2017).
• In evolutionary analysis, PHyCLIP’s architecture and APIs support integration with NGS platforms and epidemiological surveillance, revealing spreading patterns otherwise latent to single-algorithm pipelines (Silva, 2020).
• In vision–language representation learning, the structured embedding space of PHyCLIP facilitates interpretable retrieval, hierarchical decision-making, and compositional understanding in high-stakes domains (e.g., autonomous driving, medical imaging) (Yoshikawa et al., 10 Oct 2025).

6. Limitations and Future Research

Open challenges include:

• In astrophysical contexts, there are unresolved questions regarding the adequacy of tree-like hierarchical models for entities with non-tree evolution (hybridization, parallel/convergent evolution); incorporation of probabilistic and network-based phylogenetics is recommended (Fraix-Burnet, 2017).
• For DM-PhyClus, sensitivity to concentration parameter priors and robustness to tree topological uncertainties invite further refinement (Villandré et al., 2017).
• The PHyCLIP library’s algorithmic efficiency is constrained by distance matrix size; optimization for memory and computational resources remains an ongoing concern (Silva, 2020).
• In PHyCLIP for vision–language, richer inter-object relations (beyond factor activation) remain unexplored, suggesting future extensions involving advanced algebraic operations and relational reasoning (Yoshikawa et al., 10 Oct 2025).

7. Cross-Domain Conceptual Integration

Across disparate domains, PHyCLIP advances a unified conceptual framework:

• Hierarchical relationships are efficiently encoded (phylogenetic trees, hyperbolic geometry, clustering trees).
• Compositionality is explicitly modeled (additive metrics, intra-/inter-cluster dynamics, cross-family factorization).
• Probabilistic inference, modular computational architectures, and interpretable representations transcend domain boundaries, enabling robust, scalable, and extensible scientific exploration.

PHyCLIP’s methodologies and algorithms represent a convergence of phylogenetic, algebraic, and geometric principles, informing state-of-the-art approaches in astrophysics, bioinformatics, epidemiology, and machine learning.