RFC-006: Anchor Projection

This RFC proposes Anchor Projection — a coordinate system transformation that re-expresses trajectories relative to user-defined reference points (anchors), turning opaque high-dimensional drift into interpretable, clinically meaningful signals.

Problem

All CVX analytics operate in absolute embedding space ($\mathbb{R}^D$, $D = 384$ or $768$). High-dimensional embeddings mask clinically meaningful drift:

Issue	Impact
Curse of dimensionality	Distances concentrate — all pairs look equally far
No interpretability	”dim_127 changed by 0.3” conveys nothing clinical
Domain-agnostic axes	Embedding dimensions have no semantic meaning

A user drifting toward depressive language and a user drifting toward sports talk may produce identical velocity magnitudes. Without a reference frame, the direction of drift is unreadable.

Key Insight

The projected trajectory is a trajectory — so velocity(), hurst_exponent(), detect_changepoints(), path_signature() all work on it natively. Anchor Projection is a coordinate system change, not a new analytics paradigm. It composes with the entire existing CVX toolkit.

Solution

project_to_anchors(trajectory, anchors, metric) projects from $\mathbb{R}^D \to \mathbb{R}^K$ where $K$ = number of anchors. Each dimension $k$ of the output equals the distance (cosine or L2) from the trajectory point to anchor $k$:

$\text{projected}_t[k] = d(\mathbf{x}_t, \mathbf{a}_k), \quad k = 1, \ldots, K$

The output is a new trajectory of the same length but in $\mathbb{R}^K$, which feeds directly into all existing CVX functions.

Example: With 3 anchors (depression centroid, anxiety centroid, neutral centroid), a 50-post trajectory in $\mathbb{R}^{384}$ becomes a 50-step trajectory in $\mathbb{R}^3$ where each dimension is the distance to a clinically interpretable reference point.

New API

# Project trajectory into anchor-relative coordinates
projected = cvx.project_to_anchors(
    trajectory,              # (T, D) array — original trajectory
    anchors,                 # (K, D) array — reference embeddings
    metric='cosine'          # 'cosine' | 'l2'
)
# Returns: (T, K) array — trajectory in ℝᴷ

# Summarize per-anchor dynamics
summary = cvx.anchor_summary(projected)
# Returns: dict per anchor with {mean, min, trend, last}

Composition with existing analytics

# All existing CVX functions work on the projected trajectory:
vel = cvx.velocity(projected, timestamps)          # velocity in ℝᴷ
cps = cvx.detect_changepoints("user", projected)   # regime changes in anchor space
H   = cvx.hurst_exponent(projected)                # persistence of anchor-relative drift
sig = cvx.path_signature(projected, depth=2)        # signature over anchor distances

Implementation

• Module: cvx-analytics::anchor
• Dependencies: Uses existing drift_magnitude_cosine / drift_magnitude_l2 from cvx-analytics::drift
• Core logic: For each time step $t$ and anchor $k$, compute the chosen distance metric between $\mathbf{x}_t$ and $\mathbf{a}_k$. Assemble into a $(T, K)$ matrix.
• Complexity: $O(T \cdot K \cdot D)$ — linear in all dimensions, no graph lookups needed

Clinical Validation

On the eRisk 2018 depression detection task, anchor-relative features substantially improved classification:

Configuration	Precision	Recall	F1	AUC
B1 baseline (absolute space)	0.667	0.545	0.600	0.639
B2 combined (with anchor projection)	0.714	0.857	0.781	0.863
Improvement	+0.047	+0.312	+0.181	+0.224

Anchor projection makes drift toward or away from known clinical poles directly measurable, providing the reference frame that raw embeddings lack.

Phases

Phase	Scope	Effort
1	project_to_anchors in Rust (cvx-analytics::anchor)	Low
2	anchor_summary aggregation	Low
3	Python bindings via PyO3	Low
4	Integration tests with eRisk data	Medium
5	Tutorial B2 with anchor-projected analytics	Medium