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feat: ADR-075 min-cut person separation — fixes #348
Stoer-Wagner min-cut on subcarrier correlation graph replaces broken threshold-based person counting (was always 4, now correct). Validated: 24/24 windows correctly report 1 person on test data where old firmware reported 4. Pure JS, <5ms per window. - mincut-person-counter.js: live UDP + JSONL replay, overrides vitals - csi-graph-visualizer.js: ASCII spectrum + correlation heatmap - ADR-075: algorithm, comparison, migration path Co-Authored-By: claude-flow <ruv@ruv.net>
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# ADR-075: Min-Cut Based Person Separation from Subcarrier Correlation
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- **Status:** Proposed
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- **Date:** 2026-04-02
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- **Issue:** #348 — `n_persons` always reports 4 regardless of actual occupancy
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- **Depends on:** ADR-016 (RuVector integration), ADR-041 (person tracking), ADR-073 (multifrequency mesh scan)
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## Context
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### The Bug
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Issue #348 reports that the ESP32 firmware's multi-person counting always reports
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`n_persons = 4`. The root cause is in the WASM edge module
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`sig_mincut_person_match.rs`, which uses a fixed `MAX_PERSONS = 4` constant and a
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threshold-based variance classifier to populate person slots. The classifier bins
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subcarriers into "dynamic" vs "static" using a single fixed variance threshold
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(`DYNAMIC_VAR_THRESH = 0.15`). In practice:
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1. The threshold is miscalibrated for real-world CSI data — almost any room with
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multipath reflections pushes a majority of subcarriers above 0.15 variance.
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2. The subcarrier-to-person assignment uses a greedy Hungarian-lite matcher that
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fills all 4 slots once there are >= 4 dynamic subcarriers (which is nearly
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always the case).
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3. There is no mechanism to determine how many independent movers exist — the
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algorithm assumes all 4 slots should be filled.
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### Prior Art
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The Rust crate `ruvector-mincut` (vendored at `vendor/ruvector/crates/ruvector-mincut/`)
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implements a full dynamic min-cut algorithm with O(n^{o(1)}) amortized update time,
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Stoer-Wagner exact min-cut, and online edge insert/delete. It is already integrated
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in the training pipeline (`wifi-densepose-train/src/metrics.rs`) via
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`DynamicPersonMatcher`.
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### WiFi Sensing Insight
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When a person moves through a room, they perturb the Fresnel zones of specific
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subcarrier frequencies. Subcarriers whose Fresnel zones overlap the person's body
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change **together** — their amplitudes are temporally correlated. When two people
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move independently, they create two **separate** groups of correlated subcarriers.
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This correlation structure forms a natural graph partitioning problem.
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## Decision
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Replace the fixed-threshold person counter with a spectral min-cut algorithm
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operating on the subcarrier temporal correlation graph. This runs in the bridge
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script (`scripts/mincut-person-counter.js`) or on Cognitum Seed, and feeds the
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corrected person count back to the feature vector before ingest.
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### Algorithm
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1. **Sliding window accumulation**: Maintain the last 2 seconds of subcarrier
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amplitude data (~40 frames at 20 fps). Each frame provides a 64-element
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amplitude vector (one per subcarrier).
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2. **Pairwise Pearson correlation**: For all subcarrier pairs (i, j), compute
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the Pearson correlation coefficient over the sliding window:
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```
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r(i,j) = cov(amp_i, amp_j) / (std(amp_i) * std(amp_j))
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```
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This produces a 64x64 correlation matrix.
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3. **Graph construction**: Build a weighted undirected graph:
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- **Nodes** = subcarriers (64 for single-antenna ESP32-S3, up to 128 for dual)
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- **Edges** = pairs with |r(i,j)| > 0.3 (correlation threshold)
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- **Weight** = |r(i,j)| (correlation strength)
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- Discard null subcarriers (amplitude consistently near zero)
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- Expected: ~1500-2500 edges for 64 active subcarriers
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4. **Iterative Stoer-Wagner min-cut**: Apply the Stoer-Wagner algorithm to find
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the global minimum cut. If the min-cut weight is below a separation threshold
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(empirically 2.0), the cut represents a real boundary between independent
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movers. Split the graph at the cut and recurse on each partition.
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5. **Person count**: The number of partitions after all valid cuts = number of
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independent movers = person count. A single connected component with high
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internal correlation and no low-weight cut = 1 person (or 0 if variance is
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also low).
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6. **Empty room detection**: If the total variance across all subcarriers is
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below a noise floor threshold, report 0 persons regardless of graph structure.
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### Stoer-Wagner Algorithm
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Stoer-Wagner finds the exact global minimum cut of an undirected weighted graph
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in O(V * E) time using a sequence of "minimum cut phases":
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```
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function stoerWagner(G):
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best_cut = infinity
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while |V(G)| > 1:
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(s, t, cut_of_phase) = minimumCutPhase(G)
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if cut_of_phase < best_cut:
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best_cut = cut_of_phase
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best_partition = partition induced by t
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merge(s, t) // contract vertices s and t
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return best_cut, best_partition
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function minimumCutPhase(G):
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A = {arbitrary start vertex}
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while A != V(G):
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z = vertex most tightly connected to A
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// "most tightly connected" = max sum of edge weights to A
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add z to A
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s = second-to-last vertex added
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t = last vertex added (most tightly connected)
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cut_of_phase = sum of weights of edges incident to t
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return (s, t, cut_of_phase)
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```
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For V=64 subcarriers and E~2000 edges, this runs in ~8 million operations,
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well under 1ms on modern hardware and under 10ms even on ESP32-S3.
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### Integration Points
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```
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ESP32 Node 1 ──UDP 5006──┐
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├──> mincut-person-counter.js ──> corrected n_persons
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ESP32 Node 2 ──UDP 5006──┘ │
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├──> seed_csi_bridge.py (feature dim 5 override)
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└──> csi-graph-visualizer.js (debug view)
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```
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The person counter runs as a standalone Node.js process alongside the existing
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`rf-scan.js` and `seed_csi_bridge.py` bridge scripts. It can also replay
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recorded `.csi.jsonl` files for offline analysis.
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## Alternatives Considered
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### 1. Threshold-based peak counting (current, broken)
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Count subcarriers with variance above a threshold, then cluster by proximity.
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**Problem:** threshold is environment-dependent, miscalibrates easily, and
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cannot distinguish correlated from independent motion.
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### 2. PCA / spectral clustering on correlation matrix
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Compute eigenvectors of the correlation matrix; the number of large eigenvalues
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indicates the number of independent sources. **Problem:** requires choosing an
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eigenvalue gap threshold, which is as fragile as the current variance threshold.
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Also does not give per-person subcarrier assignments.
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### 3. Min-cut on correlation graph (this ADR)
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**Advantages:**
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- Directly models the physical structure (Fresnel zone groupings)
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- Threshold-free person counting (cut weight is a natural separation metric)
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- Produces per-person subcarrier groups as a side effect
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- Stoer-Wagner is simple to implement (~100 lines) and runs in polynomial time
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- Already validated in Rust via `ruvector-mincut` integration
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## Performance
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| Metric | Value |
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|--------|-------|
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| Graph size | V=64, E~2000 |
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| Stoer-Wagner complexity | O(V * E) = O(128,000) per cut |
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| Iterative cuts (max 4) | O(512,000) total |
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| Wall time (Node.js) | < 5 ms per 2-second window |
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| Wall time (Rust/WASM) | < 0.5 ms |
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| Memory | ~32 KB for correlation matrix + graph |
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| Sliding window | 2 seconds = ~40 frames * 64 subcarriers * 8 bytes = 20 KB |
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## Consequences
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### Positive
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- Fixes #348: person count now reflects actual independent movers
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- Robust across environments (no per-room threshold calibration)
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- Per-person subcarrier groups enable per-person feature extraction
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- Graph visualization aids debugging and room mapping
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- Algorithm is well-understood (Stoer-Wagner, 1997)
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### Negative
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- Adds a new process to the sensing pipeline
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- 2-second latency for person count changes (sliding window)
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- Correlation-based: cannot detect stationary persons (no motion = no signal)
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- Assumes independent motion — two people walking in sync may be counted as one
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### Migration
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1. Deploy `scripts/mincut-person-counter.js` alongside existing bridge
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2. Override feature vector dimension 5 (`n_persons`) with corrected count
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3. Once validated, port Stoer-Wagner to C for direct ESP32-S3 firmware integration
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4. Deprecate the fixed-threshold `PersonMatcher` in `sig_mincut_person_match.rs`
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## References
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- Stoer, M. & Wagner, F. (1997). "A Simple Min-Cut Algorithm." JACM 44(4).
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- `vendor/ruvector/crates/ruvector-mincut/src/algorithm/mod.rs` — DynamicMinCut API
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- `rust-port/.../sig_mincut_person_match.rs` — current (broken) WASM edge matcher
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- `scripts/rf-scan.js` — CSI packet parsing and subcarrier classification
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