# Implementation Plan - Phase 2: Major Algorithmic Improvements

**Duration**: Weeks 4-8
**Priority**: P2 - Significant Functionality Gaps
**Effort**: 100-120 hours
**Risk Level**: Low (new features, no breaking changes)

---

## Executive Summary

Phase 2 addresses algorithmic gaps in the pattern analysis system, implementing proper statistical and predictive algorithms to replace placeholder implementations. This phase focuses on ETS forecasting, DBSCAN anomaly detection, BOCPD changepoint detection, pattern extraction, and tool risk assessment.

**Focus Areas**:
1. ETS Forecasting (✅ COMPLETED)
2. DBSCAN Anomaly Detection (✅ COMPLETED)
3. BOCPD Changepoint Detection (✅ COMPLETED)
4. Pattern Extraction from Clusters
5. Tool Compatibility Risk Assessment

---

## Issue #4: ETS Forecasting Implementation - ✅ COMPLETED

**File**: `do-memory-mcp/src/patterns/predictive.rs:178-196`
**Status**: ✅ **COMPLETED** (2025-12-25)
**Impact**: Predictive analytics provide trivial results
**Expected**: Proper Exponential Smoothing Time Series model with confidence intervals
**Delivered**: ✅ Complete ETS model with all features

### Completed Implementation

**Algorithm Research & Design** (Week 1, Days 1-3) ✅
- [x] Research ETS/Exponential Smoothing algorithms
- [x] Design ETS model structure (alpha, beta, gamma parameters)
- [x] Plan confidence interval calculation
- [x] Design seasonality handling

**Core Implementation** (Week 1, Days 4-7) ✅
- [x] Implement ETS model struct and configuration
- [x] Add Holt-Winters seasonal component
- [x] Implement forecasting logic
- [x] Add confidence interval calculation

**Integration & Testing** (Week 2, Days 1-5) ✅
- [x] Integrate with existing predictive patterns
- [x] Add unit tests with known time series
- [x] Create integration tests with MCP patterns
- [x] Performance benchmarking

### Success Criteria Met

- [x] ETS model properly forecasts time series
- [x] Confidence intervals calculated
- [x] Seasonality handled correctly
- [x] Tests validate against known datasets

### Implementation Summary

**ETS Model Types**: Additive/Multiplicative error, trend, and seasonal

**State Management**: Level, trend, seasonal components

**Parameter Optimization**: Grid search with information criteria (AIC)

**Seasonality Detection**: Autocorrelation-based with strength calculation

**Test Results**: 7 tests passing (including previously ignored `test_ets_seasonality_detection`, now enabled 2025-12-25)

---

## Issue #5: DBSCAN Anomaly Detection - ✅ COMPLETED

**File**: `do-memory-mcp/src/patterns/predictive/dbscan.rs`
**Status**: ✅ **COMPLETED** (2025-12-30)
**Impact**: Uses simple thresholding instead of proper clustering
**Current**: Adaptive DBSCAN with KDTree acceleration
**Required**: Proper Density-Based Spatial Clustering (✅ Delivered)

### Implementation Tasks

**Week 2, Days 6-7 + Week 3, Days 1-4** ✅

#### 1. DBSCAN Algorithm Implementation

**Goal**: Implement DBSCAN clustering algorithm

**Tasks**:
- [x] Implement DBSCAN clustering algorithm
- [x] Add distance calculation functions
- [x] Implement core point identification
- [x] Add cluster expansion logic
- [x] Integrate KDTree for efficient neighbor queries
- [x] Add streaming cluster support
- [x] Add adaptive parameter optimization

**Implementation**:
```rust
pub struct DBSCAN {
    pub epsilon: f64,      // Neighborhood radius
    pub min_samples: usize,  // Minimum points for core point
}

impl DBSCAN {
    pub fn cluster(&self, points: &[f64]) -> Vec<Vec<usize>> {
        let mut clusters = Vec::new();
        let mut visited = vec![false; points.len()];
        let mut cluster_id = 0;

        for (i, point) in points.iter().enumerate() {
            if visited[i] {
                continue;
            }

            // Find neighbors
            let neighbors = self.region_query(points, point);

            if neighbors.len() >= self.min_samples {
                // Core point - expand cluster
                let mut cluster = Vec::new();
                self.expand_cluster(points, i, &neighbors, &mut visited, &mut cluster);
                clusters.push(cluster);
                cluster_id += 1;
            }
        }

        clusters
    }

    fn region_query(&self, points: &[f64], point: &f64) -> Vec<usize> {
        points.iter()
            .enumerate()
            .filter(|(_, p)| (p - point).abs() < self.epsilon)
            .map(|(i, _)| i)
            .collect()
    }

    fn expand_cluster(
        &self,
        points: &[f64],
        point_idx: usize,
        neighbors: &[usize],
        visited: &mut [bool],
        cluster: &mut Vec<usize>
    ) {
        // Add point to cluster and mark visited
        cluster.push(point_idx);
        visited[point_idx] = true;

        // Expand to all neighbors
        for &neighbor_idx in neighbors {
            if !visited[neighbor_idx] {
                visited[neighbor_idx] = true;
                let neighbor_neighbors = self.region_query(points, &points[neighbor_idx]);

                if neighbor_neighbors.len() >= self.min_samples {
                    // Recursively expand
                    self.expand_cluster(points, neighbor_idx, &neighbor_neighbors, visited, cluster);
                } else {
                    // Border point - add to cluster
                    cluster.push(neighbor_idx);
                }
            }
        }
    }
}
```

#### 2. Anomaly Detection Integration

**Week 3, Days 5-7**

**Goal**: Integrate DBSCAN with anomaly detection

**Tasks**:
- [ ] Integrate DBSCAN with anomaly detection
- [ ] Implement noise point identification as anomalies
- [ ] Add hyperparameter tuning (epsilon, min_samples)
- [ ] Create anomaly scoring mechanism

**Implementation**:
```rust
pub struct AnomalyDetector {
    dbscan: DBSCAN,
}

impl AnomalyDetector {
    pub fn detect_anomalies(&self, time_series: &[f64]) -> Vec<usize> {
        // Run DBSCAN clustering
        let clusters = self.dbscan.cluster(time_series);

        // Identify noise points (anomalies)
        let mut anomalies = Vec::new();
        for (i, point_clusters) in clusters.iter().enumerate() {
            if point_clusters.is_empty() {
                anomalies.push(i);
            }
        }

        anomalies
    }

    pub fn score_anomalies(&self, time_series: &[f64]) -> Vec<f32> {
        let anomalies = self.detect_anomalies(time_series);

        anomalies.iter()
            .map(|&idx| {
                // Calculate anomaly score based on distance to nearest cluster
                let point = time_series[idx];
                let min_dist = time_series.iter()
                    .enumerate()
                    .filter(|&(i, _)| !anomalies.contains(&i))
                    .map(|(_, p)| (p - point).abs())
                    .fold(f32::INFINITY, |acc, d| acc.min(d as f32));

                min_dist
            })
            .collect()
    }
}
```

#### 3. Testing & Validation

**Week 4, Days 1-3**

**Tasks**:
- [ ] Unit tests with known clustering datasets
- [ ] Integration tests with time series data
- [ ] Performance optimization
- [ ] Comparison with existing thresholding method

### Success Criteria

- [ ] DBSCAN properly identifies clusters
- [ ] Noise points correctly flagged as anomalies
- [ ] Hyperparameters configurable
- [ ] Performance acceptable for real-time use

---

## Issue #6: Bayesian Changepoint Detection - ✅ COMPLETED

**File**: `do-memory-mcp/src/patterns/statistical.rs`
**Status**: ✅ **COMPLETED** (2025-12-30)
**Impact**: Uses simple mean-shift instead of proper detection
**Current**: BOCPD with log-space arithmetic and adaptive parameters
**Required**: BOCPD (Bayesian Online Changepoint Detection) (✅ Delivered)

### Implementation Tasks

**Week 4, Days 4-7 + Week 5, Days 1-2** ✅

#### 1. BOCPD Algorithm

**Goal**: Implement Bayesian Online Changepoint Detection

**Tasks**:
- [x] Implement Bayesian Online Changepoint Detection
- [x] Add hazard rate and observation noise modeling
- [x] Implement run-length probability updates in log space
- [x] Add changepoint probability calculation
- [x] Add streaming support with circular buffers
- [x] Add multi-resolution changepoint detection

**Implementation**:
```rust
pub struct BOCPD {
    pub hazard_rate: f64,           // Prior on run length
    pub observation_noise: f64,     // Observation noise std dev
}

impl BOCPD {
    pub fn new(hazard_rate: f64, observation_noise: f64) -> Self {
        Self {
            hazard_rate,
            observation_noise,
        }
    }

    pub fn detect_changepoints(&self, time_series: &[f64]) -> Vec<usize> {
        // Initialize run-length probabilities
        let max_run_length = time_series.len();
        let mut rl_probs = vec![0.0; max_run_length + 1];
        rl_probs[0] = 1.0; // Start with run length 0

        let mut changepoint_probs = Vec::new();

        for (t, &value) in time_series.iter().enumerate() {
            // Predictive distribution for next value
            let (pred_mean, pred_var) = self.predictive_distribution(&rl_probs, time_series, t);

            // Update run-length probabilities
            self.update_run_length_probs(&mut rl_probs, &pred_mean, &pred_var, value);

            // Calculate changepoint probability
            let cp_prob = self.changepoint_probability(&rl_probs);
            changepoint_probs.push(cp_prob);
        }

        // Detect changepoints (where changepoint probability exceeds threshold)
        self.extract_changepoints(&changepoint_probs)
    }

    fn predictive_distribution(
        &self,
        rl_probs: &[f64],
        time_series: &[f64],
        t: usize
    ) -> (f64, f64) {
        // Calculate predictive mean and variance
        let mut pred_mean = 0.0;
        let mut pred_var = self.observation_noise.powi(2);

        for (run_length, &prob) in rl_probs.iter().enumerate().take(t) {
            if t > 0 {
                // Update with sufficient statistics
                let data = &time_series[t - run_length..t];
                pred_mean = prob * data.iter().sum::<f64>() / data.len() as f64;
            }
        }

        (pred_mean, pred_var)
    }

    fn update_run_length_probs(&self, rl_probs: &mut [f64], pred_mean: &f64, pred_var: &f64, observed: f64) {
        let max_rl = rl_probs.len() - 1;

        for run_length in (1..=max_rl).rev() {
            // Calculate predictive probability
            let pred_prob = self.normal_pdf(observed, *pred_mean, pred_var.sqrt());

            // Update run-length probability
            rl_probs[run_length] = rl_probs[run_length - 1] * (1.0 - self.hazard_rate) * pred_prob;
        }

        // Reset run length to 0 (changepoint)
        rl_probs[0] = rl_probs.iter().take(max_rl).map(|p| p * self.hazard_rate).sum();
    }

    fn normal_pdf(&self, x: f64, mean: f64, std_dev: f64) -> f64 {
        let exponent = -0.5 * ((x - mean) / std_dev).powi(2);
        let coefficient = 1.0 / (std_dev * (2.0 * std::f64::consts::PI).sqrt());
        coefficient * exponent.exp()
    }

    fn changepoint_probability(&self, rl_probs: &[f64]) -> f64 {
        // Probability of changepoint = sum of all run-length probabilities * hazard rate
        rl_probs.iter().map(|p| p * self.hazard_rate).sum()
    }

    fn extract_changepoints(&self, changepoint_probs: &[f64]) -> Vec<usize> {
        let threshold = 0.8; // Configurable
        changepoint_probs
            .iter()
            .enumerate()
            .filter(|(_, &prob)| prob > threshold)
            .map(|(i, _)| i)
            .collect()
    }
}
```

#### 2. Statistical Models

**Week 5, Days 3-5**

**Goal**: Implement normal distribution parameter tracking

**Tasks**:
- [ ] Implement normal distribution parameter tracking
- [ ] Add multiple model support (normal, Poisson, etc.)
- [ ] Create model selection mechanism
- [ ] Implement posterior update calculations

#### 3. Integration

**Week 5, Days 6-7**

**Goal**: Replace existing thresholding with BOCPD

**Tasks**:
- [ ] Replace existing thresholding with BOCPD
- [ ] Add configuration parameters
- [ ] Performance optimization
- [ ] Testing with synthetic changepoint data

### Success Criteria

- [ ] BOCPD properly detects changepoints
- [ ] Statistical models accurately track parameters
- [ ] Changepoint probabilities calculated correctly
- [ ] Better accuracy than thresholding approach

---

## Issue #7: Pattern Extraction Implementation

**File**: `do-memory-core/src/patterns/clustering.rs:387-391`
**Status**: 🔵 NOT STARTED
**Impact**: Returns empty results
**Current**: Empty vector return
**Required**: Actual pattern extraction algorithms

### Implementation Tasks

**Week 6, Days 1-3**

#### 1. Pattern Analysis Algorithms

**Goal**: Analyze episodes within clusters

**Tasks**:
- [ ] Implement common sequence detection
- [ ] Add tool combination pattern analysis
- [ ] Create decision point identification
- [ ] Add frequency analysis for patterns

**Week 6, Days 4-6**

#### 2. Cluster Analysis Integration

**Goal**: Extract patterns from episode clusters

**Tasks**:
- [ ] Analyze episodes within clusters
- [ ] Extract temporal patterns
- [ ] Identify tool usage patterns
- [ ] Add success/failure pattern analysis

**Week 6, Days 7 + Week 7, Days 1-2**

#### 3. Pattern Ranking & Storage

**Goal**: Implement pattern deduplication and ranking

**Tasks**:
- [ ] Implement pattern deduplication
- [ ] Add frequency-based ranking
- [ ] Integrate with pattern storage
- [ ] Create pattern visualization

### Success Criteria

- [ ] Extract meaningful patterns from clusters
- [ ] Patterns ranked by relevance and frequency
- [ ] Storage integration working
- [ ] Patterns improve retrieval accuracy

---

## Issue #8: Tool Compatibility Risk Assessment

**File**: `do-memory-core/src/patterns/optimized_validator.rs:211`
**Status**: 🔵 NOT STARTED
**Impact**: Always returns 0.0 (meaningless validation)
**Current**: Placeholder returning 0.0
**Required**: Historical usage analysis and compatibility scoring

### Implementation Tasks

**Week 7, Days 3-5**

#### 1. Historical Usage Analysis

**Goal**: Track and analyze tool usage

**Tasks**:
- [ ] Implement tool usage tracking
- [ ] Add success/failure rate calculation
- [ ] Create context compatibility analysis
- [ ] Implement usage pattern recognition

**Week 7, Days 6-7 + Week 8, Days 1-2**

#### 2. Risk Assessment Algorithm

**Goal**: Design weighted scoring algorithm

**Tasks**:
- [ ] Design weighted scoring algorithm
- [ ] Implement compatibility factors
- [ ] Add confidence intervals for risk scores
- [ ] Create risk categorization

**Week 8, Days 3-5**

#### 3. Integration & Testing

**Goal**: Integrate with validation framework

**Tasks**:
- [ ] Integrate with validation framework
- [ ] Add configuration for scoring weights
- [ ] Testing with historical data
- [ ] Performance optimization

### Success Criteria

- [ ] Risk scores vary based on actual usage
- [ ] Historical success rates influence scores
- [ ] Context compatibility factored in
- [ ] Risk assessment improves tool selection

---

## Phase 2 Success Criteria

### Overall Phase Success

- [x] ETS forecasting operational ✅ (COMPLETED)
- [x] DBSCAN anomaly detection implemented ✅ (COMPLETED)
- [x] BOCPD changepoint detection implemented ✅ (COMPLETED)
- [ ] Pattern extraction from clusters functional
- [ ] Tool compatibility risk assessment operational

### Quality Gates

- [x] **Algorithm Validation**: Mathematical correctness verified (tests pass)
- [x] **Integration Testing**: End-to-end functionality confirmed (full suite passes)
- [x] **Performance Testing**: Benchmarks meet requirements (P95 targets met)
- [ ] **User Acceptance**: Feature meets requirements
- [ ] **Production Readiness**: Deployable to production environment

---

## Cross-References

- **Status**: See [CURRENT.md](../../CURRENT.md) for live metrics
- **Phase 1**: See [IMPLEMENTATION_PHASE1.md](./IMPLEMENTATION_PHASE1.md)
- **Research Integration**: Completed — see ROADMAP_ACTIVE.md for current state
- **Current Status**: See [ROADMAP_ACTIVE.md](../../ROADMAPS/ROADMAP_ACTIVE.md)

---

*Phase Status: Ready to Begin*
*Duration: 4 weeks*
*Effort: 100-120 hours*
