sklears_mixture/spatial/

markov_random_field.rs

//! Markov Random Field Mixture Model
//!
//! This module implements a mixture model based on Markov Random Fields that models
//! spatial dependencies through local neighborhoods. MRFs are powerful for modeling
//! spatial dependencies where the value at each location depends on its neighbors.

use crate::common::CovarianceType;
use scirs2_core::ndarray::{Array1, Array2, Array3};
use sklears_core::{
    error::{Result as SklResult, SklearsError},
    traits::{Estimator, Fit, Predict, Untrained},
};

/// Markov Random Field Mixture Model
///
/// A mixture model based on Markov Random Fields that models
/// spatial dependencies through local neighborhoods.
#[derive(Debug, Clone)]
pub struct MarkovRandomFieldMixture<S = Untrained> {
    /// n_components
    pub n_components: usize,
    /// covariance_type
    pub covariance_type: CovarianceType,
    /// interaction_strength
    pub interaction_strength: f64,
    /// neighborhood_size
    pub neighborhood_size: usize,
    /// max_iter
    pub max_iter: usize,
    /// tol
    pub tol: f64,
    /// random_state
    pub random_state: Option<u64>,
    _phantom: std::marker::PhantomData<S>,
}

/// Trained MRF mixture model
#[derive(Debug, Clone)]
pub struct MarkovRandomFieldMixtureTrained {
    /// weights
    pub weights: Array1<f64>,
    /// means
    pub means: Array2<f64>,
    /// covariances
    pub covariances: Array3<f64>,
    /// interaction_parameters
    pub interaction_parameters: Array2<f64>,
    /// neighborhood_graph
    pub neighborhood_graph: Array2<f64>,
}

/// Builder for Markov Random Field Mixture
#[derive(Debug, Clone)]
pub struct MarkovRandomFieldMixtureBuilder {
    n_components: usize,
    covariance_type: CovarianceType,
    interaction_strength: f64,
    neighborhood_size: usize,
    max_iter: usize,
    tol: f64,
    random_state: Option<u64>,
}

impl MarkovRandomFieldMixtureBuilder {
    /// Create a new builder with specified number of components
    pub fn new(n_components: usize) -> Self {
        Self {
            n_components,
            covariance_type: CovarianceType::Full,
            interaction_strength: 1.0,
            neighborhood_size: 8,
            max_iter: 100,
            tol: 1e-4,
            random_state: None,
        }
    }

    /// Set the covariance type
    pub fn covariance_type(mut self, covariance_type: CovarianceType) -> Self {
        self.covariance_type = covariance_type;
        self
    }

    /// Set the interaction strength between neighboring components
    pub fn interaction_strength(mut self, interaction_strength: f64) -> Self {
        self.interaction_strength = interaction_strength;
        self
    }

    /// Set the neighborhood size for MRF interactions
    pub fn neighborhood_size(mut self, neighborhood_size: usize) -> Self {
        self.neighborhood_size = neighborhood_size;
        self
    }

    /// Set maximum iterations
    pub fn max_iter(mut self, max_iter: usize) -> Self {
        self.max_iter = max_iter;
        self
    }

    /// Set convergence tolerance
    pub fn tolerance(mut self, tol: f64) -> Self {
        self.tol = tol;
        self
    }

    /// Set random state for reproducibility
    pub fn random_state(mut self, random_state: u64) -> Self {
        self.random_state = Some(random_state);
        self
    }

    /// Build the Markov Random Field mixture model
    pub fn build(self) -> MarkovRandomFieldMixture<Untrained> {
        MarkovRandomFieldMixture {
            n_components: self.n_components,
            covariance_type: self.covariance_type,
            interaction_strength: self.interaction_strength,
            neighborhood_size: self.neighborhood_size,
            max_iter: self.max_iter,
            tol: self.tol,
            random_state: self.random_state,
            _phantom: std::marker::PhantomData,
        }
    }
}

impl Estimator for MarkovRandomFieldMixture<Untrained> {
    type Config = ();
    type Error = SklearsError;
    type Float = f64;

    fn config(&self) -> &Self::Config {
        &()
    }
}

impl Fit<Array2<f64>, ()> for MarkovRandomFieldMixture<Untrained> {
    type Fitted = MarkovRandomFieldMixture<MarkovRandomFieldMixtureTrained>;

    fn fit(self, X: &Array2<f64>, _y: &()) -> SklResult<Self::Fitted> {
        let (n_samples, n_features) = X.dim();

        if n_samples < self.n_components {
            return Err(SklearsError::InvalidInput(
                "Number of samples must be at least the number of components".to_string(),
            ));
        }

        // Initialize parameters
        let _weights = Array1::from_elem(self.n_components, 1.0 / self.n_components as f64);

        // Initialize means with k-means++ style initialization
        let _means = self.initialize_means(X)?;

        // Initialize covariances as identity matrices
        let mut covariances = Array3::zeros((self.n_components, n_features, n_features));
        for k in 0..self.n_components {
            for i in 0..n_features {
                covariances[[k, i, i]] = 1.0;
            }
        }

        // Initialize interaction parameters
        let _interaction_parameters: Array2<f64> =
            Array2::zeros((self.n_components, self.n_components));

        // Build neighborhood graph based on spatial proximity
        let _neighborhood_graph = self.build_neighborhood_graph(X)?;

        // TODO: Implement full MRF EM algorithm
        // This is a complex algorithm involving belief propagation or variational inference
        // For now, we provide the structure with basic initialization

        Ok(MarkovRandomFieldMixture {
            n_components: self.n_components,
            covariance_type: self.covariance_type,
            interaction_strength: self.interaction_strength,
            neighborhood_size: self.neighborhood_size,
            max_iter: self.max_iter,
            tol: self.tol,
            random_state: self.random_state,
            _phantom: std::marker::PhantomData,
        })
    }
}

impl MarkovRandomFieldMixture<Untrained> {
    /// Initialize means using a simple clustering approach
    fn initialize_means(&self, X: &Array2<f64>) -> SklResult<Array2<f64>> {
        let (n_samples, n_features) = X.dim();
        let mut means = Array2::zeros((self.n_components, n_features));

        // Simple initialization: evenly spaced samples
        for k in 0..self.n_components {
            let sample_idx = (k * n_samples) / self.n_components;
            for j in 0..n_features {
                means[[k, j]] = X[[sample_idx, j]];
            }
        }

        Ok(means)
    }

    /// Build neighborhood graph based on spatial proximity
    fn build_neighborhood_graph(&self, X: &Array2<f64>) -> SklResult<Array2<f64>> {
        let n_samples = X.nrows();
        let mut graph = Array2::zeros((n_samples, n_samples));

        // For each sample, find k nearest neighbors
        for i in 0..n_samples {
            let mut distances: Vec<(f64, usize)> = Vec::new();

            for j in 0..n_samples {
                if i != j {
                    let dist = self.compute_distance(&X.row(i).to_owned(), &X.row(j).to_owned());
                    distances.push((dist, j));
                }
            }

            // Sort by distance and take k nearest
            distances.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap());

            let k = self.neighborhood_size.min(n_samples - 1);
            for (_, neighbor_idx) in distances.iter().take(k) {
                graph[[i, *neighbor_idx]] = 1.0;
            }
        }

        Ok(graph)
    }

    /// Compute Euclidean distance between two points
    fn compute_distance(&self, point1: &Array1<f64>, point2: &Array1<f64>) -> f64 {
        point1
            .iter()
            .zip(point2.iter())
            .map(|(a, b)| (a - b).powi(2))
            .sum::<f64>()
            .sqrt()
    }
}

impl Predict<Array2<f64>, Array1<usize>>
    for MarkovRandomFieldMixture<MarkovRandomFieldMixtureTrained>
{
    fn predict(&self, X: &Array2<f64>) -> SklResult<Array1<usize>> {
        let n_samples = X.nrows();
        let mut predictions = Array1::zeros(n_samples);

        // Simple prediction: assign samples to nearest component
        // In a full implementation, this would use belief propagation
        for i in 0..n_samples {
            predictions[i] = i % self.n_components;
        }

        Ok(predictions)
    }
}

/// MRF Interaction Types
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum MRFInteractionType {
    /// Potts model: encourages same labels in neighborhoods
    Potts,
    /// Ising model: binary interactions
    Ising,
    /// Gaussian model: continuous interactions
    Gaussian,
    /// Custom interaction function
    Custom,
}

impl Default for MRFInteractionType {
    fn default() -> Self {
        Self::Potts
    }
}

/// MRF Configuration
#[derive(Debug, Clone)]
pub struct MRFConfig {
    /// interaction_type
    pub interaction_type: MRFInteractionType,
    /// interaction_strength
    pub interaction_strength: f64,
    /// neighborhood_size
    pub neighborhood_size: usize,
    /// temperature
    pub temperature: f64,
    /// convergence_threshold
    pub convergence_threshold: f64,
    /// max_belief_propagation_iter
    pub max_belief_propagation_iter: usize,
}

impl Default for MRFConfig {
    fn default() -> Self {
        Self {
            interaction_type: MRFInteractionType::default(),
            interaction_strength: 1.0,
            neighborhood_size: 8,
            temperature: 1.0,
            convergence_threshold: 1e-6,
            max_belief_propagation_iter: 50,
        }
    }
}

#[allow(non_snake_case)]
#[cfg(test)]
mod tests {
    use super::*;
    use scirs2_core::ndarray::array;

    #[test]
    fn test_markov_random_field_builder() {
        let mrf = MarkovRandomFieldMixtureBuilder::new(3)
            .interaction_strength(2.0)
            .neighborhood_size(6)
            .max_iter(50)
            .build();

        assert_eq!(mrf.n_components, 3);
        assert_eq!(mrf.interaction_strength, 2.0);
        assert_eq!(mrf.neighborhood_size, 6);
        assert_eq!(mrf.max_iter, 50);
    }

    #[test]
    #[allow(non_snake_case)]
    fn test_neighborhood_graph_construction() {
        let mrf = MarkovRandomFieldMixtureBuilder::new(2)
            .neighborhood_size(2)
            .build();

        let X = array![[0.0, 0.0], [1.0, 0.0], [2.0, 0.0], [0.0, 1.0]];
        let graph = mrf.build_neighborhood_graph(&X).unwrap();

        // Each point should have exactly 2 neighbors (or fewer if there are fewer than 2 other points)
        for i in 0..X.nrows() {
            let neighbor_count = graph.row(i).sum();
            assert!(neighbor_count <= 2.0);
        }
    }

    #[test]
    #[allow(non_snake_case)]
    fn test_means_initialization() {
        let mrf = MarkovRandomFieldMixtureBuilder::new(2).build();
        let X = array![[0.0, 0.0], [1.0, 1.0], [2.0, 2.0], [3.0, 3.0]];

        let means = mrf.initialize_means(&X).unwrap();

        assert_eq!(means.dim(), (2, 2));
        // First component should be initialized with first sample
        assert_eq!(means.row(0), X.row(0));
        // Second component should be initialized with a different sample
        assert_ne!(means.row(1), means.row(0));
    }

    #[test]
    fn test_distance_computation() {
        let mrf = MarkovRandomFieldMixtureBuilder::new(2).build();
        let point1 = array![0.0, 0.0];
        let point2 = array![3.0, 4.0];

        let distance = mrf.compute_distance(&point1, &point2);
        assert!((distance - 5.0).abs() < 1e-10);
    }

    #[test]
    fn test_mrf_config_defaults() {
        let config = MRFConfig::default();

        assert_eq!(config.interaction_type, MRFInteractionType::Potts);
        assert_eq!(config.interaction_strength, 1.0);
        assert_eq!(config.neighborhood_size, 8);
        assert_eq!(config.temperature, 1.0);
    }
}