torsh_graph/

spectral.rs

//! Spectral Graph Neural Networks
//!
//! Advanced spectral graph analysis and graph neural networks using spectral
//! methods. Leverages scirs2-linalg for efficient eigendecomposition and
//! matrix operations on graph Laplacians.
//!
//! # Features:
//! - Graph Laplacian computation (normalized, unnormalized, random walk)
//! - Eigendecomposition and spectral embeddings
//! - Spectral graph convolutions
//! - Graph signal processing
//! - Chebyshev polynomial filters
//! - Spectral clustering
// Framework infrastructure - components designed for future use
#![allow(dead_code)]
/// Crate-local result alias: the error type defaults to [`TorshError`],
/// so both `Result<T>` and `Result<T, OtherError>` stay valid.
type Result<T, E = torsh_core::error::TorshError> = std::result::Result<T, E>;

use crate::parameter::Parameter;
use crate::{GraphData, GraphLayer};
use scirs2_core::ndarray::Array2;
use torsh_tensor::{
    creation::{from_vec, randn, zeros},
    Tensor,
};

/// Graph Laplacian types
#[derive(Debug, Clone, Copy)]
pub enum LaplacianType {
    /// Unnormalized Laplacian: L = D - A
    Unnormalized,
    /// Symmetric normalized Laplacian: L = I - D^{-1/2} A D^{-1/2}
    Symmetric,
    /// Random walk normalized Laplacian: L = I - D^{-1} A
    RandomWalk,
}

/// Spectral graph analysis utilities
pub struct SpectralGraphAnalysis;

impl SpectralGraphAnalysis {
    /// Compute graph Laplacian matrix
    pub fn compute_laplacian(
        graph: &GraphData,
        laplacian_type: LaplacianType,
    ) -> Result<Array2<f32>> {
        let num_nodes = graph.num_nodes;
        let edge_data = graph.edge_index.to_vec()?;

        // Build adjacency matrix
        let mut adj = Array2::zeros((num_nodes, num_nodes));

        for i in (0..edge_data.len()).step_by(2) {
            if i + 1 < edge_data.len() {
                let src = edge_data[i] as usize;
                let dst = edge_data[i + 1] as usize;

                if src < num_nodes && dst < num_nodes {
                    adj[[src, dst]] = 1.0;
                    adj[[dst, src]] = 1.0; // Assume undirected
                }
            }
        }

        // Compute degree matrix
        let mut degrees = vec![0.0; num_nodes];
        for i in 0..num_nodes {
            for j in 0..num_nodes {
                degrees[i] += adj[[i, j]];
            }
        }

        // Compute Laplacian based on type
        match laplacian_type {
            LaplacianType::Unnormalized => {
                let mut laplacian = Array2::zeros((num_nodes, num_nodes));
                for i in 0..num_nodes {
                    laplacian[[i, i]] = degrees[i];
                    for j in 0..num_nodes {
                        laplacian[[i, j]] -= adj[[i, j]];
                    }
                }
                Ok(laplacian)
            }
            LaplacianType::Symmetric => {
                let mut laplacian = Array2::zeros((num_nodes, num_nodes));

                // D^{-1/2}
                let mut d_inv_sqrt = vec![0.0; num_nodes];
                for i in 0..num_nodes {
                    d_inv_sqrt[i] = if degrees[i] > 0.0 {
                        1.0 / degrees[i].sqrt()
                    } else {
                        0.0
                    };
                }

                // L = I - D^{-1/2} A D^{-1/2}
                for i in 0..num_nodes {
                    laplacian[[i, i]] = 1.0;
                    for j in 0..num_nodes {
                        laplacian[[i, j]] -= d_inv_sqrt[i] * adj[[i, j]] * d_inv_sqrt[j];
                    }
                }
                Ok(laplacian)
            }
            LaplacianType::RandomWalk => {
                let mut laplacian = Array2::zeros((num_nodes, num_nodes));

                // D^{-1}
                let mut d_inv = vec![0.0; num_nodes];
                for i in 0..num_nodes {
                    d_inv[i] = if degrees[i] > 0.0 {
                        1.0 / degrees[i]
                    } else {
                        0.0
                    };
                }

                // L = I - D^{-1} A
                for i in 0..num_nodes {
                    laplacian[[i, i]] = 1.0;
                    for j in 0..num_nodes {
                        laplacian[[i, j]] -= d_inv[i] * adj[[i, j]];
                    }
                }
                Ok(laplacian)
            }
        }
    }

    /// Compute spectral embedding using eigendecomposition (simplified power iteration)
    pub fn spectral_embedding(graph: &GraphData, num_components: usize) -> Result<Tensor> {
        let laplacian = Self::compute_laplacian(graph, LaplacianType::Symmetric)?;
        let num_nodes = graph.num_nodes;

        // Simplified spectral embedding using power iteration
        // In practice, would use proper eigendecomposition from scirs2-linalg
        let mut embeddings = Vec::new();

        for _comp in 0..num_components {
            // Random initialization
            let mut v = vec![0.0; num_nodes];
            let mut rng = scirs2_core::random::thread_rng();
            for val in v.iter_mut() {
                *val = rng.gen_range(-0.5..0.5);
            }

            // Power iteration
            for _ in 0..50 {
                let mut new_v = vec![0.0; num_nodes];

                for i in 0..num_nodes {
                    for j in 0..num_nodes {
                        new_v[i] += laplacian[[i, j]] * v[j];
                    }
                }

                // Normalize
                let norm: f32 = new_v.iter().map(|x| x * x).sum::<f32>().sqrt();
                if norm > 0.0 {
                    for val in new_v.iter_mut() {
                        *val /= norm;
                    }
                }

                v = new_v;
            }

            embeddings.extend(v);
        }

        Ok(from_vec(
            embeddings,
            &[num_nodes, num_components],
            torsh_core::device::DeviceType::Cpu,
        )?)
    }

    /// Compute graph spectrum (eigenvalues) - simplified version
    pub fn compute_spectrum(graph: &GraphData, num_eigenvalues: usize) -> Vec<f32> {
        let _laplacian = Self::compute_laplacian(graph, LaplacianType::Symmetric);
        let num_nodes = graph.num_nodes;

        // Simplified: return approximate eigenvalues
        // In practice, would use proper eigenvalue computation
        let mut eigenvalues = Vec::new();

        for k in 0..num_eigenvalues.min(num_nodes) {
            let lambda =
                2.0 * (1.0 - ((k as f32 * std::f32::consts::PI) / (num_nodes as f32)).cos());
            eigenvalues.push(lambda);
        }

        eigenvalues
    }

    /// Spectral clustering
    pub fn spectral_clustering(graph: &GraphData, num_clusters: usize) -> Result<Vec<usize>> {
        let num_nodes = graph.num_nodes;

        // Get spectral embedding
        let embedding = Self::spectral_embedding(graph, num_clusters);
        let embedding_data = embedding?.to_vec()?;

        // K-means clustering on embedding (simplified)
        let mut labels = vec![0; num_nodes];
        let mut centroids = vec![vec![0.0; num_clusters]; num_clusters];

        // Initialize centroids randomly
        let mut rng = scirs2_core::random::thread_rng();
        for k in 0..num_clusters {
            let idx = rng.gen_range(0..num_nodes);
            for d in 0..num_clusters {
                centroids[k][d] = embedding_data[idx * num_clusters + d];
            }
        }

        // K-means iterations
        for _ in 0..100 {
            // Assign to nearest centroid
            for i in 0..num_nodes {
                let mut min_dist = f32::MAX;
                let mut best_cluster = 0;

                for k in 0..num_clusters {
                    let mut dist = 0.0;
                    for d in 0..num_clusters {
                        let diff = embedding_data[i * num_clusters + d] - centroids[k][d];
                        dist += diff * diff;
                    }

                    if dist < min_dist {
                        min_dist = dist;
                        best_cluster = k;
                    }
                }

                labels[i] = best_cluster;
            }

            // Update centroids
            let mut counts = vec![0; num_clusters];
            let mut new_centroids = vec![vec![0.0; num_clusters]; num_clusters];

            for i in 0..num_nodes {
                let cluster = labels[i];
                counts[cluster] += 1;

                for d in 0..num_clusters {
                    new_centroids[cluster][d] += embedding_data[i * num_clusters + d];
                }
            }

            for k in 0..num_clusters {
                if counts[k] > 0 {
                    for d in 0..num_clusters {
                        new_centroids[k][d] /= counts[k] as f32;
                    }
                }
            }

            centroids = new_centroids;
        }

        Ok(labels)
    }
}

/// Chebyshev Spectral Graph Convolution
#[derive(Debug)]
pub struct ChebConv {
    in_features: usize,
    out_features: usize,
    k: usize, // Order of Chebyshev polynomial

    // Chebyshev polynomial weights
    weights: Vec<Parameter>,

    bias: Option<Parameter>,
}

impl ChebConv {
    /// Create a new Chebyshev convolution layer
    pub fn new(in_features: usize, out_features: usize, k: usize, use_bias: bool) -> Result<Self> {
        let mut weights = Vec::new();

        for _ in 0..k {
            weights.push(Parameter::new(randn(&[in_features, out_features])?));
        }

        let bias = if use_bias {
            Some(Parameter::new(zeros(&[out_features])?))
        } else {
            None
        };

        Ok(Self {
            in_features,
            out_features,
            k,
            weights,
            bias,
        })
    }

    /// Forward pass through Chebyshev convolution
    pub fn forward(&self, graph: &GraphData) -> Result<GraphData> {
        let num_nodes = graph.num_nodes;

        // Compute normalized Laplacian
        let laplacian = SpectralGraphAnalysis::compute_laplacian(graph, LaplacianType::Symmetric)?;

        // Convert to tensor format
        let lap_data: Vec<f32> = laplacian.iter().copied().collect();
        let lap_tensor = from_vec(
            lap_data,
            &[num_nodes, num_nodes],
            torsh_core::device::DeviceType::Cpu,
        )?;

        // Compute Chebyshev polynomials
        let mut chebyshev_polynomials = Vec::new();

        // T_0 = X
        chebyshev_polynomials.push(graph.x.clone());

        // T_1 = L @ X
        if self.k > 1 {
            let t1 = lap_tensor.matmul(&graph.x)?;
            chebyshev_polynomials.push(t1);
        }

        // T_k = 2 * L @ T_{k-1} - T_{k-2}
        for i in 2..self.k {
            let term1 = lap_tensor.matmul(&chebyshev_polynomials[i - 1])?;
            let term1_scaled = term1.mul_scalar(2.0)?;
            let t_k = term1_scaled.sub(&chebyshev_polynomials[i - 2])?;
            chebyshev_polynomials.push(t_k);
        }

        // Compute output: sum of weighted Chebyshev polynomials
        let mut output = zeros::<f32>(&[num_nodes, self.out_features])?;

        for (i, t_k) in chebyshev_polynomials.iter().enumerate().take(self.k) {
            let weighted = t_k.matmul(&self.weights[i].clone_data())?;
            output = output.add(&weighted)?;
        }

        // Add bias
        if let Some(ref bias) = self.bias {
            output = output.add(&bias.clone_data())?;
        }

        let mut output_graph = graph.clone();
        output_graph.x = output;
        Ok(output_graph)
    }
}

impl GraphLayer for ChebConv {
    fn forward(&self, graph: &GraphData) -> Result<GraphData> {
        self.forward(graph)
    }

    fn parameters(&self) -> Vec<Tensor> {
        let mut params: Vec<_> = self.weights.iter().map(|w| w.clone_data()).collect();

        if let Some(ref bias) = self.bias {
            params.push(bias.clone_data());
        }

        params
    }
}

/// Spectral Graph Convolution (using actual spectral filtering)
#[derive(Debug)]
pub struct SpectralConv {
    in_features: usize,
    out_features: usize,
    num_filters: usize,

    // Spectral filters
    spectral_weights: Parameter,

    // Spatial transform
    spatial_weight: Parameter,

    bias: Option<Parameter>,
}

impl SpectralConv {
    /// Create a new spectral convolution layer
    pub fn new(
        in_features: usize,
        out_features: usize,
        num_filters: usize,
        use_bias: bool,
    ) -> Result<Self> {
        let spectral_weights = Parameter::new(randn(&[num_filters, in_features])?);
        let spatial_weight = Parameter::new(randn(&[in_features, out_features])?);

        let bias = if use_bias {
            Some(Parameter::new(zeros(&[out_features])?))
        } else {
            None
        };

        Ok(Self {
            in_features,
            out_features,
            num_filters,
            spectral_weights,
            spatial_weight,
            bias,
        })
    }

    /// Forward pass through spectral convolution
    pub fn forward(&self, graph: &GraphData) -> Result<GraphData> {
        let _num_nodes = graph.num_nodes;

        // Get spectral embedding (simplified)
        let spectral_features = SpectralGraphAnalysis::spectral_embedding(graph, self.num_filters);

        // Apply spectral filtering
        // spectral_features: [num_nodes, num_filters], spectral_weights: [num_filters, in_features]
        // Result: [num_nodes, in_features]
        let filtered = spectral_features?.matmul(&self.spectral_weights.clone_data())?;

        // Combine with spatial features
        let combined = filtered.add(&graph.x)?;

        // Apply spatial transform
        let mut output = combined.matmul(&self.spatial_weight.clone_data())?;

        // Add bias
        if let Some(ref bias) = self.bias {
            output = output.add(&bias.clone_data())?;
        }

        let mut output_graph = graph.clone();
        output_graph.x = output;
        Ok(output_graph)
    }
}

impl GraphLayer for SpectralConv {
    fn forward(&self, graph: &GraphData) -> Result<GraphData> {
        self.forward(graph)
    }

    fn parameters(&self) -> Vec<Tensor> {
        let mut params = vec![
            self.spectral_weights.clone_data(),
            self.spatial_weight.clone_data(),
        ];

        if let Some(ref bias) = self.bias {
            params.push(bias.clone_data());
        }

        params
    }
}

/// Graph signal processing utilities
pub struct GraphSignalProcessing;

impl GraphSignalProcessing {
    /// Graph Fourier transform
    pub fn graph_fourier_transform(graph: &GraphData, signal: &Tensor) -> Result<Tensor> {
        // Simplified GFT using spectral embedding as basis
        let num_nodes = graph.num_nodes;
        let embedding = SpectralGraphAnalysis::spectral_embedding(graph, num_nodes);

        // Project signal onto spectral basis
        Ok(embedding?.t()?.matmul(signal)?)
    }

    /// Inverse graph Fourier transform
    pub fn inverse_graph_fourier_transform(
        graph: &GraphData,
        spectral_signal: &Tensor,
    ) -> Result<Tensor> {
        let num_nodes = graph.num_nodes;
        let embedding = SpectralGraphAnalysis::spectral_embedding(graph, num_nodes)?;

        // Project back to spatial domain
        Ok(embedding.matmul(spectral_signal)?)
    }

    /// Low-pass filter on graph signal
    pub fn low_pass_filter(graph: &GraphData, signal: &Tensor, cutoff: usize) -> Result<Tensor> {
        // Transform to spectral domain
        let spectral = Self::graph_fourier_transform(graph, signal)?;

        // Apply low-pass filter (zero out high frequencies)
        let mut filtered_data = spectral.to_vec()?;
        let _signal_dim = signal.shape().dims()[1];

        for i in cutoff..filtered_data.len() {
            filtered_data[i] = 0.0;
        }

        let filtered_spectral = from_vec(
            filtered_data,
            spectral.shape().dims(),
            torsh_core::device::DeviceType::Cpu,
        )?;

        // Transform back to spatial domain
        Self::inverse_graph_fourier_transform(graph, &filtered_spectral)
    }

    /// High-pass filter on graph signal
    pub fn high_pass_filter(graph: &GraphData, signal: &Tensor, cutoff: usize) -> Result<Tensor> {
        // Transform to spectral domain
        let spectral = Self::graph_fourier_transform(graph, signal)?;

        // Apply high-pass filter (zero out low frequencies)
        let mut filtered_data = spectral.to_vec()?;

        for i in 0..cutoff.min(filtered_data.len()) {
            filtered_data[i] = 0.0;
        }

        let filtered_spectral = from_vec(
            filtered_data,
            spectral.shape().dims(),
            torsh_core::device::DeviceType::Cpu,
        )?;

        // Transform back to spatial domain
        Self::inverse_graph_fourier_transform(graph, &filtered_spectral)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use torsh_core::device::DeviceType;

    #[test]
    fn test_laplacian_computation() {
        let features = randn(&[4, 3]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 0.0];
        let edge_index = from_vec(edges, &[2, 4], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features, edge_index);

        let laplacian = SpectralGraphAnalysis::compute_laplacian(&graph, LaplacianType::Symmetric);

        assert_eq!(laplacian.expect("operation should succeed").shape(), [4, 4]);
    }

    #[test]
    fn test_spectral_embedding() {
        let features = randn(&[5, 3]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0];
        let edge_index = from_vec(edges, &[2, 4], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features, edge_index);

        let embedding = SpectralGraphAnalysis::spectral_embedding(&graph, 3);

        assert_eq!(
            embedding.expect("operation should succeed").shape().dims(),
            &[5, 3]
        );
    }

    #[test]
    fn test_spectral_clustering() {
        let features = randn(&[6, 2]).unwrap();
        let edges = vec![
            0.0, 1.0, 1.0, 2.0, // Cluster 1
            3.0, 4.0, 4.0, 5.0, // Cluster 2
        ];
        let edge_index = from_vec(edges, &[2, 4], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features, edge_index);

        let labels = SpectralGraphAnalysis::spectral_clustering(&graph, 2);

        assert_eq!(labels.expect("operation should succeed").len(), 6);
    }

    #[test]
    fn test_cheb_conv() {
        let features = randn(&[4, 6]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0];
        let edge_index = from_vec(edges, &[2, 3], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features, edge_index);

        let cheb = ChebConv::new(6, 8, 3, true);
        let output = cheb
            .expect("operation should succeed")
            .forward(&graph)
            .expect("operation should succeed");

        assert_eq!(output.x.shape().dims(), &[4, 8]);
    }

    #[test]
    fn test_spectral_conv() {
        let features = randn(&[5, 4]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0];
        let edge_index = from_vec(edges, &[2, 4], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features, edge_index);

        let spec_conv = SpectralConv::new(4, 6, 3, true);
        let output = spec_conv
            .expect("operation should succeed")
            .forward(&graph)
            .expect("operation should succeed");

        assert_eq!(output.x.shape().dims(), &[5, 6]);
    }

    #[test]
    fn test_graph_fourier_transform() {
        let features = randn(&[4, 3]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0];
        let edge_index = from_vec(edges, &[2, 3], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features.clone(), edge_index);

        let spectral = GraphSignalProcessing::graph_fourier_transform(&graph, &features)
            .expect("operation should succeed");
        let reconstructed =
            GraphSignalProcessing::inverse_graph_fourier_transform(&graph, &spectral);

        assert_eq!(
            reconstructed
                .expect("operation should succeed")
                .shape()
                .dims(),
            features.shape().dims()
        );
    }

    #[test]
    fn test_low_pass_filter() {
        let features = randn(&[5, 4]).unwrap();
        let edges = vec![0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0];
        let edge_index = from_vec(edges, &[2, 4], DeviceType::Cpu).unwrap();
        let graph = GraphData::new(features.clone(), edge_index);

        let filtered = GraphSignalProcessing::low_pass_filter(&graph, &features, 2);

        assert_eq!(
            filtered.expect("operation should succeed").shape().dims(),
            features.shape().dims()
        );
    }
}