ecm.py

import numpy as np
import networkx as nx
from scipy.sparse import csr_matrix
from scipy.sparse.linalg import eigsh
from geomstats.manifold import RiemannianManifold
from geomstats.geometry.hyperbolic import Hyperbolic
from sklearn.decomposition import PCA
from gudhi import RipsComplex, SimplexTree
from gudhi.wasserstein import wasserstein_distance

class EventContinuumMapping:
    def __init__(self, manifold_dim=100):
        self.manifold = Hyperbolic(dim=manifold_dim)
        self.event_graph = nx.Graph()
        self.event_tensor = None
        self.pca = PCA(n_components=manifold_dim)

    def add_event(self, event_data):
        event_id = len(self.event_graph)
        self.event_graph.add_node(event_id, **event_data)
        self._update_manifold()
        return event_id

    def add_relation(self, event1_id, event2_id, relation_type, strength):
        self.event_graph.add_edge(event1_id, event2_id, type=relation_type, weight=strength)
        self._update_manifold()

    def _update_manifold(self):
        adj_matrix = nx.adjacency_matrix(self.event_graph)
        self.event_tensor = self._adjacency_to_tensor(adj_matrix)
        
        # Use PCA to reduce dimensionality of the event tensor
        flattened_tensor = self.event_tensor.reshape(-1, self.event_tensor.shape[-1])
        pca_result = self.pca.fit_transform(flattened_tensor)
        
        # Update the manifold's metric tensor
        metric_tensor = np.dot(pca_result.T, pca_result)
        self.manifold.metric.set_metric_matrix(metric_tensor)

    def _adjacency_to_tensor(self, adj_matrix):
        n = adj_matrix.shape[0]
        tensor = np.zeros((n, n, n))
        for i in range(n):
            for j in range(n):
                if adj_matrix[i, j] != 0:
                    tensor[i, j, :] = adj_matrix[i, :].toarray()
        return tensor

    def get_manifold_curvature(self):
        n = self.manifold.dim
        curvature_tensor = np.zeros((n, n, n, n))
        metric_tensor = self.manifold.metric.metric_matrix()
        
        for i in range(n):
            for j in range(n):
                for k in range(n):
                    for l in range(n):
                        curvature_tensor[i, j, k, l] = self.manifold.metric.curvature(
                            np.eye(n)[i],
                            np.eye(n)[j],
                            np.eye(n)[k],
                            np.eye(n)[l]
                        )
        
        return curvature_tensor

    def analyze_event_patterns(self):
        centrality = nx.eigenvector_centrality(self.event_graph)
        communities = nx.community.louvain_communities(self.event_graph)
        
        # Persistent homology analysis
        points = np.array([self.event_graph.nodes[node]['features'] for node in self.event_graph.nodes])
        rips_complex = RipsComplex(points=points)
        simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)
        diag = simplex_tree.persistence()
        
        # Topological features
        betti_numbers = simplex_tree.betti_numbers()
        
        return {
            'centrality': centrality,
            'communities': communities,
            'persistence_diagram': diag,
            'betti_numbers': betti_numbers
        }

    def temporal_analysis(self, time_window):
        # Create a time-ordered list of events
        events = sorted(self.event_graph.nodes(data=True), key=lambda x: x[1]['timestamp'])
        
        # Sliding window analysis
        temporal_patterns = []
        for i in range(len(events) - time_window + 1):
            window_events = events[i:i+time_window]
            window_graph = nx.Graph()
            for event in window_events:
                window_graph.add_node(event[0], **event[1])
            
            # Add edges within the time window
            for j in range(len(window_events)):
                for k in range(j+1, len(window_events)):
                    if self.event_graph.has_edge(window_events[j][0], window_events[k][0]):
                        window_graph.add_edge(window_events[j][0], window_events[k][0])
            
            # Analyze the window
            pattern = {
                'time_start': window_events[0][1]['timestamp'],
                'time_end': window_events[-1][1]['timestamp'],
                'num_events': len(window_events),
                'density': nx.density(window_graph),
                'clustering_coefficient': nx.average_clustering(window_graph)
            }
            temporal_patterns.append(pattern)
        
        return temporal_patterns

    def calculate_wasserstein_distance(self, other_ecm):
        # Calculate Wasserstein distance between persistence diagrams
        diag1 = self.analyze_event_patterns()['persistence_diagram']
        diag2 = other_ecm.analyze_event_patterns()['persistence_diagram']
        
        return wasserstein_distance(diag1, diag2)

    def get_event_embeddings(self):
        # Get node embeddings using the manifold
        embeddings = {}
        for node in self.event_graph.nodes():
            point = self.manifold.random_point()  # Initialize randomly
            embeddings[node] = self.manifold.to_tangent_space(point)
        
        return embeddings