embed_graph.c

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/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property 
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: Details at https://graphviz.org
 *************************************************************************/
 
 
/************************************************
 
        Functions for computing the high-dimensional
        embedding and the PCA projection.
 
************************************************/
 
#include <neatogen/dijkstra.h>
#include <neatogen/bfs.h>
#include <neatogen/kkutils.h>
#include <neatogen/embed_graph.h>
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <util/alloc.h>
 
void embed_graph(vtx_data * graph, int n, int dim, DistType *** Coords,
                 int reweight_graph)
{
/* Compute 'dim'-dimensional high-dimensional embedding (HDE) for the 'n' nodes
  The embedding is based on choosing 'dim' pivots, and associating each
  coordinate with a unique pivot, assigning it to the graph-theoretic distances 
  of all nodes from the pivots
*/
 
    int i, j;
    int node;
    DistType *storage = gv_calloc(n * dim, sizeof(DistType));
    DistType **coords = *Coords;
    DistType *dist = gv_calloc(n, sizeof(DistType)); // this vector stores  the
                                                     // distances of each nodes
                                                     // to the selected “pivots”
    float *old_weights = graph[0].ewgts;
    DistType max_dist = 0;
 
    /* this matrix stores the distance between each node and each "pivot" */
    *Coords = coords = gv_calloc(dim, sizeof(DistType *));
    for (i = 0; i < dim; i++)
        coords[i] = storage + i * n;
 
    if (reweight_graph) {
        compute_new_weights(graph, n);
    }
 
    /* select the first pivot */
    node = rand() % n;
 
    if (reweight_graph) {
        dijkstra(node, graph, n, coords[0]);
    } else {
        bfs(node, graph, n, coords[0]);
    }
 
    for (i = 0; i < n; i++) {
        dist[i] = coords[0][i];
        if (dist[i] > max_dist) {
            node = i;
            max_dist = dist[i];
        }
    }
 
    /* select other dim-1 nodes as pivots */
    for (i = 1; i < dim; i++) {
        if (reweight_graph) {
            dijkstra(node, graph, n, coords[i]);
        } else {
            bfs(node, graph, n, coords[i]);
        }
        max_dist = 0;
        for (j = 0; j < n; j++) {
            dist[j] = MIN(dist[j], coords[i][j]);
            if (dist[j] > max_dist) {
                node = j;
                max_dist = dist[j];
            }
        }
 
    }
 
    free(dist);
 
    if (reweight_graph) {
        restore_old_weights(graph, n, old_weights);
    }
 
}
 
 /* Make each axis centered around 0 */
void center_coordinate(DistType ** coords, int n, int dim)
{
    int i, j;
    double sum, avg;
    for (i = 0; i < dim; i++) {
        sum = 0;
        for (j = 0; j < n; j++) {
            sum += coords[i][j];
        }
        avg = sum / n;
        for (j = 0; j < n; j++) {
            coords[i][j] -= (DistType) avg;
        }
    }
}