lwkmeans.c

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/*-------------------------------------------------------------------------
 *
 * Copyright (c) 2018-2021, Darafei Praliaskouski <me@komzpa.net>
 * Copyright (c) 2016, Paul Ramsey <pramsey@cleverelephant.ca>
 *
 *------------------------------------------------------------------------*/
 
#include "liblwgeom_internal.h"
 
/*
 * When clustering lists with NULL or EMPTY elements, they will get this as
 * their cluster number. (All the other clusters will be non-negative)
 */
#define KMEANS_NULL_CLUSTER -1
 
/*
 * If the algorithm doesn't converge within this number of iterations,
 * it will return with a failure error code.
 */
#define KMEANS_MAX_ITERATIONS 1000
 
static uint32_t kmeans(POINT4D *objs,
                       uint32_t *clusters,
                       uint32_t n,
                       POINT4D *centers,
                       double *radii,
                       uint32_t min_k,
                       double max_radius);
 
inline static double
distance3d_sqr_pt4d_pt4d(const POINT4D *p1, const POINT4D *p2)
{
        double hside = p2->x - p1->x;
        double vside = p2->y - p1->y;
        double zside = p2->z - p1->z;
 
        return hside * hside + vside * vside + zside * zside;
}
 
/* Split the clusters that need to be split */
static uint32_t
improve_structure(POINT4D *objs,
                  uint32_t *clusters,
                  uint32_t n,
                  POINT4D *centers,
                  double *radii,
                  uint32_t k,
                  double max_radius)
{
        /* Input check: radius limit should be measurable */
        if (max_radius <= 0)
                return k;
 
        double max_radius_sq = max_radius * max_radius;
 
        /* Do we have the big clusters to split at all? */
        uint32_t first_cluster_to_split = 0;
        for (; first_cluster_to_split < k; first_cluster_to_split++)
                if (radii[first_cluster_to_split] > max_radius_sq)
                        break;
        if (first_cluster_to_split == k)
                return k;
 
        POINT4D *temp_objs = lwalloc(sizeof(POINT4D) * n);
        uint32_t *temp_clusters = lwalloc(sizeof(uint32_t) * n);
        double *temp_radii = lwalloc(sizeof(double) * n);
        POINT4D *temp_centers = lwalloc(sizeof(POINT4D) * n);
 
        uint32_t new_k = k;
 
        for (uint32_t cluster = first_cluster_to_split; cluster < k; cluster++)
        {
                if (radii[cluster] <= max_radius_sq)
                        continue;
 
                /* copy cluster alone */
                uint32_t cluster_size = 0;
                for (uint32_t i = 0; i < n; i++)
                        if (clusters[i] == cluster)
                                temp_objs[cluster_size++] = objs[i];
                if (cluster_size <= 1)
                        continue;
 
                /* run 2-means on the cluster */
                kmeans(temp_objs, temp_clusters, cluster_size, temp_centers, temp_radii, 2, 0);
 
                /* replace cluster with split */
                uint32_t d = 0;
                for (uint32_t i = 0; i < n; i++)
                        if (clusters[i] == cluster)
                                if (temp_clusters[d++])
                                        clusters[i] = new_k;
 
                centers[cluster] = temp_centers[0];
                centers[new_k] = temp_centers[1];
                radii[cluster] = temp_radii[0];
                radii[new_k] = temp_radii[1];
                new_k++;
        }
        lwfree(temp_centers);
        lwfree(temp_radii);
        lwfree(temp_clusters);
        lwfree(temp_objs);
        return new_k;
}
 
/* Refresh mapping of point to closest cluster */
static uint8_t
update_r(POINT4D *objs, uint32_t *clusters, uint32_t n, POINT4D *centers, double *radii, uint32_t k)
{
        uint8_t converged = LW_TRUE;
        if (radii)
                memset(radii, 0, sizeof(double) * k);
 
        for (uint32_t i = 0; i < n; i++)
        {
                POINT4D obj = objs[i];
 
                /* Initialize with distance to first cluster */
                double curr_distance = distance3d_sqr_pt4d_pt4d(&obj, &centers[0]);
                uint32_t curr_cluster = 0;
 
                /* Check all other cluster centers and find the nearest */
                for (uint32_t cluster = 1; cluster < k; cluster++)
                {
                        double distance = distance3d_sqr_pt4d_pt4d(&obj, &centers[cluster]);
                        if (distance < curr_distance)
                        {
                                curr_distance = distance;
                                curr_cluster = cluster;
                        }
                }
 
                /* Store the nearest cluster this object is in */
                if (clusters[i] != curr_cluster)
                {
                        converged = LW_FALSE;
                        clusters[i] = curr_cluster;
                }
                if (radii)
                        if (radii[curr_cluster] < curr_distance)
                                radii[curr_cluster] = curr_distance;
        }
        return converged;
}
 
/* Refresh cluster centroids based on all of their objects */
static void
update_means(POINT4D *objs, uint32_t *clusters, uint32_t n, POINT4D *centers, uint32_t k)
{
        memset(centers, 0, sizeof(POINT4D) * k);
        /* calculate weighted sum */
        for (uint32_t i = 0; i < n; i++)
        {
                uint32_t cluster = clusters[i];
                centers[cluster].x += objs[i].x * objs[i].m;
                centers[cluster].y += objs[i].y * objs[i].m;
                centers[cluster].z += objs[i].z * objs[i].m;
                centers[cluster].m += objs[i].m;
        }
        /* divide by weight to get average */
        for (uint32_t i = 0; i < k; i++)
        {
                if (centers[i].m)
                {
                        centers[i].x /= centers[i].m;
                        centers[i].y /= centers[i].m;
                        centers[i].z /= centers[i].m;
                }
        }
}
 
/* Assign initial clusters centroids heuristically */
static void
kmeans_init(POINT4D *objs, uint32_t n, POINT4D *centers, uint32_t k)
{
        double *distances;
        uint32_t p1 = 0, p2 = 0;
        uint32_t duplicate_count = 1; /* a point is a duplicate of itself */
        double max_dst = -1;
 
        /* k=0, k=1: any point will do */
        assert(n > 0);
        if (k < 2)
        {
                centers[0] = objs[0];
                return;
        }
 
        /* k >= 2: find two distant points greedily */
        for (uint32_t i = 1; i < n; i++)
        {
                /* if we found a larger distance, replace our choice */
                double dst_p1 = distance3d_sqr_pt4d_pt4d(&objs[i], &objs[p1]);
                double dst_p2 = distance3d_sqr_pt4d_pt4d(&objs[i], &objs[p2]);
                if ((dst_p1 > max_dst) || (dst_p2 > max_dst))
                {
                        if (dst_p1 > dst_p2)
                        {
                                max_dst = dst_p1;
                                p2 = i;
                        }
                        else
                        {
                                max_dst = dst_p2;
                                p1 = i;
                        }
                }
                if ((dst_p1 == 0) || (dst_p2 == 0))
                        duplicate_count++;
        }
        if (duplicate_count > 1)
                lwnotice(
                    "%s: there are at least %u duplicate inputs, number of output clusters may be less than you requested",
                    __func__,
                    duplicate_count);
 
        /* by now two points should be found and non-same */
        assert(p1 != p2 && max_dst >= 0);
 
        /* accept these two points */
        centers[0] = objs[p1];
        centers[1] = objs[p2];
 
        if (k > 2)
        {
                /* array of minimum distance to a point from accepted cluster centers */
                distances = lwalloc(sizeof(double) * n);
 
                /* initialize array with distance to first object */
                for (uint32_t j = 0; j < n; j++)
                        distances[j] = distance3d_sqr_pt4d_pt4d(&objs[j], &centers[0]);
                distances[p1] = -1;
                distances[p2] = -1;
 
                /* loop i on clusters, skip 0 and 1 as found already */
                for (uint32_t i = 2; i < k; i++)
                {
                        uint32_t candidate_center = 0;
                        double max_distance = -DBL_MAX;
 
                        /* loop j on objs */
                        for (uint32_t j = 0; j < n; j++)
                        {
                                /* empty objs and accepted clusters are already marked with distance = -1 */
                                if (distances[j] < 0)
                                        continue;
 
                                /* update minimal distance with previously accepted cluster */
                                double current_distance = distance3d_sqr_pt4d_pt4d(&objs[j], &centers[i - 1]);
                                if (current_distance < distances[j])
                                        distances[j] = current_distance;
 
                                /* greedily take a point that's farthest from any of accepted clusters */
                                if (distances[j] > max_distance)
                                {
                                        candidate_center = j;
                                        max_distance = distances[j];
                                }
                        }
 
                        /* Checked earlier by counting entries on input, just in case */
                        assert(max_distance >= 0);
 
                        /* accept candidate to centers */
                        distances[candidate_center] = -1;
                        /* Copy the point coordinates into the initial centers array
                         * Centers array is an array of pointers to points, not an array of points */
                        centers[i] = objs[candidate_center];
                }
                lwfree(distances);
        }
}
 
static uint32_t
kmeans(POINT4D *objs,
       uint32_t *clusters,
       uint32_t n,
       POINT4D *centers,
       double *radii,
       uint32_t min_k,
       double max_radius)
{
        uint8_t converged = LW_FALSE;
        uint32_t cur_k = min_k;
 
        kmeans_init(objs, n, centers, cur_k);
        /* One iteration of kmeans needs to happen without shortcuts to fully initialize structures */
        update_r(objs, clusters, n, centers, radii, cur_k);
        update_means(objs, clusters, n, centers, cur_k);
        for (uint32_t t = 0; t < KMEANS_MAX_ITERATIONS; t++)
        {
                /* Standard KMeans loop */
                for (uint32_t i = 0; i < KMEANS_MAX_ITERATIONS; i++)
                {
                        LW_ON_INTERRUPT(break);
                        converged = update_r(objs, clusters, n, centers, radii, cur_k);
                        if (converged)
                                break;
                        update_means(objs, clusters, n, centers, cur_k);
                }
                if (!converged || !max_radius)
                        break;
 
                /* XMeans-inspired improve_structure pass to split clusters bigger than limit into 2 */
                uint32_t new_k = improve_structure(objs, clusters, n, centers, radii, cur_k, max_radius);
                if (new_k == cur_k)
                        break;
                cur_k = new_k;
        }
 
        if (!converged)
        {
                lwerror("%s did not converge after %d iterations", __func__, KMEANS_MAX_ITERATIONS);
                return 0;
        }
        return cur_k;
}
 
int *
lwgeom_cluster_kmeans(const LWGEOM **geoms, uint32_t n, uint32_t k, double max_radius)
{
        uint32_t num_non_empty = 0;
 
        assert(k > 0);
        assert(n > 0);
        assert(max_radius >= 0);
        assert(geoms);
 
        if (n < k)
        {
                lwerror(
                    "%s: number of geometries is less than the number of clusters requested, not all clusters will get data",
                    __func__);
                k = n;
        }
 
        /* An array of objects to be analyzed. */
        POINT4D *objs_dense = lwalloc(sizeof(POINT4D) * n);
 
        /* Array to mark unclusterable objects. Will be returned as KMEANS_NULL_CLUSTER. */
        uint8_t *geom_valid = lwalloc(sizeof(uint8_t) * n);
        memset(geom_valid, 0, sizeof(uint8_t) * n);
 
        /* Array to fill in with cluster numbers. */
        int *clusters = lwalloc(sizeof(int) * n);
        for (uint32_t i = 0; i < n; i++)
                clusters[i] = KMEANS_NULL_CLUSTER;
 
        /* An array of clusters centers for the algorithm. */
        POINT4D *centers = lwalloc(sizeof(POINT4D) * n);
        memset(centers, 0, sizeof(POINT4D) * n);
 
        /* An array of clusters radii for the algorithm. */
        double *radii = lwalloc(sizeof(double) * n);
        memset(radii, 0, sizeof(double) * n);
 
        /* Prepare the list of object pointers for K-means */
        for (uint32_t i = 0; i < n; i++)
        {
                const LWGEOM *geom = geoms[i];
                /* Unset M values will be 1 */
                POINT4D out = {0, 0, 0, 1};
 
                /* Null/empty geometries get geom_valid=LW_FALSE set earlier with memset */
                if ((!geom) || lwgeom_is_empty(geom))
                        continue;
 
                /* If the input is a point, use its coordinates */
                if (lwgeom_get_type(geom) == POINTTYPE)
                {
                        out.x = lwpoint_get_x(lwgeom_as_lwpoint(geom));
                        out.y = lwpoint_get_y(lwgeom_as_lwpoint(geom));
                        if (lwgeom_has_z(geom))
                                out.z = lwpoint_get_z(lwgeom_as_lwpoint(geom));
                        if (lwgeom_has_m(geom))
                        {
                                out.m = lwpoint_get_m(lwgeom_as_lwpoint(geom));
                                if (out.m <= 0)
                                        lwerror("%s has an input point geometry with weight in M less or equal to 0",
                                                __func__);
                        }
                }
                else if (!lwgeom_has_z(geom))
                {
                        /* For 2D, we can take a centroid */
                        LWGEOM *centroid = lwgeom_centroid(geom);
                        if (!centroid)
                                continue;
                        if (lwgeom_is_empty(centroid))
                        {
                                lwgeom_free(centroid);
                                continue;
                        }
                        out.x = lwpoint_get_x(lwgeom_as_lwpoint(centroid));
                        out.y = lwpoint_get_y(lwgeom_as_lwpoint(centroid));
                        lwgeom_free(centroid);
                }
                else
                {
                        /* For 3D non-point, we can have a box center */
                        const GBOX *box = lwgeom_get_bbox(geom);
                        if (!gbox_is_valid(box))
                                continue;
                        out.x = (box->xmax + box->xmin) / 2;
                        out.y = (box->ymax + box->ymin) / 2;
                        out.z = (box->zmax + box->zmin) / 2;
                }
                geom_valid[i] = LW_TRUE;
                objs_dense[num_non_empty++] = out;
        }
 
        if (num_non_empty < k)
        {
                lwnotice(
                    "%s: number of non-empty geometries (%d) is less than the number of clusters (%d) requested, not all clusters will get data",
                    __func__,
                    num_non_empty,
                    k);
                k = num_non_empty;
        }
 
        uint8_t converged = LW_TRUE;
 
        if (num_non_empty > 0)
        {
                uint32_t *clusters_dense = lwalloc(sizeof(uint32_t) * num_non_empty);
                memset(clusters_dense, 0, sizeof(uint32_t) * num_non_empty);
                uint32_t output_cluster_count = kmeans(objs_dense, clusters_dense, num_non_empty, centers, radii, k, max_radius);
 
                uint32_t d = 0;
                for (uint32_t i = 0; i < n; i++)
                        if (geom_valid[i])
                                clusters[i] = (int)clusters_dense[d++];
 
                converged = output_cluster_count > 0;
                lwfree(clusters_dense);
        }
 
        /* Before error handling, might as well clean up all the inputs */
        lwfree(objs_dense);
        lwfree(centers);
        lwfree(geom_valid);
        lwfree(radii);
 
        /* Good result */
        if (converged)
                return clusters;
 
        /* Bad result, not going to need the answer */
        lwfree(clusters);
        return NULL;
}