From 314f4b1a505c4bfad7f13f3580e6245ce3beb82f Mon Sep 17 00:00:00 2001
From: Sergey Lisitsyn <blackburn91@gmail.com>
Date: Wed, 3 Aug 2011 21:04:59 +0400
Subject: [PATCH] Changed isomap geodesic distance with Dijkstra Heap instead
 of Floyd

---
 src/shogun/preprocessor/Isomap.cpp | 136 ++++++++++++++++++++---------
 1 file changed, 97 insertions(+), 39 deletions(-)

diff --git a/src/shogun/preprocessor/Isomap.cpp b/src/shogun/preprocessor/Isomap.cpp
index 06979ae7622..b0dbe123cfd 100644
--- a/src/shogun/preprocessor/Isomap.cpp
+++ b/src/shogun/preprocessor/Isomap.cpp
@@ -11,6 +11,7 @@
 #include <shogun/preprocessor/Isomap.h>
 #ifdef HAVE_LAPACK
 #include <shogun/lib/common.h>
+#include <shogun/lib/FibonacciHeap.h>
 #include <shogun/distance/CustomDistance.h>
 #include <shogun/mathematics/Math.h>
 #include <shogun/io/SGIO.h>
@@ -21,65 +22,122 @@ using namespace shogun;
 CCustomDistance* CIsomap::isomap_distance(CDistance* distance)
 {
 	int32_t N,k,i,j;
+	float64_t tmp;
 	SGMatrix<float64_t> D_matrix=distance->get_distance_matrix();
 	N=D_matrix.num_cols;
+	ASSERT(m_k<N);
+	CFibonacciHeap* heap = new CFibonacciHeap(N);
 
-	if (m_type==EISOMAP)
+	// cut by k-nearest neighbors
+	int32_t* edges_idx_matrix = SG_MALLOC(int32_t, N*m_k);
+	float64_t* edges_matrix = SG_MALLOC(float64_t, N*m_k);
+			
+	// query neighbors and edges to neighbors
+	heap->clear();
+	for (i=0; i<N; i++)
 	{
-		// just replace distances >e with infty
-		for (i=0; i<N*N; i++)
+		// insert distances to heap
+		for (j=0; j<N; j++)
+			heap->insert(j,D_matrix.matrix[i*N+j]);
+
+		// extract nearest neighbor: the jth object itself
+		heap->extract_min(tmp);
+
+		// extract m_k neighbors and distances
+		for (j=0; j<m_k; j++)
 		{
-			if (D_matrix.matrix[i]>m_epsilon)
-				D_matrix.matrix[i] = CMath::ALMOST_INFTY;
+			edges_idx_matrix[i*m_k+j] = heap->extract_min(tmp);
+			edges_matrix[i*m_k+j] = tmp;
 		}
+		// clear heap
+		heap->clear();
 	}
-	if (m_type==KISOMAP)
-	{
-		// cut by k-nearest neighbors
-
-		float64_t* col = SG_MALLOC(float64_t, N);
-		int32_t* col_idx = SG_MALLOC(int32_t, N);
-			
-		// -> INFTY edges connecting NOT neighbors
-		for (i=0; i<N; i++)
-		{
-			for (j=0; j<N; j++)
-			{
-				col[j] = D_matrix.matrix[j*N+i];
-				col_idx[j] = j;
-			}
+	// cleanup
+	D_matrix.destroy_matrix();
 
-			CMath::qsort_index(col,col_idx,N);
+	// Dijkstra with Fibonacci Heap (not very efficient yet)
+	// allocate (s)olution
+	bool* s = SG_MALLOC(bool,N);
+	// allocate (f)rontier
+	bool* f = SG_MALLOC(bool,N);
+	// temporary float to store distance
+	float64_t dist;
+	// temporary ints to represent nodes
+	int32_t min_item, w;
+	// init matrix to store shortest distances
+	float64_t* shortest_D = SG_MALLOC(float64_t,N*N);
+	// clear heap
+	heap->clear();
 
-			for (j=m_k+1; j<N; j++)
-			{
-				D_matrix.matrix[col_idx[j]*N+i] = CMath::ALMOST_INFTY;
-			}
+	// for each vertex k
+	for (k=0; k<N; k++)
+	{
+		// fill s and f with false, fill shortest_D with infinity
+		for (j=0; j<N; j++)
+		{
+			shortest_D[k*N+j] = CMath::ALMOST_INFTY;
+			s[j] = false;
+			f[j] = false;
 		}
+		// set distance from k to k as zero
+		shortest_D[k*N+k] = 0.0;
 
-		SG_FREE(col);
-		SG_FREE(col_idx);
-	}
+		// insert kth object to heap with zero distance and set f[k] true
+		heap->insert(k,0.0);
+		f[k] = true;
 
-	// Floyd-Warshall on distance matrix
-	// TODO replace by dijkstra
-	for (k=0; k<N; k++)
-	{
-		for (i=0; i<N; i++)
+		// while heap is not empty
+		while (heap->get_num_nodes()>0)
 		{
-			for (j=0; j<N; j++)
+			// extract min and set (s)olution state as true and (f)rontier as false
+			min_item = heap->extract_min(tmp);
+			s[min_item] = true;
+			f[min_item] = false;
+			
+			// for-each edge (min_item->w)
+			for (i=0; i<m_k; i++)
 			{
-				D_matrix.matrix[i*N+j] =
-						CMath::min(D_matrix.matrix[i*N+j],
-								   D_matrix.matrix[i*N+k] + D_matrix.matrix[k*N+j]);
+				// get w idx
+				w = edges_idx_matrix[min_item*m_k+i];
+				// if w is not in solution yet
+				if (s[w] == false)
+				{
+					// get distance from k to i through min_item
+					dist = shortest_D[k*N+min_item] + edges_matrix[min_item*m_k+i];
+					// if distance can be relaxed
+					if (dist < shortest_D[k*N+w])
+					{
+						// relax distance
+						shortest_D[k*N+w] = dist;
+						// if w is in (f)rontier 
+						if (f[w])
+						{
+							// decrease distance in heap
+							heap->decrease_key(w, dist);
+						}
+						else 
+						{
+							// insert w to heap and set (f)rontier as true
+							heap->insert(w, dist);
+							f[w] = true;
+						}
+					} 
+				}
 			}
 		}
+		// clear heap to re-use
+		heap->clear();
 	}
+	// cleanup
+	delete heap;
+	SG_FREE(edges_matrix);
+	SG_FREE(s);
+	SG_FREE(f);
 
-	CCustomDistance* geodesic_distance = new CCustomDistance(D_matrix.matrix,N,N);
+	CCustomDistance* geodesic_distance = new CCustomDistance(shortest_D,N,N);
 
 	// should be removed if custom distance doesn't copy the matrix
-	SG_FREE(D_matrix.matrix);
+	SG_FREE(shortest_D);
 
 	return geodesic_distance;
 }