graph/layout: add Isomap layout

graph/layout/isomap.go

@@ -0,0 +1,63 @@
+// Copyright ©2019 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package layout
+
+import (
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/path"
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/spatial/r2"
+	"gonum.org/v1/gonum/stat/mds"
+)
+
+// IsomapR2 implements a graph layout algorithm based on the Isomap
+// non-linear dimensionality reduction method. Coordinates of nodes
+// are computed by finding a Torgerson multidimensional scaling of
+// the shortest path distances between all pairs of node in the graph.
+// The all pair shortest path distances are calculated using the
+// Floyd-Warshall algorithm and so IsomapR2 will not scale to large
+// graphs. Graphs with more than one connected component cannot be
+// layed out by IsomapR2.
+type IsomapR2 struct{}
+
+// Update is the IsomapR2 spatial graph update function.
+func (IsomapR2) Update(g graph.Graph, layout LayoutR2) bool {
+	nodes := graph.NodesOf(g.Nodes())
+	v := isomap(g, nodes, 2)
+	if v == nil {
+		return false
+	}
+
+	// FIXME(kortschak): The Layout types do not have the capacity to
+	// be cleared in the current API. Is this a problem? I don't know
+	// at this stage. It might be if the layout is reused between graphs.
+	// Someone may do this.
+
+	for i, n := range nodes {
+		layout.SetCoord2(n.ID(), r2.Vec{X: v.At(i, 0), Y: v.At(i, 1)})
+	}
+	return false
+}
+
+func isomap(g graph.Graph, nodes []graph.Node, dims int) *mat.Dense {
+	p, ok := path.FloydWarshall(g)
+	if !ok {
+		return nil
+	}
+
+	dist := mat.NewSymDense(len(nodes), nil)
+	for i, u := range nodes {
+		for j, v := range nodes {
+			dist.SetSym(i, j, p.Weight(u.ID(), v.ID()))
+		}
+	}
+
+	k, v, _ := mds.TorgersonScaling(nil, nil, dist)
+	if k < dims {
+		return nil
+	}
+
+	return v
+}

graph/layout/isomap_test.go

@@ -0,0 +1,180 @@
+// Copyright ©2019 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package layout
+
+import (
+	"path/filepath"
+	"testing"
+
+	"gonum.org/v1/gonum/graph"
+	"gonum.org/v1/gonum/graph/simple"
+	"gonum.org/v1/gonum/spatial/r2"
+	"gonum.org/v1/plot"
+	"gonum.org/v1/plot/vg"
+)
+
+var isomapR2Tests = []struct {
+	name string
+	g    graph.Graph
+}{
+	{
+		name: "line_isomap",
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(1)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+	{
+		name: "square_isomap",
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(1)},
+				{simple.Node(0), simple.Node(2)},
+				{simple.Node(1), simple.Node(3)},
+				{simple.Node(2), simple.Node(3)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+	{
+		name: "tetrahedron_isomap",
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(1)},
+				{simple.Node(0), simple.Node(2)},
+				{simple.Node(0), simple.Node(3)},
+				{simple.Node(1), simple.Node(2)},
+				{simple.Node(1), simple.Node(3)},
+				{simple.Node(2), simple.Node(3)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+	{
+		name: "sheet_isomap",
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(1)},
+				{simple.Node(0), simple.Node(3)},
+				{simple.Node(1), simple.Node(2)},
+				{simple.Node(1), simple.Node(4)},
+				{simple.Node(2), simple.Node(5)},
+				{simple.Node(3), simple.Node(4)},
+				{simple.Node(3), simple.Node(6)},
+				{simple.Node(4), simple.Node(5)},
+				{simple.Node(4), simple.Node(7)},
+				{simple.Node(5), simple.Node(8)},
+				{simple.Node(6), simple.Node(7)},
+				{simple.Node(7), simple.Node(8)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+	{
+		name: "tube_isomap",
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(1)},
+				{simple.Node(0), simple.Node(2)},
+				{simple.Node(0), simple.Node(3)},
+				{simple.Node(1), simple.Node(2)},
+				{simple.Node(1), simple.Node(4)},
+				{simple.Node(2), simple.Node(5)},
+				{simple.Node(3), simple.Node(4)},
+				{simple.Node(3), simple.Node(5)},
+				{simple.Node(3), simple.Node(6)},
+				{simple.Node(4), simple.Node(5)},
+				{simple.Node(4), simple.Node(7)},
+				{simple.Node(5), simple.Node(8)},
+				{simple.Node(6), simple.Node(7)},
+				{simple.Node(6), simple.Node(8)},
+				{simple.Node(7), simple.Node(8)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+	{
+		name: "wp_page_isomap", // https://en.wikipedia.org/wiki/PageRank#/media/File:PageRanks-Example.jpg
+		g: func() graph.Graph {
+			edges := []simple.Edge{
+				{simple.Node(0), simple.Node(3)},
+				{simple.Node(1), simple.Node(2)},
+				{simple.Node(1), simple.Node(3)},
+				{simple.Node(1), simple.Node(4)},
+				{simple.Node(1), simple.Node(5)},
+				{simple.Node(1), simple.Node(6)},
+				{simple.Node(1), simple.Node(7)},
+				{simple.Node(1), simple.Node(8)},
+				{simple.Node(3), simple.Node(4)},
+				{simple.Node(4), simple.Node(5)},
+				{simple.Node(4), simple.Node(6)},
+				{simple.Node(4), simple.Node(7)},
+				{simple.Node(4), simple.Node(8)},
+				{simple.Node(4), simple.Node(9)},
+				{simple.Node(4), simple.Node(10)},
+			}
+			g := simple.NewUndirectedGraph()
+			for _, e := range edges {
+				g.SetEdge(e)
+			}
+			return orderedGraph{g}
+		}(),
+	},
+}
+
+func TestIsomapR2(t *testing.T) {
+	for _, test := range isomapR2Tests {
+		o := NewOptimizerR2(test.g, IsomapR2{}.Update)
+		var n int
+		for o.Update() {
+			n++
+		}
+		p, err := plot.New()
+		if err != nil {
+			t.Errorf("unexpected error: %v", err)
+			continue
+		}
+		p.Add(render{o})
+		p.HideAxes()
+		path := filepath.Join("testdata", test.name+".png")
+		err = p.Save(10*vg.Centimeter, 10*vg.Centimeter, path)
+		if err != nil {
+			t.Errorf("unexpected error: %v", err)
+			continue
+		}
+		ok := checkRenderedLayout(t, path)
+		if !ok {
+			got := make(map[int64]r2.Vec)
+			nodes := test.g.Nodes()
+			for nodes.Next() {
+				id := nodes.Node().ID()
+				got[id] = o.Coord2(id)
+			}
+			t.Logf("got node positions: %#v", got)
+		}
+	}
+}