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View Code? Open in Web Editor NEWA k-d tree implementation in Go.
License: Apache License 2.0
A k-d tree implementation in Go.
License: Apache License 2.0
FindLargest
, FindSmallest
are used when removing a node from the k-d tree. These functions do not take into account the axis of the currently expanded node
Lines 357 to 368 in 70830f8
Given we are calling node.Remove
recursively, this seems to suggest our actual runtime complexity to be O(nlogn), whereas general BST remove should take O(n).
As per Wikipedia, if we are okay with O(nlogn) complexity, we can alternatively just rebuild the node.
Alternatively, we can tombstone the node instead, which optimizes Remove
for a slightly larger lookup time.
tree := new(kdtree.KDTree)
for i := 0; i < length; i++ {
R, G, B, _ := img.At(0, i).RGBA()
tree.Insert(points.NewPoint([]float64 {
float64(R),
float64(G),
float64(B)}, Data{Value: i}))
}
I have built my KDTree with the above code.
When I perform a KNN search, returned points don't have the "Data" interface.
Using fmt.Println() shows related data in the console, however point.Data is impossible to use.
Hey, I submitted PR with code, which will ease process of using module in projects. Can you give it a thought ?
This might be a case of "using it wrong", but KNN does not always return the nearest neighbour(s) unless the tree is balanced before the query.
My understanding is that KNN search might be slow/not-optimal on an unbalanced tree, but should still work correctly. If this isn't the case then just adding that in the doc for KNN is likely enough.
This issue is demonstrated by the attached test program, which iteratively mutates a random tree, and makes two KNN queries against it without any modifications to the tree in-between. The first has 'k' set to some low number (few
), and the second has 'k' set to a higher number (many
).
I would expect the first 'k' entries in the many
query to match the entries in the few
query, but the few
query often omits the closest neighbours. In the output below, you can see that the t.KNN(p, 1)
says that a point at a distance of 14.32 is the closest, whereas t.KNN(p, 10)
gives the correct result of 11.66. After balancing, the results are correct. The value of few
isn't critical - in my tests, any value of k < (number of entries - 1) shows the problem, but less frequently than smaller 'k's
Getting 1 NNs out of 10 entries
Failure on iteration 618
KNN((186.00, 218.00), 1)
NN 0: distance((186.00, 218.00)->(172.00, 215.00)) = 14.32
KNN((186.00, 218.00), 10)
NN 0: distance((186.00, 218.00)->(176.00, 212.00)) = 11.66
NN 1: distance((186.00, 218.00)->(172.00, 215.00)) = 14.32
NN 2: distance((186.00, 218.00)->(206.00, 196.00)) = 29.73
NN 3: distance((186.00, 218.00)->(214.00, 188.00)) = 41.04
NN 4: distance((186.00, 218.00)->(218.00, 253.00)) = 47.42
NN 5: distance((186.00, 218.00)->(269.00, 176.00)) = 93.02
NN 6: distance((186.00, 218.00)->(276.00, 181.00)) = 97.31
NN 7: distance((186.00, 218.00)->(279.00, 264.00)) = 103.75
NN 8: distance((186.00, 218.00)->(287.00, 244.00)) = 104.29
NN 9: distance((186.00, 218.00)->(299.00, 205.00)) = 113.75
After balance:
KNN((186.00, 218.00), 1)
NN 0: distance((186.00, 218.00)->(176.00, 212.00)) = 11.66
KNN((186.00, 218.00), 10)
NN 0: distance((186.00, 218.00)->(176.00, 212.00)) = 11.66
NN 1: distance((186.00, 218.00)->(172.00, 215.00)) = 14.32
NN 2: distance((186.00, 218.00)->(206.00, 196.00)) = 29.73
NN 3: distance((186.00, 218.00)->(214.00, 188.00)) = 41.04
NN 4: distance((186.00, 218.00)->(218.00, 253.00)) = 47.42
NN 5: distance((186.00, 218.00)->(269.00, 176.00)) = 93.02
NN 6: distance((186.00, 218.00)->(276.00, 181.00)) = 97.31
NN 7: distance((186.00, 218.00)->(279.00, 264.00)) = 103.75
NN 8: distance((186.00, 218.00)->(287.00, 244.00)) = 104.29
NN 9: distance((186.00, 218.00)->(299.00, 205.00)) = 113.75
Code follows:
package main
import (
"fmt"
"math"
"math/rand"
"time"
"github.com/kyroy/kdtree"
"github.com/kyroy/kdtree/points"
)
func distance(a, b *points.Point2D) float64 {
return math.Sqrt(math.Pow(a.X - b.X, 2) + math.Pow(a.Y - b.Y, 2))
}
func dumpNNs(p kdtree.Point, nns []kdtree.Point) {
p2d1 := p.(*points.Point2D)
fmt.Printf("KNN((%3.2f, %3.2f), %d)\n", p2d1.X, p2d1.Y, len(nns))
for i, n := range nns {
p2d2 := n.(*points.Point2D)
fmt.Printf(" NN %d: distance((%3.2f, %3.2f)->(%3.2f, %3.2f)) = %3.2f\n",
i, p2d1.X, p2d1.Y, p2d2.X, p2d2.Y, distance(p2d1, p2d2))
}
}
func main() {
w, h := 300, 300
maxSize := 10
maxTime := time.Minute
t := kdtree.New([]kdtree.Point{})
arr := make([]kdtree.Point, 0, maxSize)
many := maxSize
few := maxSize - 1
for ; few > 0; few-- {
fmt.Printf("Getting %d NNs out of %d entries\n", few, maxSize)
start := time.Now()
for i := 0; ; i++ {
p := &points.Point2D{
X: float64(rand.Intn(w / 2) + w / 2),
Y: float64(rand.Intn(h / 2) + h / 2),
}
// Two KNN queries
fewNN := t.KNN(p, few)
manyNN := t.KNN(p, many)
// Check if the nearest is the same
if len(fewNN) > 0 {
if distance(p, fewNN[0].(*points.Point2D)) >
distance(p, manyNN[0].(*points.Point2D)) {
fmt.Println("Failure on iteration", i)
dumpNNs(p, fewNN)
dumpNNs(p, manyNN)
// Balance the tree and try again
t.Balance()
fmt.Println("After balance:")
fewNN = t.KNN(p, few)
manyNN = t.KNN(p, many)
dumpNNs(p, fewNN)
dumpNNs(p, manyNN)
break
}
}
// Add in the new point
arr = append(arr, p)
//fmt.Printf("Insert (%3.2f, %3.2f)\n", p.X, p.Y)
t.Insert(p)
// Limit the max number of elements - which will also
// introduce some churn in the tree
if len(arr) > maxSize {
idx := rand.Intn(len(arr))
//fmt.Printf("Remove (%3.2f, %3.2f)\n", p.X, p.Y)
t.Remove(arr[idx])
p = arr[idx].(*points.Point2D)
arr[idx] = arr[len(arr)-1]
arr = arr[:len(arr)-1]
}
if since := time.Since(start); since > maxTime {
fmt.Printf("No failure after %d iterations (%v)\n", i, since)
break
}
}
fmt.Println("================================================")
t.Balance()
}
}
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