Chapter 1 Introduction
4.5 Parameter Tuning Details
4.5.3 Hierarchical K-Means
HKM has two parameters: D the depth of the tree and k the branching factor. We tried depths of 5, 6, and 7 with branching factor of 10. Results for quick tuning are in Figure 4.13(a), and full results are in Figure 4.13(b). From the quick tuning, all the combinations
69
10−2 100 102 104
10 20 30 40 50
No. of distractors: 100
Time per feature (ms)
Percentage Correct Matches
exhaust−l2 lsh−l2−t1−f10−w.01 lsh−l2−t1−f25−w.01 lsh−l2−t1−f50−w.01 lsh−l2−t1−f100−w.01 lsh−l2−t1−f10−w.1 lsh−l2−t1−f25−w.1 lsh−l2−t1−f50−w.1 lsh−l2−t1−f100−w.1 lsh−l2−t1−f10−w.25 lsh−l2−t1−f25−w.25 lsh−l2−t1−f50−w.25 lsh−l2−t1−f100−w.25 lsh−l2−t4−f10−w.01 lsh−l2−t4−f25−w.01 lsh−l2−t4−f50−w.01 lsh−l2−t4−f100−w.01 lsh−l2−t4−f10−w.1 lsh−l2−t4−f25−w.1 lsh−l2−t4−f50−w.1 lsh−l2−t4−f100−w.1 lsh−l2−t4−f10−w.25 lsh−l2−t4−f25−w.25 lsh−l2−t4−f50−w.25 lsh−l2−t4−f100−w.25 lsh−l2−t4−f50−w.5 lsh−l2−t4−f100−w1 lsh−l2−t8−f10−w.1 lsh−l2−t8−f25−w.1 lsh−l2−t8−f25−w.25 lsh−l2−t8−f50−w.25 lsh−l2−t8−f50−w.5 lsh−l2−t8−f100−w1
10−2 100 102 104
10 20 30 40 50
No. of distractors: 1k
Time per feature (ms)
Percentage Correct Matches
10−2 100 102 104
10 20 30 40 50
No. of distractors: 10k
Time per feature (ms)
Percentage Correct Matches
(a)Quick Tuning for LSH-L2. The plot shows the percentage of correctly matched features as a function of time for different dataset sizes for different combinations of LSH-L2. The parameters areT =1, 4, and 8 tables,H=10, 25, 50, 100 hash functions, andw=0.1, 0.25, 0.5, and 1 bin size. Based on these results, we used(T,H,w) ={4,10,0.1},{4,25,0.25},{4,50,0.5}, and{4,100,1}for the full tuning in (b) below.
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 1
lsh−l2−t4−f10−w.1 lsh−l2−t4−f25−w.25 lsh−l2−t4−f50−w.5 lsh−l2−t4−f100−w1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 2
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 2
lsh−l2−t4−f10−w.1 lsh−l2−t4−f25−w.25 lsh−l2−t4−f50−w.5 lsh−l2−t4−f100−w1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 3
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 3
lsh−l2−t4−f10−w.1 lsh−l2−t4−f25−w.25 lsh−l2−t4−f50−w.5 lsh−l2−t4−f100−w1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 4
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 4
lsh−l2−t4−f10−w.1 lsh−l2−t4−f25−w.25 lsh−l2−t4−f50−w.5 lsh−l2−t4−f100−w1
(b)Full Tuning for LSH-L2. The plot shows tuning results on the four scenarios for the parameters chosen from (a) above. Based on these results, we chose(T,H,w) ={4,25,0.25}as the representative combi- nation.
Figure 4.10:LSH-L2 Parameter Tuning.
10−2 100 102 104 0.1
1 10 20 30 4050
No. of distractors: 100
Time per feature (ms)
Percentage Correct Matches
exhaust−l2 lsh−sph−sim−t1−f3 lsh−sph−sim−t1−f5 lsh−sph−sim−t1−f7 lsh−sph−sim−t4−f3 lsh−sph−sim−t4−f5 lsh−sph−sim−t4−f7
10−2 100 102 104
0.1 1 10 20 30 4050
No. of distractors: 1k
Time per feature (ms)
Percentage Correct Matches
10−2 100 102 104
0.1 1 10 20 30 4050
No. of distractors: 10k
Time per feature (ms)
Percentage Correct Matches
(a)Quick Tuning for LSH-Sim.The plot shows the percentage of correctly matched features as a function of time for different dataset sizes for different combinations of LSH-Sim. The parameters areT=1 and 4 tables, andH=3, 5, and 7 hash functions. Based on these results, we used(T,H) ={4,5}and{4,7}, for the full tuning in (b) below.
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 1
lsh−sph−sim−t4−f5 lsh−sph−sim−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 2
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 2
lsh−sph−sim−t4−f5 lsh−sph−sim−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 3
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 3
lsh−sph−sim−t4−f5 lsh−sph−sim−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 4
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 4
lsh−sph−sim−t4−f5 lsh−sph−sim−t4−f7
(b) Full Tuning for LSH-Sim. The plot shows tuning results on the four scenarios for the parameters chosen from (a) above. Based on the results, we choseT=4 tables andH=5 hash functions per table.
Figure 4.11:LSH-Sim Parameter Tuning
71
10−2 100 102 104
0.1 1 10 20 30 4050
No. of distractors: 100
Time per feature (ms)
Percentage Correct Matches
exhaust−l2 lsh−sph−or−t1−f3 lsh−sph−or−t1−f5 lsh−sph−or−t1−f7 lsh−sph−or−t4−f3 lsh−sph−or−t4−f5 lsh−sph−or−t4−f7
10−2 100 102 104
0.1 1 10 20 30 4050
No. of distractors: 1k
Time per feature (ms)
Percentage Correct Matches
10−2 100 102 104
0.1 1 10 20 30 4050
No. of distractors: 10k
Time per feature (ms)
Percentage Correct Matches
(a)Quick Tuning for LSH-Orth.The plot shows the percentage of correctly matched features as a function of time for different dataset sizes for different combinations of LSH-Orth. The parameters areT =1 and 4 tables, andH=3, 5, and 7 hash functions. Based on these results, we used(T,H) ={4,5}and{4,7}, for the full tuning in (b) below.
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 1
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 1
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 1
lsh−sph−or−t4−f5 lsh−sph−or−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 2
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 2
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 2
lsh−sph−or−t4−f5 lsh−sph−or−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 3
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 3
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 3
lsh−sph−or−t4−f5 lsh−sph−or−t4−f7
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (before)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Search time (sec/image)
Scenario 4
102 103 104
30 40 50 60 70 80 90 100
Number of Images
Performance (after)
Scenario 4
102 103 104
10−2 100 102
Number of Images
Geometric Check time (sec/image)
Scenario 4
lsh−sph−or−t4−f5 lsh−sph−or−t4−f7
(b)Full Tuning for LSH-Orth. The plot shows tuning results on the four scenarios for the parameters chosen from (a) above. Based on the results, we choseT=4 tables andH=5 hash functions per table.
Figure 4.12:LSH-Orth Parameter Tuning
are quite similar, so we ran those on the four scenarios. We notice that they have similar performance, with using a depth of 5 yielding slightly better performance. We chose this combination{D,k}={5,10}as the representative of the method in later comparisons.