1. Selectivity Estimation for Optimizing Similarity Query in Multimedia Databases IDEAL 2003 Paper review

2. Query optimization in traditional database  Query: find the employee who’s age between 30-40 and work for Engineering Faculty  Running time of different execution plans depend on  Number of employees between 30-40  Number of employees work for Engineering Faculty  Task: Estimate the number in advance and select the best execution plan (selectivity estimation)  Statistics are stored in database (metadata)

3. Techniques: one dimension  Parametric – unrealistic  Curve fitting – negative value problem  Sampling – large overhead  Non-parametric (Histogram technique) – widely used age 10 1520253035404550

4. Problem in multimedia database  (Color = ‘red’) ^ (Shape = ‘round’)  Color, shape – feature vector  Multi-dimension  Number of buckets increases exponentially with dimension  Histogram technique fails  1d – 5  2d – 25  3d – 125  4d – 625

5. Previous Work – SIGMOD 99  Use DCT to compress information of histogram  2D example  Store DCT coefficient 101513 142016 9131140.33-2.86-5.422.04-0.50-0.29 -6.84-0.291.167 DCT Histogram valueDCT coefficients0000-2 200-0.331.630.47-1.230.00 1.18-0.581.33 DCT

6. Reconstruction of histogram value 10 12 30 15 15 24 36 81 10 30 9 40 42 23 20 18 13 35 60 70 10 15 34 43 60 151.0000 -39.1747 -25.2604 -11.2001 24.9442 -24.0137 42.2456 -24.0044 -8.9490 16.2098 -15.0187 -14.2921 15.5469 9.8779 0.0979 -9.2651 -19.4490 19.4228 16.7544 -20.1256 -27.0396 12.9394 -4.5979 -4.8360 -17.5469 151.0000 -39.1747 -25.2604 -11.2001 24.9442 -24.0137 42.2456 -24.0044 -8.9490 0 -15.0187 -14.2921 15.5469 0 0 -9.2651 -19.4490 0 0 0 -27.0396 0 0 0 0 1.6184 17.9451 34.7007 10.3893 17.3465 31.0059 44.7644 57.9655 25.3113 21.9529 11.2059 25.0820 47.2188 25.3614 25.1319 12.6449 19.9000 49.6779 49.1996 64.5775 14.5248 8.3085 32.4371 40.7383 65.9913 DCT Zone sampling IDCT

7. Selectivity estimation 25 9 13 2 10 23 6 19 14 10 28 10 3 17 8 22 26 13 14 21 30 16 2 20 19

8. Current Work - IDEAL 2003  Extend the range query from hyper-cube to hyper- sphere  Model hyper-sphere as combination of hyper-cube  Task  Find combination of hyper-cubes to represent hyper-sphere  Find the area of overlapping

9. Generate combination of hyper- cube

16. Overlapping of hyper-cube with hyper- sphere  Monte-Carlo method  Generate uniformly distributed random point inside the hypercube  Count the number of points within the hyper-sphere  Use the ratio to estimate area of overlapping

17. Generate uniformly distributed points inside a hyper-sphere  Accept / Reject method  Generate points within hyper-cube  Accept those fall within the hyper-sphere  Greedy method  Generate θ uniformly [0,2π]  Generate r according to F -1 (U(0,1)) θ r

18. Experiment