1. Fast VQ Encoding by an Efficient Kick-Out Condition Kuang-Shyr Wu and Ja-Chen Lin IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, FEB. 2000

2. jinho Introduction Query vector x=(x1,x2, …,xk) and codebook Used squared Euclidean distance, distortion is Nearest codebook search Kick-out condition: guarantee,rule out yi

3. jinho Existing Techniques Partial Distance Elimination (PDE) Soleymani and Morgera Triangular inequality Elimination (TIE) A1

4. jinho Existing Techniques(cont.) Torres and Huguet: kick out yi if Lin and Tai, integral projection method Massive projection A3 A2

5. jinho Existing Techniques(cont.) Vertical projection Horizontal projection Kick out if yi satisfies

6. jinho Proposed Algorithm (15) (16)

7. jinho Smallest d1 distortion by (15)(16) Due to Cauchy-Schwarz inequality d1(x,yi) >= d1min is guaranteed,Kick-out yi

8. jinho Finding the nearest codeword for a query sequence {x} in the k-dimension vector space. Preprocessing:Evaluate Steps: 1. read in an x 2. Evaluate 2 ||x||

9. jinho 3. choose an,let 4. (a) R empty goto 5 (b) choose yi from R (c) if ||yi||(||yi||-2||x||)>= d1min then do 4ci or 4cii i) if (||yi|| >=||x||) then delete from R all yj whose j>=i and goto 4a ii) if (||yi|| <=||x||) then delete from R all yj whose j<=i and goto 4a (d) Evaluate d1(x, yi); delete yi from R; if (d1(x,yi)>=d1min) goto 4a (e) d1min = d1(x, yi) ; ymin = yi;(update ymin) 5. Print out the y min, it minimizes (16) and (15) for given x.

10. jinho Kick-out condition : Kick out not only yi, but also many yj by Suggest y min (guess) whose norm is closest to ||x||; f(t)=t ( t – 2 ||x|| ), as function of t absolute minimum at t = ||x||

11. jinho Experiments

12. jinho

15. Conclusions A kick-out condition using the Cauchy- Schwarz inequality is proposed for the fast codeword searching algorithm. Compared to A2,the O(N 2 ) preprocessing time and O(N 2 ) memory space are reduced to O(NlogN) and O(N) in our method. Compared to A3, our method uses not only one inequality instead of three but also independent of block size.