1. Data Mining and Its Applications to Image Processing
資料挖掘技術及其在影像處理之應用
指導教授： Chang, Chin-Chen (張真誠)
研究生： Lin, Chih-Yang (林智揚)
Department of Computer Science and Information Engineering,
National Chung Cheng University

2. The Fields of Data Mining
Mining Association Rules
Sequential Mining
Clustering (Declustering)
Classification
……………

3. Outline Part I: Design and Analysis Data Mining Algorithms
Part II: Data Mining Applications to Image Processing

4. Part I: Design and Analysis Data Mining Algorithms
1. Perfect Hashing Schemes for Mining Association Rules (or for Mining Traversal Patterns)

5. Mining Association Rules
Support
Obtain Large Itemset
Confidence
Generate Association Rules

6. D C1 L1 Apriori Scan D C2 Sup=2 C2 L2 Scan D C3 C3 L3 Scan D TID Items
100
A C D
200
B C E
300
A B C E
400
B E
Itemset
Sup.
{A} 2
{B} 3
{C}
{D} 1
{E}
Itemset
Sup.
{A} 2
{B} 3
{C}
{E}
Scan D C2
Sup=2 C2 L2
Itemset
{A B}
{A C}
{A E}
{B C}
{B E}
{C E}
Itemset
Sup.
{A B} 1
{A C} 2
{A E}
{B C}
{B E} 3
{C E}
Itemset
Sup.
{A C} 2
{B C}
{B E} 3
{C E}
Scan D
名詞解釋
因為求初始Large Itemset為整個演算法最花執行時間所在，而在initial的表現以Apriori的表現為最佳，所以以此與DHP做比較的基準
Minimum Support=2
C3因為{BC},{BE}有共同的第一項，所以測試{CE}是否也為Large Itemset，是，所以得到{BCE}為候選 C3 C3 L3
Scan D
Itemset
{B C E}
Itemset
Sup.
{B C E} 2
Itemset
Sup.
{B C E} 2

7. Apriori Cont. Disadvantages Inefficient
Produce much more useless candidates

8. DHP Prune useless candidates in advance
Reduce database size at each iteration

9. D C1 Count {A} 2 {B} 3 {C} {D} 1 {E} L1 {A} {B} {C} {E} Min sup=2 TID
Items
100
A C D
200
B C E
300
A B C E
400
B E
Making a hash table
100
{A C}
200
{B C},{B E},{C E}
300
{A B},{A C},{A E},{B C},{B E},{C E}
400
{B E}
H{[x y]}=((order of x )*10+(order of y)) mod 7;
{A E}
{B E}
{C E}
{B C}
{A C}
{A B} 3 2 1 4 5 6
Hash 方法的介紹，包括雜湊函數，方法等
在資料庫D完成1-subset support掃瞄後，2-item的雜湊表也同時完成，依照資料庫D用2-item做區分
照排序帶入雜湊函數，並丟入Hash table
計算每個bucket的數量
利用buckets count(大於s=2)可得到bit vector，再用其過濾L1*L1就可得到較小的C2
Hash table H2
Hash address
Bit vector
The number of items hashed to bucket 0

10. Perfect Hashing Schemes (PHS) for Mining Association Rules

11. Motivation
Apriori and DHP produce Ci from Li-1 that may be the bottleneck
Collisions in DHP
Designing a perfect hashing function for every transaction databases is a thorny problem

12. Definition
Definition. A Join operation is to join two different (k-1)-itemsets, , respectively, to produces a k-itemset, where
= p1p2…pk-1
= q1q2…qk-1 and
p2=q1, p3=q2,…,pk-2=qk-3, pk-1=qk-2.
Example: ABC, BCD
3-itemsets of ABCD: ABC, ABD, ACD, BCD
only one pair that satisfies the join definition

13. Algorithm
PHS (Perfect Hashing and Data Shrinking)

14. (BC)(BD)(BE)(CD)(CE)(DE)L1
Itemset
Sup.
{B} 3
{C}
{D} 2
{E}
Example1 (sup=2)
TID
Items
100
ACD
200
BCE
300
BCDE
400 BE
TID
Items
100
(CD)
200
(BC) (BE)(CE)
300
(BC)(BD)(BE)(CD)(CE)(DE)
400
(BE)
Itemsets
(BC)
(BD)
(BE)
(CD)
(CE)
(DE)
Support 2 1 3
Encoding A B C D
Original
(BC)
(BE)
(CD)
(CE)

15. Decode: AD -> (BC)(CE) = BCE
Example2 (sup=2)
TID
Items
100
Null
200
(AD)
300
(AC)(AD)
400
Itemsets
(AB)
(AC)
(AD)
(BC)
(BD)
(CD)
Support 1 2
Encoding A
Original
(AD)
Decode: AD -> (BC)(CE) = BCE

16. Problem on Hash Table
Consider a database contains p transactions, which are comprised of unique items and are of equal length N, and the minimum support of 1.
At iteration k, the # of candidate k-itemsets is
The # of buckets required in the next pass is= , where m =
While the actual # of the next candidates is
Loading density :

17. How to Improve the Loading Density
Two level perfect hash scheme (parital hash)
Itemsets
(AB)
(AC)
(AD)
(BC)
(BD)
(CD)
Support 1 2 A B C
Hash Table D
Null
Count 1 2

18. Experiments

19. Experiments

20. Experiments

21. Part II: Data Mining Applications to Image Processing
1. A Prediction Scheme for Image Vector Quantization
based on Mining Association Rules
2. Reversible Steganography for VQ-compressed Images
Using Clustering and Relocation
3. A Reversible Steganographic Method Using SMVQ Approach
based on Declustering

22. A Prediction Scheme for Image Vector Quantization Based on Mining Association Rules

23. Vector Quantization (VQ)
Image encoding and decoding techniques

24. SMVQ(cont.)
Codebook
State Codebook

25. Framework of the Proposed Method
v/10
(Quantized)

26. If “X  y' , there is no such rule X'  y',
Condition
Horizontal,
Vertical,
Diagonal,
Association
Rules
If “X  y' , there is no such rule X'  y',
where X'  X and y' = y.

27. The Prediction Strategy

28. Example Rules DB ? may be 5, 1, 8, or 10. How to decide? Query Result
Matched set of rules
Matched vertical rules
Matched horizontal rules
Matched diagonal rules
(4, 2, 3, 3  5)
confv = 90%
(12, 12, 1, 3  5)
confh = 90%
(6, 4, 2, 2, 3  5)
confd=100%
(4, 2, 3  1)
confv = 85%
(12, 12  1)
confh = 95%
(6, 4, 2, 2  8)
confd =70% X
(6, 4, 2  10)
confd = 75%
? may be 5, 1, 8, or 10. How to decide?

29. Example cont. The weight of 5: 4*90%+4*90%+5*100%= 12.2
Matched set of rules
Matched vertical rules
Matched horizontal rules
Matched diagonal rules
(4, 2, 3, 3  5)
confv = 90%
(12, 12, 1, 3  5)
confh = 90%
(6, 4, 2, 2, 3  5)
confd=100%
(4, 2, 3  1)
confv = 85%
(12, 12  1)
confh = 95%
(6, 4, 2, 2  8)
confd =70% X
(6, 4, 2  10)
confd = 75%
The weight of 5: 4*90%+4*90%+5*100%= 12.2
The weight of 1: 3*85%+2*95% = 4.45
The weight of 8: 4*70% = 2.8
The weight of 10: 3*75% = 2.25
{5, 1} is called the consequence list, which
size is determined by the user

30. Experiments Reconstructed image by the proposed method Original Image
Reconstructed image by full-search VQ

31. Experiments cont. The performance comparisons on various methods
Performance
Lena
Pepper
F16
Full-search VQ
PSNR (dB)
32.25
31.41
31.58
Bit-rate (bpp)
0.5
SMVQ
28.57
28.04
27.94
0.33
0.32
Our Scheme
30.64
30.05
29.74
0.34

32. Experiments cont.
Overfitting problem

33. Advantages
Mining association rules can be applied to image prediction successfully
Broader spatial correlation is considered than that of SMVQ
More efficient than that of SMVQ since no Euclidean distances should be calculated

34. Reversible Steganography for VQ-compressed Images Using Clustering and Relocation

35. Flowchart of the Proposed MethodX

36. Construction of the Hit Map13 1 13 7 13 4 6 7 1 1 4 4 2 7 3 11 . . .
Sorted codebook
Hit map

37. Assume that the size of a codebook is 15: cw0, cw1, …, cw14
Clustering Codebook
Assume that the size of a codebook is 15: cw0, cw1, …, cw14
Clustering:
C1: cw0, cw1, cw3, cw6, cw8, cw10
C2: cw4, cw14
C3: cw2, cw5, cw9
C4: cw12
C5: cw7, cw11, cw13

38. Assume that the size of the state codebook is 4L
cw14
Assume that the size of the state codebook is 4
Relocation
cw0, cw1
cw3, cw6
cw8, cw10
cw2, cw5
cw9
cw4, cw14
cw7, cw11
cw13
cw12

39. Embedding Secret bits: 1011
Only the codewords in G0 can embed the secret bits
Embedding
The codewords in G1 should be replaced with the codewords in G2
cw14
cw12
cw1
cw2
cw6
cw3
cw10
cw8
Secret bits: 1011
cw4
cw12
cw0
cw2
cw6
cw5
cw3
cw8
cw1

40. Extraction & Reversibility
cw4
cw12
cw0
cw2
cw6
cw5
cw3
cw8
cw1 1 1 1
recover
cw14
cw12
cw1
cw2
cw6
cw3
cw10
cw8
Secret bits:

41. 12 hit maps (600 bits), 250 clusters
Experiments
Method
Measure
Lena
Pepper
Sailboat
Baboon
Modified Tian’s
method
PSNR (dB)
26.92
26.45
25.05
22.70
Payload (bits)
2777
3375
3283
2339
MFCVQ
28.03
26.43
26.60
24.04
5892
5712
5176
1798
Proposed method
30.23
29.15
28.00
8707
8421
7601
3400
12 hit maps (600 bits), 250 clusters

42. Experiments
Tian’s method
MFCVQ

43. Using clustering and multiple hit maps
Single hit map
Multiple hit maps
without clustering
Using clustering and multiple hit maps

44. Using Lena as the cover image
Experiments
Using Lena as the cover image

45. A Reversible Steganographic Method Using SMVQ Approach based on Declustering

46. Find the most dissimilar pairs
(De-clustering) …
CW1
CW8
CW2
CW9
CW3
CW10
CW4
CW11
CW5
CW12
CW6
CW13
CW7
CW14 1
Dissimilar

47. Embedding Using Side-Match
CW1
CW8
:Dissimilar Pair
Assume X = CW1
V0 = ((U13+L4)/2, U14, U15, U16, L8, L12, L16)
V1 = (X1, X2, X3, X4, X5, X9, X13)CW1
V8 = (X1, X2, X3, X4, X5, X9, X13)CW8
d1=Euclidean_Distance(V0, V1)
d8=Euclidean_Distance(V0, V8)
If (d1<d8), then Block X is replaceable
Otherwise, Block X is non-replaceable

48. A secret message: 1 1 1 1 1 1 1 1
Secret bits
Index Table
If (d6<d13)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6
Embedding Result 1

49. A secret message: 1 1 1 1 1 1 1 1
Secret bits
Index Table
If (d2<d9)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7, CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 9
Embedding Result 1

50. A secret message: 1 1 1 1 1 1 1 1
Secret bits
Index Table
If (d12>=d5)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 9
15||12
Embedding Result 1
CW15: embed 1

51. A secret message: 1 1 1 1 1 1 1 1
Secret bits
Index Table
If (d9>=d2)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 9
15||12
0||9
Embedding Result 1
CW0: embed 0

52. Steganographic Index Table
Extraction and Recovery 6 9
15||12
0||9 1
Extract Secret bits
Steganographic Index Table
If (d6<d13)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6
Recovery 1

53. Steganographic Index Table
Extraction and Recovery 6 9
15||12
0||9 1
Extract Secret bits
Steganographic Index Table
If (d9>=d2)
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 2
Recovery 1

54. Steganographic Index Table
Extraction and Recovery 6 9
15||12
0||9 1 1
Extract Secret bits
Steganographic Index Table
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 2 12
Recovery 1

55. Steganographic Index Table
Extraction and Recovery 6 9
15||12
0||9 1 1
Extract Secret bits
Steganographic Index Table
CW1, CW2,
CW3, CW4
CW5, CW6
CW7 , CW15
CW8, CW9
CW10, CW11
CW12, CW13
CW14 , CW0 6 2 12 9
Recovery 1

56. Find Dissimilar Pairs
PCA projection

57. Improve Embedding Capacity
Partition into more groups

58. Experiments Codebook size: 512 Codeword size: 16
The number of original image blocks:128*128=16384
The number of non-replaceable blocks: 139

59. Experiments Codebook size: 512 Codeword size: 16
The number of original image blocks:128*128=16384
The number of non-replaceable blocks: 458

60. Size of the state codebook
Experiments
Embedding capacity
Images
Tian’s method
MFCVQ
Chang et al.’s method
Proposed Method
(3 groups)
(9 groups)
(17 groups)
Lena
2,777
5,892
10,111
16,129
45,075
55,186
Baboon
2,339
1,798
4,588
36,609
39,014
Time Comparison
Image
Lena
Methods
Tian’s
method
MFCVQ
Chang et al.’s method
Proposed mehtod
Time (sec)
0.55
1.36
Size of the state codebook
Number of groups 4 8 16 32 3 5 9 17
14.59
29.80
58.8
161.2
0.11
0.13
0.14
0.19

61. Future Research Directions
Extend the proposed reversible steganographic methods to other image formats
Apply perfect hashing schemes to other applications

62. Thanks all