University of Venice, Italy

1. Y X Time IBM Research University of Chicago University of Venice, Italy IBM Research C. Lucchese, M. Vlachos, D. Rajan, P.S. Yu

2. Objective: Ownership seal with Mining Guarantees the trajectories are modified imperceptibly,but their neighboring objects are not distorted NN Search Clustering Final Destination … Classification Embed a stamp so that we can claim ownership of the data Output on database and data mining operations is the same as on the original data

3. Search operations remains same outsource data to a mining company maintain principal rights of the dataset x Applications: Database Search Watermark does not change the nearest neighbor NN(x) y1 y2 We want to retain the Nearest Neighbors of each object. Determine the maximum watermark embedding power p which maintains NN for all objects:Dp(x, NN(x)) < Dp(x,y)

4. Modified Dataset including watermark Unacceptable Acceptable Applications: Classification Preservation Dataset of time-series/trajectories with class labels Class A Objective: Distort the data imperceptibly so that class labels are maintained. Class A Class A Class B Class B Class B

5. Results of clustering remains the same geodesic distances will remain the same hierarchical clustering will not be affected Applications: Clustering Preservation Gray-necked Owl Monkey Female Gray-necked Owl Monkey Male Orangutan juvenile Mandrill male Red Howler Monkey Male Orangutan2 male Mandrill2 male Juvenile Baboon Mantled HowlerMonkey De Brazza Monkey Juvenile Male De Brazza Monkey Male Common Chimpanzee male Common Chimpanzee Male 2

6. Phase Magnitude The secret key is embedded in a domain resilient to common trajectory transformations Frequency Domain Frequency Domain same Phase ft ift Magnitude modified watermarked magnitudes watermark original data watermarked data p (embedding power) Example:w = [-1 1 -1 -1 1 1 ] Additive Embedding in Magnitudes

7. Techniques are also applicable for image shapes (shapes can be treated as trajectories) Conversion of skull shape into a two-dimensional sequence Red Howler Monkey Male(Alouatta seniculus seniculus) Embed the key in the k most important coefficients Extracted Shape Orangutan skull

8. Secret information is hidden in some of the frequency components Y X Select the frequency coefficients that best describe the shape of the trajectoryOne can select either highest energy coefficients, or low frequency coefficients. Removal of the watermark will be more difficult without destroying the important trajectory characteristics Time 2 coeffs 4 coeffs 8 coeffs 16 coeffs 32 coeffs 64 coeffs

9. Phase Magnitude watermarked data key is detected very efficiently even when it is inserted with low embedding power Threshold Frequency Domain ft correlation watermark Detection of the embedded key is virtually perfect w = [-1 1 -1 -1 1 1 ] Better Detection (semi-blind):Remove ‘background noise’ bias before the embedding and during the detection

10. example of using our techniquefor spanning tree preservation MST before watermarking MST after watermarking

11. x the proposed fast algorithm prunes a significant amount of the search space Finding the maximum embedding power NN(x) z y We need to examine for each power p, how many times the following is violated:Dp(x, NN(x)) > Dp(x,y) Express distance parametrized by the embedding power of the key

12. our approach can embed the hidden information more than 300 times faster than the brute-force approach The fast search techniques find the same result as the exhaustive search, but are 2-3 orders of magnitude faster Running Time

13. The efficient key embedding + detectionallow for effective key recovery even under attacks • Geometric Attacks: perfect detection under Translation/Rotation/Scaling attacks • Gaussian Noise attack has to destroy the data in order to be effective • Decimation attack can be perfectly withstood • Data Reduction attack (even when pruning 50% of dataset) is not effective