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Conclusion of Multimedia Databases and Data Mining: Similarity Search Strategies

This lecture by C. Faloutsos concludes a series on multimedia databases and data mining, emphasizing the goal of finding similar and interesting items across various data types. It discusses key indexing techniques for similarity search, including R-trees, z-ordering, and M-trees, while highlighting the challenges of high intrinsic dimensionality. The lecture also touches on text searching methods, time series analysis, and the surprising patterns observed in real-world graphs. Essential concepts such as fractals, power laws, and data mining techniques like association rules are reviewed, offering insights into effective data analysis.

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Conclusion of Multimedia Databases and Data Mining: Similarity Search Strategies

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Presentation Transcript

  1. 15-826: Multimedia Databasesand Data Mining Lecture #30: Conclusions C. Faloutsos

  2. Outline Goal: ‘Find similar / interesting things’ • Intro to DB • Indexing - similarity search • Points • Text • Time sequences; images etc • Graphs • Data Mining (c) 2012, C. Faloutsos

  3. Indexing - similarity search (c) 2012, C. Faloutsos

  4. Indexing - similarity search • R-trees • z-ordering / hilbert curves • M-trees • (DON’T FORGET … ) P1 P3 I C A G H F B J E P4 P2 D (c) 2012, C. Faloutsos

  5. Indexing - similarity search • R-trees • z-ordering / hilbert curves • M-trees • beware of high intrinsic dimensionality P1 P3 I C A G H F B J E P4 P2 D (c) 2012, C. Faloutsos

  6. Outline Goal: ‘Find similar / interesting things’ • Intro to DB • Indexing - similarity search • Points • Text • Time sequences; images etc • Graphs • Data Mining (c) 2012, C. Faloutsos

  7. Text searching • ‘find all documents with word bla’ (c) 2012, C. Faloutsos

  8. Text searching • Full text scanning (‘grep’) • Inversion (B-tree or hash index) • (signature files) • Vector space model • Ranked output • Relevance feedback • String editing distance (-> dynamic prog.) (c) 2012, C. Faloutsos

  9. S1 1 365 1 365 day day Sn Multimedia indexing (c) 2012, C. Faloutsos

  10. S1 F(S1) 1 365 1 365 F(Sn) day day Sn ‘GEMINI’ - Pictorially eg,. std eg, avg (c) 2012, C. Faloutsos

  11. Multimedia indexing • Feature extraction for indexing (GEMINI) • Lower-bounding lemma, to guarantee no false alarms • MDS/FastMap (c) 2012, C. Faloutsos

  12. Outline Goal: ‘Find similar / interesting things’ • Intro to DB • Indexing - similarity search • Points • Text • Time sequences; images etc • Graphs • Data Mining (c) 2012, C. Faloutsos

  13. Time series & forecasting Goal: given a signal (eg., sales over time and/or space) Find: patterns and/or compress count lynx caught per year year (c) 2012, C. Faloutsos

  14. Wavelets • Q: baritone/silence/soprano - DWT? f t value time (c) 2012, C. Faloutsos

  15. Time series + forecasting • Fourier; Wavelets • Box/Jenkins and AutoRegression • non-linear/chaotic forecasting (fractals again) • ‘Delayed Coordinate Embedding’ ~ nearest neighbors (c) 2012, C. Faloutsos

  16. Outline Goal: ‘Find similar / interesting things’ • Intro to DB • Indexing - similarity search • Points • Text • Time sequences; images etc • Graphs • Data Mining (c) 2012, C. Faloutsos

  17. Graphs • Real graphs: surprising patterns • ?? (c) 2012, C. Faloutsos

  18. Graphs • Real graphs: surprising patterns • ‘six degrees’ • Skewed degree distribution (‘rich get richer’) • Super-linearities (2x nodes -> 3x edges ) • Diameter: shrinks (!) • Might have no good cuts (c) 2012, C. Faloutsos

  19. Outline Goal: ‘Find similar / interesting things’ • Intro to DB • Indexing - similarity search • Data Mining (c) 2012, C. Faloutsos

  20. Data Mining - DB (c) 2012, C. Faloutsos

  21. Data Mining - DB • Association Rules (‘diapers’ -> ‘beer’ ) • [ OLAP (DataCubes, roll-up, drill-down) ] • [ Classifiers ] (c) 2012, C. Faloutsos

  22. Taking a step back: We saw some fundamental, recurring concepts and tools: (c) 2012, C. Faloutsos

  23. Powerful, recurring tools • Fractals/ self similarity • Zipf, Korcak, Pareto’s laws • intrinsic dimension (Sierpinski triangle) • correlation integral • Barnsley’s IFS compression • (Kronecker graphs) (c) 2012, C. Faloutsos

  24. Powerful, recurring tools • Fractals/ self similarity • Zipf, Korcak, Pareto’s laws • intrinsic dimension (Sierpinski triangle) • correlation integral • Barnsley’s IFS compression • (Kronecker graphs) • ‘Take logarithms’ • AVOID ‘avg’ (c) 2012, C. Faloutsos

  25. Powerful, recurring tools • SVD (optimal L2 approx) • LSI, KL, PCA, ‘eigenSpokes’, (& in ICA ) • HITS (PageRank) first singular vector v1 (c) 2012, C. Faloutsos

  26. Powerful, recurring tools • Discrete Fourier Transform • Wavelets (c) 2012, C. Faloutsos

  27. Powerful, recurring tools • Matrix inversion lemma • Recursive Least Squares • Sherman-Morrison(-Woodbury) (c) 2012, C. Faloutsos

  28. Summary • fractals / power laws probably lead to the most startling discoveries (‘the mean may be meaningless’) • SVD: behind PageRank/HITS/tensors/… • Wavelets: Nature seems to prefer them • RLS: seems to achieve the impossible • (approximate counting – NOT in the exam) (c) 2012, C. Faloutsos

  29. Thank you! • Feel free to contact me: • christos@cs GHC 8019 • Reminder: faculty course eval’s: • www.cmu.edu/hub/fce/ • Final: Thu. Dec 13,  5:30-8:30pm @DH A302 • Double-check at • www.cmu.edu/hub/docs/final-exams.pdf • Have a great break! (c) 2012, C. Faloutsos

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