Outline : Multimedia Databases and Data Mining. Indexing - similarity search. Indexing - similarity search. C.
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1 Outline : Multimedia Databases and Data Mining Lecture #30: Conclusions C. Faloutsos Goal: Find similar / interesting things Intro to DB Indexing - similarity search Points Text Time sequences; images etc Graphs (c) 2017, C. Faloutsos 2 Indexing - similarity search Indexing - similarity search R-trees z-ordering / hilbert curves M-trees (DON T FORGET ) P1 P3 I AC G B F H D E P4 J P (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 4 1
2 Indexing - similarity search R-trees z-ordering / hilbert curves M-trees beware of high intrinsic dimensionality P1 P3 I AC G B F H D E P4 J P (c) 2017, C. Faloutsos 5 Outline Goal: Find similar / interesting things Intro to DB Indexing - similarity search Points Text Time sequences; images etc Graphs (c) 2017, C. Faloutsos 6 Text searching find all documents with word bla (c) 2017, C. Faloutsos 7 Text searching Full text scanning ( grep ) Inversion (B-tree or hash index) signature files Bloom filters Vector space model Ranked output Relevance feedback String editing distance (-> dynamic prog.) (c) 2017, C. Faloutsos 8 2
3 Multimedia indexing GEMINI - Pictorially S1 S1 eg,. std F(S1) day day F(Sn) Sn Sn eg, avg day (c) 2017, C. Faloutsos day (c) 2017, C. Faloutsos #10 Multimedia indexing Feature extraction for indexing (GEMINI) Lower-bounding lemma, to guarantee no false dismissals MDS/FastMap Outline Goal: Find similar / interesting things Intro to DB Indexing - similarity search Points Text Time sequences; images etc Graphs (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 12 3
4 Time series & forecasting Goal: given a signal (eg., sales over time and/or space) Find: patterns and/or compress f Wavelets Q: baritone/silence/soprano - DWT? count DFT value f t?? year (c) 2017, C. Faloutsos 13 time (c) 2017, C. Faloutsos 14 Time series + forecasting Fourier; Wavelets Box/Jenkins and AutoRegression non-linear/chaotic forecasting (fractals again) Delayed Coordinate Embedding ~ nearest neighbors xt Outline Goal: Find similar / interesting things Intro to DB Indexing - similarity search Points Text Time sequences; images etc Graphs xt (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 16 4
5 Graphs Real graphs: surprising patterns?? 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) 2017, C. Faloutsos (c) 2017, C. Faloutsos 18 Graphs - SVD Hubs/Authorities (SVD on adjacency matrix) M products meat-eaters steaks vegetarians plants kids cookies Graphs - PageRank Hubs/Authorities (SVD on adjacency matrix) PageRank (fixed point -> eigenvector) N users ~ + + u (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 20 5
6 Tensors Eg., time evolving graphs; Subject-verbobject triplets; etc politicians artists athletes Taking a step back: We saw some fundamental, recurring concepts and tools: subject = + + object (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 25 T1: Powerful, recurring tools Fractals/ self similarity T1: Powerful, recurring tools Fractals/ self similarity <-> Power laws Zipf, Korcak, Pareto s laws intrinsic dimension (Sierpinski triangle) correlation integral Barnsley s IFS compression Kronecker graphs (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 27 6
7 T1: Powerful, recurring tools Fractals/ self similarity Zipf, Korcak, Pareto s laws intrinsic dimension (Sierpinski triangle) correlation integral Barnsley s IFS compression (Kronecker graphs) (c) 2017, C. Faloutsos 28 T2: Powerful, recurring tools SVD (optimal L2 approx) v1 first singular vector (c) 2017, C. Faloutsos 29 T2: Powerful, recurring tools SVD (optimal L2 approx) LSI, KL, PCA, eigenspokes, (& in ICA ) HITS (PageRank) T3: Powerful, recurring tools Discrete Fourier Transform Wavelets v1 first singular vector (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 31 7
8 T4: Powerful, recurring tools Matrix inversion lemma Recursive Least Squares Sherman-Morrison(-Woodbury) Summary T1: fractals / power laws lead to startling discoveries the mean may be meaningless Don t assume Gaussian (average, k-means, etc) T2: SVD: behind PageRank/HITS/tensors/ T3: Wavelets: Nature seems to prefer them T4: RLS: matrix inversion, without inverting (c) 2017, C. Faloutsos (c) 2017, C. Faloutsos 33 Thank you! Feel free to contact me: Cell#; christos@cs; GHC 8019 Reminder: faculty course eval s: Final: as announced in Hub Mo 5/8/2017, 8:30-11:30am, DH 2315 (double-check with ) Have a great summer! (c) 2017, C. Faloutsos 35 8
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