Yousef Saad Department Of Computer Science And Engineering

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Introduction: What is data mining? ➤ Common goal of data mining methods: to extract meaningful information or patterns from data. Very broad area – includes: data analysis, machine learning, pattern recognition, information retrieval, ... ➤ Main tools used: linear algebra; graph theory; approximation theory; optimization; ... ➤ In this talk: brief overview with emphasis on dimension reduction techniques. interrelations between techniques, and graph theory tools. CSE Colloquium 11/09/09 p. 20
Major tool of Data Mining: Dimension reduction ➤ Goal is not just to reduce computational cost but to: • Reduce noise and redundancy in data • Discover ‘features’ or ‘patterns’ (e.g., supervised learning) ➤ Techniques depend on application: Preserve angles? Preserve distances? Maximize variance? .. CSE Colloquium 11/09/09 p. 21
Page 1 and 2: From data-mining to nanotechnology
Page 3 and 4: ➤ Then the stock market tanked ..
Page 5 and 6: Electronic structure ➤ Quantum me
Page 7 and 8: ➤ Hamiltonian H is of the form :
Page 9 and 10: The underlying physical laws necess
Page 11 and 12: Kohn-Sham equations → nonlinear e
Page 13 and 14: The physical domain CSE Colloquium
Page 15 and 16: CHEBYSHEV FILTERING
Page 17 and 18: Chebyshev Subspace iteration - expe
Page 19: NUMERICAL LINEAR ALGEBRA IN DATA MI
Page 23 and 24: Linear Dimensionality Reduction Giv
Page 25 and 26: 2-D ‘reductions’: 15 10 5 0 −
Page 27 and 28: 2-D ’reductions’: 6 4 2 0 −2
Page 29 and 30: Sparse Matrices viewpoint * Joint w
Page 31 and 32: Supervised learning: classification
Page 33 and 34: A harder case: 4 3 2 1 0 −1 −2
Page 35 and 36: Fisher’s Linear Discriminant Anal
Page 37 and 38: ➤ Project set on a one-dimensiona
Page 39 and 40: Trace ratio problem * Joint work wi
Page 41 and 42: Background: The Lanczos procedure A
Page 43 and 44: Information Retrieval: Vector Space
Page 45 and 46: Common approach: Use the SVD ➤ Ne
Page 47 and 48: Polynomial filters - examples Appro
Page 49 and 50: IR: Use of the Lanczos algorithm (1
Page 51 and 52: ➤ Theory well understood: works w
Page 53 and 54: Average query times average query t
Page 55 and 56: In summary: ➤ Results comparable
Page 57 and 58: Difficulty Positions, Expressions,
Page 59 and 60: Tests: Face Recognition Tests with
Page 61 and 62: GRAPH-BASED METHODS
Page 63 and 64: Example: The Laplacean eigenmaps La
Page 65 and 66: A unified view * Joint work with Ef
Page 67 and 68: Graph-based methods in a supervised
Page 69 and 70: Repulsion Laplaceans * Joint work w
Page 71 and 72:
Materials informatics at work. Illu
Page 73 and 74:
Conclusion ➤ Many, many, interest
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Yousef Saad Department Of Computer Science And Engineering

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