Yousef Saad Department Of Computer Science And Engineering

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Methods can be adapted to supervised mode by building the graph to use class labels. Idea: Build G so that nodes in the same class are neighbors. If c = # classes, G consists of c cliques. ➤ Matrix W is block-diagonal W = ⎛ ⎜ ⎝ W1 W2 ➤ Note: rank(W ) = n − c. W3 ➤ Can be used for LPP, ONPP, etc.. W4 W5 ⎞ ⎟ ⎠ CSE Colloquium 11/09/09 p. 68
Repulsion Laplaceans * Joint work with E. Kokiopoulou (’09) ➤ Idea: Create repulsion forces (energies) between items that are close but *not* in the same class. Class 1 Class 2 Class 3 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 ORL −− TrainPer−Class=5 onpp pca olpp−R laplace fisher onpp−R olpp 0.8 10 20 30 40 50 60 70 80 90 100 CSE Colloquium 11/09/09 p. 69
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From data-mining to nanotechnology
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➤ Then the stock market tanked ..
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Electronic structure ➤ Quantum me
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➤ Hamiltonian H is of the form :
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The underlying physical laws necess
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Kohn-Sham equations → nonlinear e
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The physical domain CSE Colloquium
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CHEBYSHEV FILTERING
Page 17 and 18: Chebyshev Subspace iteration - expe
Page 19 and 20: NUMERICAL LINEAR ALGEBRA IN DATA MI
Page 21 and 22: Major tool of Data Mining: Dimensio
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: Graph-based methods in a supervised
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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