Scalar products angles and norms x y x y x y n k 1 x k y k dot product x 2 x x

Scalar products angles and norms x y x y x y n k 1 x

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Scalar products, angles and norms x, y = x · y = x * y = n k =1 x k y k (dot product) || x || 2 = x, x = n k =1 x 2 k ( 2 norm) | x, y | || x |||| y || (Cauchy-Schwartz inequality) cos( ( x, y )) = x, y || x |||| y || (angle and cosine) || x + y || 2 = || x || 2 + || y || 2 + 2 x, y (law of cosines) || x || p p = n k =1 | x k | p , p 1 ( p norm) || x + y || p || x || p + || y || p (triangular inequality) Orthogonality, vector space, basis, dimension x y x, y = 0 (Orthogonality) x y ⇔ || x + y || 2 = || x || 2 + || y || 2 (Pythagorean) Let d vectors x i be st x i x j , || x i || = 1 . Define V = Span( { x i } ) = y \ ∃ α C d , y = d i =1 α i x i V is a vector space, { x i } is an orthonormal basis of V and y V, y = d i =1 y, x i x i and d = dim V is called the dimensionality of V . We have dim( V W ) = dim V + dim W - dim( V W ) Column/Range/Image and Kernel/Null spaces Im [ A ] = { y R m \ ∃ x R n such that y = Ax } (image) Ker[ A ] = { x R n \ Ax = 0 } (kernel) Im [ A ] and Ker[ A ] are vector spaces satisfying Im [ A ] = Ker[ A * ] and Ker[ A ] = Im [ A * ] rank A + dim(Ker[ A ]) = n (rank-nullity theorem) where rank A = dim( Im [ A ]) (matrix rank) Note also rank A = rank A * rank A + dim(Ker[ A * ]) = m 19 Subscribe to view the full document.

How? How? – Piazza If you cannot get access to it contact me asap at [email protected] (title: “ [ECE285-MLIP][Piazza] Access issues ”). 20 Misc Misc Programming environment: Python/PyTorch/Jupyter We will use UCSD’s DSMLP cluster with GPU/CUDA. Great but busy. We recommend you to install Conda/Python 3/Jupyter on your laptop. Please refer to additional documentations on Piazza. Communication: All your emails must have a title starting with “ [ECE285-MLIP] or it will end up in my spam/trash. Note: “ [ECE 285-MLIP] ”, “ [ece285 MLIP] ”, “ (ECE285MLIP) ” are invalid! But avoid emails, use Piazza to communicate instead. For questions that may interest everyone else, post on Piazza forums. 21 Subscribe to view the full document.

Some references Reference books C. Bishop Pattern recognition and Machine Learning Springer, 2006 T. Hastie, R. Tibshirani, J. Friedman The Elements of Statistical Learning: Data Mining, Inference, and Prediction Springer, 2009 ~ hastie/ElemStatLearn/ D. Barber Bayesian Reasoning and Machine Learning Cambridge University Press, 2012 I. Goodfellow, Y. Bengio and A. Courville. Deep Learning MIT Press book, 2017 22 Some references Reference online classes Fei-Fei Li, Justin Johnson and Serena Yeung, 2017 (Stanford) CS231n: Convolutional Neural Networks for Visual Recognition Gir´o et al, 2017 (Catalonia) Deep Learning for Artificial Intelligence Leonardo Araujo dos Santos. Artificial Inteligence 23 Subscribe to view the full document.

Image sciences Imaging sciences – Overview Image sciences Imaging: Modeling the image formation process 24 Subscribe to view the full document.

Imaging sciences – Overview Image sciences Imaging: Modeling the image formation process Computer graphics: Rendering images/videos from symbolic representation 24 Imaging sciences – Overview Image sciences Computer vision: Extracting information from images/videos 25 Subscribe to view the full document. • Fall '08
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