Part1: TheoryLinear systemAx = b,AERnxm一口SimpleDefiniteProfoundTimelessLinear system is the foundation for many differentapplications,such as automatic controltheory,signalprocessing,andtelecommunications
Part1: Theory Linear system Simple Definite Timeless Profound Linear system is the foundation for many different applications, such as automatic control theory, signal processing, and telecommunications
Part1: TheoryLinear systemDα =xLet D = [di, d2,.., dml E Rnxmbe a set ofbasis vector , D is called the dictionary.Bag of words,DFT.Wavelet,Curvelet
Bag of words, DFT, Wavelet, Curvelet, . Part1: Theory Linear system
Part1: TheoryLinear systemBagof wordsJohn":1,"likes":2,to".AssumeDisthewords listdefinebyhand"watD5.movalsoJohn likes to watch movies. Mary likes movies too.football":7games":8,John alsoIn computer vision,the bag-of-wordsmodel(BoWmodel)canbeappliedtoimageclassification,bytreatingimagefeaturesaswords.[1,2,11,120.1.αOJ[1,1,1,01.01
Assume D is the words list define by hand In computer vision, the bag-of-words model (BoW model) can be applied to image classification, by treating image features as words. Part1: Theory Linear system
Part1: TheoryLinear systemAssume D is set of cosine functionswith differentfrequencesα is the vector comprised bycoefficients ofeachbasisfunctionDFT(discrete Fouriertransform)
• Assume D is set of cosine functions with different frequences. • α is the vector comprised by coefficients of each basis function Part1: Theory Linear system
Part1: TheorySparsity ?The existence of simple laws is,then,apparently,to be regarded as a guality ofnatureand accordingly we may inferthat it is justifiable to prefer a simple law toamore complex one thatfits ourobservafionsslightlybetfer-WrinchandJeffreys
The existence of simple laws is, then, apparently, to be regarded as a quality of nature; and accordingly we may infer that it is justifiable to prefer a simple law to a more complex one that fits our observations slightly better. - Wrinch and Jeffreys Part1: Theory Sparsity ?