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Linear Equations np. linalg. eig (a) # feature Decomposition "Automatic" Reshaping a = np.arange(30)a.shape = 2,-1,3a.shape # (2L, 5L, 3L)print(a)array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]]) X = np. arange (0, 10, 2) y = np. arange (5) m = np. vstack ([x, y]) Output: array ([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]) n = np. hstack ([x, y]) Output: ar

'))); % ===================================================== ======================================= figure ('name ', 'visualisation of covariance matrix '); imagesc (covar ); % ===================================================== ========================================= k = 0; % Set k accordingly egis = eig (covar) egis = sort (egis, 'descend') for I = 1: size (covar, 1) if (sum (egis (1: i)/sum (egis)> 0.99) k = I break; end % ==================

eig/EfM4mPp3scuH7ZU/OKkZsQEaesj1hZJ+ZMFzdSiFSvVaIJtuQQJAH3sXQ3DV EoeSW40TyYviq2K1pEpz9fGcS1TrjI+Yt1Mf0mvO6eupNZCfuhiAqJ5ZGRzTv1Pu G7pgz+ey5sWBcA==";var public_key = @"MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCRh7vKq7r6EhSg9y6iD38Vy08z umEJXhNTIGe8vRjdpE118Nu1cPRZ0AU9FbMIx8cnQtgCqGgW3DPDLj4VmlmdnJ8P cFHBBWgh85P1hicv8BQ0nLLjqezaBcS9EmO1C7zhdONVrvMFyHc1j76e+Fv+XfC6 CRvwKfqX+j5OMmWtowIDAQAB";var rsa = new RSACryptoServiceProvider();rsa.FromX5

)B =-0.0971-0.0178 0.06361.3591 1.5820-1.52660.0149-0.0178 0.06361.1351 1.0487-0.8905-0.0971-0.0178 0.0636-0.0971-0.0178 0.0636-0.9932-0.8177-0.8905-0.9932-0.8177 1.0178-1.6653-1.8842 1.9719-1.2173-1.3509 1.65392.0312 1.8486-1.52660.6870 0.5155-0.2544-0.0971-0.0178 0.06360.0149-0.0178 0.06360.0149-0.0178 0.0636Calculating the coefficients of the principal components and their respective variances are done by finding the Eigenfuncti ONS of the sample covariance matrix:>> [V D] =

\ foreigners \ Desktop \ orl \ s', num2str (I ), '\', num2str(j),'.bmp '); % imshow (a); B = a (* 92); % B is the row vector 1 × n, where n = 10304, the extraction sequence is to first run the column, that is, from top to bottom, from left to right B = double (B); allsamples = [allsamples; B]; % allsamples is an M * n matrix, each row of data in allsamples represents an image, where M = 200 endendsamplem EAN = mean (allsamples); % average image, 1 × Nfor I = xmean (I, :) = allsamples (I, :)-sam

5 Data = NP. matrix (NP. transpose (MAT) 6 data_adjust = data-mean 7 # returns the covariance matrix 8 covariance = NP. transpose (data_adjust) * data_adjust/9 9 # obtain the feature values and feature vectors of the covariance matrix 10 eigenvalues, eigenvectors = NP. linalg. EIG (covariance) 11 feature_vectors = NP. transpose (eigenvectors) 12 # converted data 13 final_data = feature_vectors * NP. transpose (data_adjust) 2. Call PCA in WEKA: Import

ascending order:-sort (-y) or filplr (sort (r )) Find: locate the position (not the element value) of the vector matrix element that meets the conditions or expressions specified by the user ). Y = [-1 2-3 4]. S = Y [find (Y Ones: One = ones (R, c ). Create a (RXC) matrix with 1 elements. Zeros: ZER = zeros (R, c ). Create a (RXC) matrix with zero elements. Magic: Magic (n ). Generates a special matrix, that is, the sum of elements in any row or column in the matrix, and the sum of elements on

[Mathematical model] python Implementation of principal component analysis and python Analysis Def pca (dataMat, topNfeat = 9999999): # data matrix. The top feat meanVals = mean (dataMat, axis = 0) is output) # calculate the average meanRemoved = dataMat-meanVals covMat = cov (meanRemoved, rowvar = 0) # Calculate the covariance matrix eigVals, eigVects = linalg. eig (mat (covMat) # feature value, eigValInd = argsort (eigVals) # Sort To find the large

going on here?Well, first of all, (i + (i >> 4)) 0x0F0F0F0F does exactly the same as the previous line, except it adds the adjacent four-bit Bitcou NTS together to give the bitcounts of each eight-bit block (i.e. byte) of the input. (Here, unlike to the previous line, we can get away with moving the outside the addition, since we know that the Eig Ht-bit Bitcount can never exceed 8, and therefore would fit inside four bits without overflowing.)Now

) ([1,1,3,8,5]) print (K[i]) #线性代数 #a=array ([[[2,3],[3,4]]) #inv (a) inverse trace (a) Find Trace A.transpose () Transpose # Solve (A, b) solve ax=b# eigvals solve eigenvalue # EIG (C) The C1 returned is a characteristic value C2 is a feature vector # U,SIGMA,V=NP.LINALG.SVD (d,full_matric=false) SVD singular value decomposition # pinv generalized inverse # det determinant # Matrix Class #amatrix (' 1.0 2.0;3.0 4.0 ') #A. TL = Arange (L.shape=3,4prin

) generates a sample value for the beta distribution, and the parameter must be greater than 0 chisquare () generates sample values for Chi-square distribution gamma () produces a gamma distribution of sample values uniform () produces sample values that are evenly distributed in [0,1] 2.1.c.1 Random Common functionsD Numpy.linalg functions and properties: Function Description

def zeroMean(dataMat): # 求各列特征的平均值 meanVal = np.mean(dataMat, axis=0) newData = dataMat - meanVal return newData, meanValnewData, meanVal = zeroMean(data)print ‘the newData is \n‘, newDataprint ‘the meanVal is \n‘, meanVal 1 2 3 4 5 6 7 8 9 the newData is [[ 0.69 0.49] [-1.31 -1.21] [ 0.39 0.99] [ 0.09 0.29] [ 1.29 1.09] [ 0.49 0.79] [ 0.19 -0.31] [-0.81 -0.81] [-0.31 -0.31] [-0.71 -1.01]]the meanVal is [ 1.81 1.91] 1 2 3 4

/intersect1d/union1d/setdiff1d/setxor1d file input and OUTPUT functions Loadtxt/savetxt Save/load Saves the array as a binary format disk or read (NPY) Savez Save multiple arrays to a compressed file Linear algebraic functions (LINALG) Dot Matrix Inner Product XTX Qr QR decomposition Inv Inverse matrix Svd

Ord_to_number (' eleven ') = = one assert Spoken_word_to_number (' twenty two ') = = Assert Spoken_word_to_number (' Thirty-two ') = = (' Forty two ') = = Spoken_word_to_number assert spoken_word_to_number (' two hundred thirty two ') = = 232 Assert Spoken_word_to_number (' two thirty two ') = = 232 assert spoken_word_to_number (' Nineteen Hundred Eighty Nine ') = = 1989 Assert Spoken_word_to_number (' Nineteen Eighty Nine ') = = 1989 Assert Spoken_word_to_number (' One thousand nine hundred an

, it is generally necessary to use the direct search method when the objective function of the problem is difficult to be represented by the analytic formula of the Guide function. At the same time, because these methods are generally more intuitive and easy to understand, they are often used in practical applications. Powell method: Basic Search Accelerated Search Adjust Search Specific steps ^ See page 54 ^ Matlab to seek unconstrained extremum problem Symbolic Solution: % calculation of the M

function Q=AHP (A) [M,n]=size (A); Ri=[0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51]; R=rank (A); The rank of the Judgment matrix [V,d]=eig (A); % to determine the eigenvalues and eigenvectors of the Matrix, v eigenvalues, D eigenvectors; Tz=max (D); B=max (TZ); % Maximum characteristic value [Row, Col]=find (d==b); % Maximum Eigenvalue location C=v (:, col); % corresponding feature vector Ci= (b-n)/(n-1); % Calculation Consistency Test indicator

matrix, the poly (a) command evaluates the characteristic polynomial of a, Det (Lambda*eye (Size (a))-a)Poly (v) when V is a vector, command poly (v) generates a polynomial with V as its rootRoot to find the roots of the polynomialRoot (P) Cases Clear CLC a=[1 2 3;4 5 6;7 8 0]; P=poly (A)% to find the characteristic polynomial |λe-a| R=roots (p)%, based on the above characteristic polynomial, to find eigenvaluesResults p = 1.0000 -6.0000 -72.0000 -27.0000 r = 12.1229 -5.734

(Size (R), i); R.sum () //SUM (R (:)) sum r.colwise (). SUM () //SUM (r) column sum 1xN r.rowwise (). SUM () //SUM (r, 2) or SUM (R ') ' line sum Nx1 r.prod () //prod (R (:)) all product r.colwise (). PROD () //prod (r) column product r.rowwise (). Prod () //prod (r, 2) or prod (r ') ' line product r.trace () //Trace (R) trace R.all () //All (R (:)) and Operation R.colwise (). All () /-All

Recent exposure to LDA (linear discriminant analysis), LFDA (local discriminant analysis), Flda (Fisher linear discriminant analysis), MMDA (multi-modal discriminant analysis) and other methods for feature extraction, all of which involve the same problem--fisher The Criterion (Fisher discriminant criterion), which requires the minimization of intra-class discretization and the largest inter-class dispersion, describes the problem as shown in the figure: This leads to the generalized eigenval

= 8 1 6 3 5 7 4 9 2 >> inv (a) ans = 0.1472- 0.1444 0.0639-0.0611 0.0222 0.1056-0.0194 0.1889-0.1028 >> det (a) ans = -360 >> D IAG (a) ans = 8 5 2 >> sqrt (a) ans = 2.8284 1.0000 2.4495 1.7321 2.2361 2.645 8 2.0000 3.0000 1.4142 >> Eig (a) ans = 15.0000 4.8990-4.8990 >> a ' ans = 8 3 4 1 5 9 6 7 2 >> A A = 8 1 6 3 5 7 4 9 2 >> Rot90 (a) ans = 6 7 2 1 5 9 8 3 4 >> FLIPLR (a) ans = 6 1 8 7 5 3 2 9 4 >> flipud (a) ans = 4 9 2 3 5 7 8