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  • Python与矩阵论——特征值与特征向量

    Python与矩阵论——特征值与特征向量


    The Unknown Word

    The First Column The Second Column
    receptive field [ri'septiv] [fild]感受野
    filter 滤波器['filte]
    toggle movement ['ta:gl]转换 ['muvment]动作
    recurrent 循环的[ri'ke:rent]
    ReLU The Rectified Linear Unit
    rectified ['rekte faie]整流器
    leaky 有漏洞的['liki]
    tuning ['tju:ning]调谐
    SGD Stochastic gradient descent
    stochastic [ste'kae stik]随机的
    hypothesis [hai'pa:thesis]假设
    SVD Singular Value Decomposition 万能矩阵分解
    singular ['singjule(r)]奇特的
    decomposition [dikamlpe'zition]分解
    format n.版式 vt.格式化

    PCA 降维举例

    1.X=(egin{bmatrix} -1 & -1 & 0 & 2 & 0 \-2 & 0 & 0 & 1 & 1 \ end{bmatrix})(C_x)=(egin{bmatrix} 6/5 & 4/5 \ 4/5 & 6/5 \ end{bmatrix})
    2.计算(C_x)特征值为:(lambda)=2,(lambda_2)=2/5,特征值特征向量为$egin{bmatrix} sqrt{2} sqrt{2} end{bmatrix} $ ,可验证(Lambda)=(U^T)(C_x)U
    3.降维:(egin{bmatrix} 1/sqrt{2} & -1/sqrt{2} end{bmatrix})X=(egin{bmatrix} -3/sqrt{2} & -1/sqrt{2} & 0 & 3/sqrt{2} & -1/sqrt{2} end{bmatrix})

    Gradient vector and Hessian matrix

    • Function : f(x)=2(x_1^3+3x_2^2+3x_1^2x_2-24x_2)
    • calculate(Gradient vector and Hessian matrix): ( abla)f(x)=(egin{bmatrix} 6x_1^2+6x_1x_2 \ 6x_2+3x_1^2-24 \ end{bmatrix})( abla^2)f(x)=6(egin{bmatrix} 2x_1+x_2 & x_1 \ x_1 & 1 \ end{bmatrix})

    The Unknown Word

    The First Column The Second Column
    convex optimization 凸规划
    optimization [optemi'zetion]最优化
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  • 原文地址:https://www.cnblogs.com/hugeng007/p/9446067.html
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