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 |