Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T

Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T

Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T

Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T

Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T

Introduction

$$$$theta**ast == arg min_theta * sum(L_D(theta ; x_i) == arg min_theta

sum(norm(f_theta(x_i) - x_i)**2))

Principal Component Analysis

$$$$min_(W**T * W == I) * norm_F(X -(XW) W**T)**2 == norm_F(X - X_hat)

**2

Principal Component Analysis

$$$$A ==(X - X_hat) Sigma(X - X_hat)**T