binary plot2 pasir

Introduction to Pasir 0.0.5 in how to generate artificial datasets with two features for binary classification.

Info:

• Intro to Pasir 0.05: Binary classification data with two features
  • url https://osf.io/jftmw
  • version 20241128_v5
• Outline
  • Intro 3
  • Generate and visualize datasets 13
  • Range of x1 and x2 23
  • Labels 33
  • Markers 43
  • Equations 63
  • Linear lines 67
  • Quadratic lines 77
  • Other curved lines 87
  • Tasks 94
  • Closing 98

Sketch:

$$\tag{1} f(x) = \left\{ \begin{matrix} 1, & x > 0, \newline 0, & x \le 0. \end{matrix} \right. $$

$$\tag{2} \begin{array}{rcl} f(x) & = & (c _{00}) \newline & + & (c _{10} x + c _{01} y) \newline & + & (c _{20} x^2 + c _{11} xy + c _{02} y^2) \newline & + & (c _{30} x^3 + c _{21} x^2y + c _{12} xy^2 + c _{03} y^3) \newline & + & \dots \newline & + & (c _{n0} x^n + c _{n-1,1} x^{n-1}y + \dots + c _{1,n-1} xy^{n-1} + c _{0n} y^n) \end{array} $$

$$\tag{3} c _{00} + c _{10} x + c _{01} y = 0. $$

$$\tag{4} (c _{00}) + (c _{10} x + c _{01} y) + (c _{20} x^2 + c _{11} xy + c _{02} y^2) = 0. $$