✍️
mathematics_basic_for_ML
  • README
  • README
    • Summary
    • Geometry
      • EulerAngle
      • Gimbal lock
      • Quaternion
      • RiemannianManifolds
      • RotationMatrix
      • SphericalHarmonics
    • Information
      • Divergence
      • 信息熵 entropy
    • LinearAlgebra
      • 2D仿射变换(2D Affine Transformation)
      • 2DTransformation
      • 3D变换(3D Transformation)
      • ComplexTransformation
      • Conjugate
      • Hessian
      • IllConditioning
      • 逆变换(Inverse transform)
      • SVD
      • det
      • eigendecomposition
      • 矩阵
      • norm
      • orthogonal
      • special_matrix
      • trace
      • vector
    • Mathematics
      • Complex
      • ExponentialDecay
      • average
      • calculus
      • convex
      • derivative
      • 距离
      • function
      • space
      • Formula
        • euler
        • jensen
        • taylor
        • trigonometric
    • Numbers
      • 几何级数
      • SpecialNumbers
    • NumericalComputation
      • ConstrainedOptimization
      • GradientDescent
      • Newton
      • Nominal
      • ODE_SDE
      • Preprocessing
    • Probability
      • bayes
      • distribution
      • expectation_variance
      • 贝叶斯公式
      • functions
      • likelihood
      • mixture_distribution
      • 一些术语
      • probability_distribution
Powered by GitBook
On this page
  • 两点之间的距离
  • 点到平面之间的距离
  • 符号距离

Was this helpful?

  1. README
  2. Mathematics

距离

两点之间的距离

Lp(xi,xj)=(∑l=1n∣xi(l)−yi(l)∣p)1pL_p(x_i, x_j) = (\sum_{l=1}^{n}|x_i^{(l)}-y_i^{(l)}|^p)^{\frac{1}{p}}Lp​(xi​,xj​)=(l=1∑n​∣xi(l)​−yi(l)​∣p)p1​

p=1时,曼哈顿距离 p=2时,欧氏距离 p=3时,各个坐标距离的最大值

点到平面之间的距离

点x0x_0x0​到超平面y=w⋅x+by = w \cdot x + by=w⋅x+b的距离为:

dis=∣w⋅x0+b∣∣∣w∣∣dis = \frac {|w \cdot x_0 + b|}{||w||}dis=∣∣w∣∣∣w⋅x0​+b∣​

其中∣∣w∣∣||w||∣∣w∣∣是www的L2L_2L2​范数

符号距离

符号距离函数(sign distance function),简称SDF,又可以称为定向距离函数(oriented distance function),在空间中的一个有限区域上确定一个点到区域边界的距离并同时对距离的符号进行定义:点在区域边界内部为正,外部为负,位于边界上时为0。

PreviousderivativeNextfunction

Last updated 2 years ago

Was this helpful?