Mathematics

External Resources

Articles:

• The top 10 algorithms
  • A quick overview of some of the most important algorithms out there
• Fast Randomized SVD

Papers:

• The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
• Robust Principal Component Analysis?

Courses:

• Essence of linear algebra by 3Blue1Brown
• Computational Linear Algebra

Internal Resources

• Miscellaneous
  • Averages
• Calculus
  • Derivatives
• Linear Algebra
  • Vectors
    • Linear Combinations of Vectors
    • Basis
      • Changing basis
    • Eigenvectors
      • Eigenbasis
  • Linear Transformations
    • Matrix Multiplication as Composition
    • Space Orientation
    • Column Space
    • Rank
    • Null Space / Kernel
    • Determinants
    • Inverse
    • Non Square Matrices
    • Cross Product
      • 2D Space
      • 3D Space
    • Dot Product
    • Duality
• Computational Linear Algebra
  • Introduction of the course; presentation of the problems we are trying to solve - Course 1: Why are we here?
  • The problem of trying to assign a topic to a post; different approaches; how to speed them up - Course 2: Topic modelling with SVD and NMF
  • SVD and NMF in depth; calculating smaller SVD (maintains high accuracy while speeding up compute significantly - Course 3: Topic modelling with SVD and NMF
  • PCA, decomposing matrices into sparse matrices and low rank matrices to help with tasks such as background removal - Course 4: Background Removal with Robust PCA

Minimizing a function multiplied by a constant

Let’s say we have an optimization problem.

$\underset{u}{min}(u-5)^2+1 => u=5$

If we multiply it all by some constant, the result does not change.

$\underset{u}{min} 10*((u-5)^2+1) => \underset{u}{min} 10(u-5)^2+10 => u=5$

EWMA

Exponentially weighted moving average

<figcaption>Exponentially weighted moving average</figcaption>

S**t = Y1 for t = 1

St* = *α* * *Yt + (1 − α)*S**t − 1 for t > 1