Why do we care about eigenvalues, eigenvectors, and singular values? Intuitively, what do they tell us about a matrix? When I first studied eigenvalues in college, I regarded it as yet another theoretical math trick that is hardly applicable to my life. Once I passed the final exam, I shelved all my eigen-knowledge to a corner in my memory. Years have passed, and I gradually realize the importance and brilliance of eigenvalues, particularly in the realm of machine learning. In this post, I will discuss how and why we perform eigendecomposition and singular value decomposition in machine learning.

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Posts in the *Connect the Dots* category:

# Everything you need to know about matrix in machine learning (I): Solve Ax = b

In machine learning, we are often dealing with high-dimension data. For convenience, we often use matrix to represent data. Numerical optimization in machine learning often involves matrix transformation and computation. To make matrix computation more efficiently, we always factorize a matrix into several special matrices such as triangular matrices and orthogonal matrices. In this post, I will review essential concepts of matrix used in machine learning.

# Numerical optimization in machine learning (I): the basics

During logistic regression, in order to compute the optimal parameters in the model, we have to use an iterative numerical optimization approach (Newton method or Gradient descent method, instead of a simple analytical approach). Numerical optimization is a crucial mathematical concept in machine learning and function fitting, and it is deeply integrated in model training, regularization, support vector machine, neural network, and so on. In the next few posts, I will summarize key concepts and approaches in numerical optimization, and its application in machine learning.

# Goal setting for function fitting (classification)

In the previous post, I have discussed loss function in regression. In this post, I will elaborate how we develop loss function in classification when the output is discrete, rather than continuous.

# Do you write production code as a data scientist?

In the past month, I posted this question to my friends, peers, online tech forum, and got responses from more than 30 data scientists in various industries and different academic background and career path. The responses show a wide spectrum of data scientists’ involvement in production, and reveal some shared concerns about career development among data scientists.

# Goal setting for function fitting (regression)

Whenever we see the word “optimization”, the first question to ask is “what is to be optimized?” Defining an optimization goal that is meaningful and approachable is the starting point in function fitting. In this post, I will discuss goal setting for function fitting in regression.

# Restrict function search space by assumptions

In the previous post, I discussed the function fitting view of supervised learning. It is theoretically impossible to find the best fitting function from an infinite search space. In this post, I will discuss how we can restrict the search space in function fitting with assumptions.

# Set up the supervised learning problem as function fitting

In this very first post of the Connect the Dots series, I set up the supervised learning problem from a function fitting perspective and discuss the objective of function fitting.