# Analysis of Gene Expression Data

University of the Philippines Manila (UPM) invited us to talk about our research in Bioinformatics. I will discuss our research on visualization of yeast gene expression data.

# Review of Linear Algebra for Machine Learning Definition 1. The inner product of two vectors x and y is

Note that   , that is

Definition 2.

The Euclidean Norm of vector x is ||x||

Note that

If ||x|| = 1, then x is normalized

Otherwise, we can normalize x to x’ as follows

Definition 3.

Vector x and y are orthogonal, if their scalar product is zero.

The angle between two vectors x and y is    if

Geometric interpretation is shown below Note that the orthogonal projection of y onto x is

# Introduction to Machine Learning

## Machine Learning

is useful when

1. the pattern exists.
2. it is difficult to pin down the problem mathematically.
3. you have a data.

Pattern is an entity vaguely defined that could be given a name

Watanabe

Examples of patterns are palindromes in a sequence, spatial configuration of pixels in character recognition, speech signal in spectrogram, the salary, age, and debt records in credit card applications.

Learning is a process by which parameters of a learning machine are modified through a continuous process of stimulation by the environment in which it is embedded. In Figure 1, parameters of the learning machine are tweaked based from the error signal.