Linear regression How to measure the accuracy of linear regression - PowerPoint PPT Presentation

Linear regression

How to measure the accuracy of linear regression models

Linear Regression disease disease disease disease disease disease disease disease normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal X y i = x T i � + ✏ i = � j X i,j + ✏ i j Fitting error: ✏ i

Linear Regression disease disease disease disease disease disease disease disease normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal Assumption: errors are Gaussian noises y = X � + ✏ β ∗ = arg min X X β j X i,j ) 2 ( y i − β i j

Linear Regression β ∗ = arg min X X β j X i,j ) 2 ( y i − β i j β ( y − X β ) T ( y − X β ) = arg min = ( X T X ) − 1 X T y Question: How to derive the closed-form solution?

Clustering

Finding hidden structure in data

Expression analysis Blood Brain Liver

Single-cell expression analysis

Clustering: examples

Network clustering

Clustering

Clustering

Clustering algorithms

K-means

K-means for segmentation

When will K-means fail?

Hierarchical clustering

Agglomerative clustering

Complete Single

Application to breast cancer expression data