WEEK 7 Principal Component Analysis, Self-Organizing Maps, Network-Based Clustering and Hierarchical Clustering

Principal Component Analysis (PCA) - Part 1

mean-平均值

Variance-方差：Measure of the spread of the data

Covariance协方差Measure of the co-dependence of two random variables

特征值和特征向量，矩阵

Principal Component Analysis (PCA) - Part 2

▶PCA is a method of revealing underling trends in large amounts of data

▶A new coordinate system is constructed by rotating the axes

▶The first coordinate is the direction in which the data varies most, and so on…

▶Select a few new variables which contain most of the variation of the data, and can be visualized

Principal Component Analyis (PCA) Plotting in MATLAB

有MATLAB License截止到2017.11.27，一个PCA的示例
软件下载https://www.mathworks.com/licensecenter/classroom/netsysbio
软件学习https://matlabacademy.mathworks.com/

Clustergram in MATLAB

Hierarchical Clustering层次聚类

根据距离聚类 距离的计算包括Euclidean 、Correlation 、Hamming等，其中以Euclidean最常见。
下图中subtype1-3三种压型分开，红色是高表达的区域。上部的基因在左上角区域高表达、中部的基因在中部区域高表达、下部的基因在右下角区域高表达。

层次聚类

Linkage Function

有以下几种
Average
Median
Single
Complete

Standardization

▶Standardization convert data into standardized z-scores.
▶Standardization is a normalization process that forces the values to fall into the range that is most suitable to be visualized in a clustergram.
▶There are two standardize options: row standardization or column standardization.
▶For gene expression data we generally use row standardization.

一个基于matlab的聚类示例

Self-Organizing Maps

K-means

找一个或多个点，mk使得该点到其余点的距离最短。

Self-Organizing Maps

与k-means的区别是，它是三维的，适用于非线性的数据。

Network-Based Clustering

将网络进行聚类

Gephi可以看network

Popular Network Clustering Methods