### Hopkins Statistic and Heatmap Plot

### Distance

Before applying cluster methods, the first step is to assess whether the data is clusterable, a process defined as the assessing of clustering tendency. get_clust_tendency() assesses clustering tendency using Hopkins' statistic and a visual approach. An ordered dissimilarity image (ODI) is shown. Objects belonging to the same cluster are displayed in consecutive order using hierarchical clustering. For more details and interpretation, see STHDA website: Assessing clustering tendency.

1.Hopkins statistic:

If the value of Hopkins statistic is close to 1 (far above 0.5), then we can conclude that the dataset is significantly clusterable.

2.VAT (Visual Assessment of cluster Tendency):

The VAT detects the clustering tendency in a visual form by counting the number of square shaped dark (or colored) blocks along the diagonal in a VAT image.

### Hopkins statistic

Hopkins statistic:

If the value of Hopkins statistic is close to 1 (far above 0.5), then we can conclude that the dataset is significantly clusterable.

### Hopkins heatmap

### Options

### Network

### Options

### Network

### Tables

### Tables

### Tables

### Author Information

Author: benben-miao

Email: benben.miao@outlook.com

Institution: Xiamen University

Github: https://github.com/benben-miao

BioSciTools: https://github.com/bioscitools

Researchgate: https://researchgate.net/profile/Benben-Miao

### Author Information

### 1.Application Introduction:

App Name: PCA & t-SNE Analysis Online Serve

Platform: Shinyapps Base on R 3.6.1

R Packages: ggplot2, DT, shiny, shinyjs, factoextra

Note: Cite: Please Cite R Packages above

### 2.Author Introduction:

Author: benben miao

Email: benben.miao@outlook.com

Github: https://github.com/benben-miao/

Omics: https://omics.netlify.app

Pro: Bioinformatics, AI

Program: Python, R, Java, Julia, Shell, HTML,CSS,Javascript, Ruby, Perl, C, C++, SQL, GO, Linux.etc

### 3.Using Application:

DevFor: Bioinformatics Analysis

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables (entities each of which takes on various numerical values) into a set of values of linearly uncorrelated variables called principal components.

This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components.

The resulting vectors (each being a linear combination of the variables and containing n observations) are an uncorrelated orthogonal basis set.

PCA is sensitive to the relative scaling of the original variables.

### 4.Knowledge about Cluster:

clustering function including kmeans, pam, clara, fanny, hclust, agnes and diana. Abbreviation is allowed.

calculating dissimilarities between observations. Allowed values are those accepted by the function dist() [including euclidean, manhattan, maximum, canberra, binary, minkowski].

And correlation based distance measures [pearson, spearman or kendall]. Used only when FUNcluster is a hierarchical clustering function such as one of hclust, agnes or diana.

The agglomeration method to be used (?hclust): ward.D, ward.D2, single, complete, average, ...

Cluster Analysis: Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).

It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields,

including machine learning, pattern recognition, image analysis, information retrieval, bioinformatics, data compression, and computer graphics.

Cluster analysis is an exploratory data analysis tool for organizing observed data or cases into two or more groups.