SMHS SciVisualization

MS Excel provides a large number of charts that can be used to quickly and effectively render complex multivariate data. For instance, the table below contains the principal component analysis (PCA) of 50 derived neuroimaging biomarkers (region of interest (ROI) by shape morphometry metric). The loadings of these 50 variables on the top 5 (most significant) principal component directions are shown in the table. Experiment with effective visualizations of these data.

Hemi	ROI	measure	ROI_Measure	Dim.1	Dim.2	Dim.3	Dim.4	Dim.5
L	insular	AvgMeanCurvature	L_insular_cortex_AvgMeanCurvature	0.72	0	0.06	0.06	0
L	insular	ComputeArea	L_insular_cortex_ComputeArea	0.77	0.06	0.04	0.01	0
L	insular	Volume	L_insular_cortex_Volume	0.72	0.09	0.04	0.03	0.01
L	insular	ShapeIndex	L_insular_cortex_ShapeIndex	0.46	0.06	0.01	0.02	0.01
L	insular	Curvedness	L_insular_cortex_Curvedness	0.78	0	0.05	0.03	0.01
R	insular	AvgMeanCurvature	R_insular_cortex_AvgMeanCurvature	0.79	0	0.03	0.08	0
R	insular	ComputeArea	R_insular_cortex_ComputeArea	0.79	0.09	0.03	0.01	0
R	insular	Volume	R_insular_cortex_Volume	0.73	0.11	0.03	0.03	0
R	insular	ShapeIndex	R_insular_cortex_ShapeIndex	0.27	0.17	0	0.07	0
R	insular	Curvedness	R_insular_cortex_Curvedness	0.84	0.02	0.03	0.01	0
L	cingulate	AvgMeanCurvature	L_cingulate_gyrus_AvgMeanCurvature	0.72	0	0.05	0.02	0.02
L	cingulate	ComputeArea	L_cingulate_gyrus_ComputeArea	0.74	0.05	0.06	0.04	0.01
L	cingulate	Volume	L_cingulate_gyrus_Volume	0.69	0.08	0.05	0.05	0.01
L	cingulate	ShapeIndex	L_cingulate_gyrus_ShapeIndex	0.53	0	0.05	0	0.03
L	cingulate	Curvedness	L_cingulate_gyrus_Curvedness	0.7	0.01	0.05	0.04	0.03
R	cingulate	AvgMeanCurvature	R_cingulate_gyrus_AvgMeanCurvature	0.6	0	0.02	0.03	0.01
R	cingulate	ComputeArea	R_cingulate_gyrus_ComputeArea	0.73	0.06	0.04	0.03	0.01
R	cingulate	Volume	R_cingulate_gyrus_Volume	0.68	0.09	0.04	0.04	0.01
R	cingulate	ShapeIndex	R_cingulate_gyrus_ShapeIndex	0.56	0.01	0.05	0	0.01
R	cingulate	Curvedness	R_cingulate_gyrus_Curvedness	0.25	0	0.01	0.04	0
L	caudate	AvgMeanCurvature	L_caudate_AvgMeanCurvature	0.52	0	0.05	0	0.01
L	caudate	ComputeArea	L_caudate_ComputeArea	0.51	0.09	0.03	0.04	0.02
L	caudate	Volume	L_caudate_Volume	0.44	0.09	0.03	0.06	0.03
L	caudate	ShapeIndex	L_caudate_ShapeIndex	0.2	0.03	0.04	0.04	0
L	caudate	Curvedness	L_caudate_Curvedness	0.51	0.12	0.02	0.01	0.01
R	caudate	AvgMeanCurvature	R_caudate_AvgMeanCurvature	0.68	0.04	0.04	0.02	0
R	caudate	ComputeArea	R_caudate_ComputeArea	0.67	0.17	0.03	0.02	0.01
R	caudate	Volume	R_caudate_Volume	0.61	0.16	0.02	0.03	0.01
R	caudate	ShapeIndex	R_caudate_ShapeIndex	0.18	0.02	0.03	0.11	0
R	caudate	Curvedness	R_caudate_Curvedness	0.65	0.19	0.01	0	0
L	putamen	AvgMeanCurvature	L_putamen_AvgMeanCurvature	0.62	0	0.04	0.03	0.02
L	putamen	ComputeArea	L_putamen_ComputeArea	0.56	0.05	0.04	0.03	0.05
L	putamen	Volume	L_putamen_Volume	0.52	0.07	0.04	0.05	0.05
L	putamen	ShapeIndex	L_putamen_ShapeIndex	0.06	0.13	0	0.15	0
L	putamen	Curvedness	L_putamen_Curvedness	0.64	0.11	0.03	0.01	0.03
R	putamen	AvgMeanCurvature	R_putamen_AvgMeanCurvature	0.62	0	0.07	0.04	0.01
R	putamen	ComputeArea	R_putamen_ComputeArea	0.66	0.08	0.03	0.01	0.03
R	putamen	Volume	R_putamen_Volume	0.64	0.12	0.03	0.02	0.03
R	putamen	ShapeIndex	R_putamen_ShapeIndex	0.15	0.24	0	0.08	0.03
R	putamen	Curvedness	R_putamen_Curvedness	0.65	0.05	0.05	0	0.02
L	hippocampus	AvgMeanCurvature	L_hippocampus_AvgMeanCurvature	0.78	0	0.01	0.04	0
L	hippocampus	ComputeArea	L_hippocampus_ComputeArea	0.75	0.07	0.01	0	0.02
L	hippocampus	Volume	L_hippocampus_Volume	0.72	0.09	0.01	0.01	0.01
L	hippocampus	ShapeIndex	L_hippocampus_ShapeIndex	0.45	0.17	0	0.04	0.02
L	hippocampus	Curvedness	L_hippocampus_Curvedness	0.79	0.03	0.01	0	0.02
R	hippocampus	AvgMeanCurvature	R_hippocampus_AvgMeanCurvature	0.72	0	0	0.1	0.01
R	hippocampus	ComputeArea	R_hippocampus_ComputeArea	0.71	0.09	0	0	0.05
R	hippocampus	Volume	R_hippocampus_Volume	0.68	0.1	0	0	0.04
R	hippocampus	ShapeIndex	R_hippocampus_ShapeIndex	0.37	0.18	0	0.02	0.03
R	hippocampus	Curvedness	R_hippocampus_Curvedness	0.77	0.03	0	0.02	0.04

R-Charts

There are 100’s of packages and 1,000 of different charts, plots and graphs that can be generated using R. Such interactive visualizations enable deeper exploration of data, models and results. JavaScript libraries, e.g., D3, provide advantages for data visualization as these involve HTML5 and are easily shareable online. The R community is developing R interfaces to some popular JavaScript libraries to allow users to create interactive visualizations without detailed knowledge of JavaScript.

Examples of powerful R interactive visualization packages

• ggplot2 – http://ggplot2.org

• ggvis – interactive plots extending the static ggplot2 charts, http://ggvis.rstudio.com

• rCharts – R interface to multiple JavaScript charting libraries, http://rcharts.io

• plotly – transforming ggplot2 charts into interactive plots, https://plot.ly/r

• googleVis – Google Charts using R, http://cran.r-project.org/web/packages/googleVis/vignettes/googleVis_examples.html

• HTMLWidgets

o leaflet – library for creating dynamic maps, supports panning and zooming, annotations, markers, polygons, etc. http://www.htmlwidgets.org/showcase_leaflet.html

o dygraphs – provides mechanism for charting time-series data, supports interactive navigation features including series/point highlighting, zooming, and panning, http://www.htmlwidgets.org/showcase_dygraphs.html

o networkD3 – library for creating D3 network graphs including force directed networks, Sankey diagrams, and Reingold-Tilford tree networks, http://www.htmlwidgets.org/showcase_networkD3.html

o DataTables – displays R matrices or data frames as interactive HTML tables that support filtering, pagination, and sorting, http://www.htmlwidgets.org/showcase_datatables.html

o Rthreejs – features 3D scatterplots and globes based on WebGL, http://www.htmlwidgets.org/showcase_threejs.html

• Other R graphic examples

o To write out plots out to file use:

# pdf() command all graphs are redirected to test.pdf.  Also works with other common formats:  jpeg, png, ps, tiff.
pdf("C:\\Users\\Dinov\\Desktop\\test.pdf"); plot(1:100, 1:100); dev.off()
# Generates Scalable Vector Graphics (SVG) that can be edited by vector graphics software
svg("test.svg"); plot(1:100, 1:100); dev.off()

Paired ScatterPlots

set.seed(100)
x <- matrix(runif(50), ncol=5, dimnames=list(letters[1:10], LETTERS[1:5]))
describe(x)    # library("Hmisc")
plot(x[,1], x[,2], pch=20, col="red", main="Symbols and Labels")
text(x[,1]+0.03, x[,2], rownames(x))

pairs(x)

Another way to generate scatterplots is by using ggplot:

# library(ggplot2)
x <- sample(1:20, 20); y <- sample(1:20, 20); cat <- rep(c("A", "B", "C", "D"), 5)  
#vs. cat <- rep(c("A", "B", "C", "D"), each=5)
plot.1 <- qplot(x, y, geom="point", size=5*x, color=cat, main="GGplot with Relative Dot Size and Color") + theme(legend.position = "topleft")
print(plot.1)

# Use Case-Studies: https://umich.instructure.com/courses/38100/files/folder/Case_Studies
#  Case_03_MentalHealthServicesSurvey
# data1 <- read.table('https://umich.instructure.com/files/399128/download?download_frd=1&verifier=AG2e9QUKUm1jvDBpkX7D9jbEjKNc4irA0ECk0f7p', header=T)	
head(data1)
attach(data1)
# library("Hmisc")
describe(data1)

plot(data1[,3], data1[,4], pch=20, col="red", main="Symbols and Labels")
# text(data1 [,3]+0.03, data1 [,4], rownames(data1))
plot.1 <- qplot(x, y, geom="point", size=5*x, color=cat, main="GGplot with Relative Dot Size and Color") + theme(legend.position = "topleft")
print(plot.1)

# redo plots using majorfundtype FacilityType Ownership Focus
# pairs(data1, na.action=na.omit)

# Scatterplot with regression line. Use the “diamonds” dataset, which is a data frame with
# 53,940 rows and 10 variables ()
# describe(diamonds)

# Use Case-Studies: https://umich.instructure.com/courses/38100/files/folder/Case_Studies
# CaseStudy01_Divorce_YoungAdults
# data1 <- read.csv('https://umich.instructure.com/files/399118/download?download_frd=1&verifier=ESACv31KcyiHbkPZPuT8Oo4V7XzPtgTTbs6PQLTv', header=T)	
attach(data1)
# plot variables: DIVYEAR momint dadint momclose depression livewithmom gethitched

set.seed(110)
# par(mfrow=c(1,2))
data.2 <- diamonds[sample(nrow(diamonds), 500), ]
plot.2 <- qplot(price, depth, data = data.2, geom = c("point", "smooth"), method = "lm")
plot.3 <- qplot(carat, price, data=data.2, geom=c("point", "smooth"), span=0.4)
print(plot.2); print(plot.3)

Barplots

x <- matrix(runif(50), ncol=5, dimnames=list(letters[1:10], LETTERS[1:5]))
barplot(x[1:4,], ylim=c(0, max(x[1:4,])+0.3), beside=TRUE, legend.text = letters[1:4],
       args.legend = list(x = "topleft"))
text(labels=round(as.vector(as.matrix(x[1:4,])),2), x=seq(1.5, 21, by=1) + sort(rep(c(0,1,2,3,4), 4)), y=as.vector(as.matrix(x[1:4,]))+0.1)

# to put error bars on barplot:

# 10 rows (a, b, c, …):
bar <- barplot(m <- rowMeans(x) * 10, ylim=c(0, 10))
stdev <- sd(t(x))
arrows(bar, m, bar, m + stdev, length=0.15, angle = 90)

# Case_04_ChildTrauma
# data1 <- read.table('https://umich.instructure.com/files/399129/download?download_frd=1&verifier=Hmv0YW2Kie5ZTV9CKBUNArSHR66f3GWSmVzZDBxc', header=T)	
attach(data1)
head(x)
head(data1)
# plot data
data2 <- data1[,-5]   # remove the 5th columns text
data1 <- data2[,-5]   # remove the 6th columns text
# or data1 <- data1[,c(-5,-6)]

data2 <- as.data.frame(data1)
Blacks <- data2[which(data2$\$$race=="black"),]
 Other <- data2[which(data2$\$$race=="other"),]
Hispanic <- data2[which(data2$\$$race=="hispanic"),]
 White <- data2[which(data2$\$$race=="white"),]

A <- c(mean(Blacks$\$$age), mean(Blacks$\$$service))
#colnames(A) <- c("age "," service ")  
B <- c(mean(Other$\$$age), mean(Other$\$$service))
C <- c(mean(Hispanic$\$$age), mean(Hispanic$\$$service))
D <- c(mean(White$\$$age), mean(White$\$$service))

x <- cbind(A, B, C, D)

bar <- barplot(x[1:2,], ylim=c(0, max(x[1:2,])+2.0), beside=TRUE, 
legend.text = c("age","service") ,  args.legend = list(x = "right"))
text(labels=round(as.vector(as.matrix(x[1:2,])),2), x=seq(1.4, 21, by=1.5), #y=as.vector(as.matrix(x[1:2,]))+0.3)

y=11.5)

m <- x; stdev <- sd(t(x))
arrows(bar, m, bar, m + stdev, length=0.15, angle = 90)

barplot(as.matrix(data1[1:4,]), ylim=c(0, max(data1[1:4,])+0.3), beside=TRUE, legend.text = data1[1:4,1], args.legend = list(x = "topleft"))
text(labels=round(as.vector(as.matrix(data1[1:4,])),2), x=seq(1.5, 21, by=1), y=as.vector(as.matrix(data1[1:4,]))+0.1)

# Columns (A, B, C, D, E):
bar <- barplot(m <- colMeans(x) * 5, ylim=c(0, 5))
stdev <- sd(t(x))
arrows(bar, m, bar, m + stdev, length=0.15, angle = 90)

Histograms and Density Plots

hist(x, freq=TRUE, breaks=10)

plot(density(x), lwd = 10, col="green")

Pie Chart

# first , “A”, and second, “B”, columns
par (mfrow=c(1,2))
pie(x[,1], col=rainbow(length(x[,1]), start=0.1, end=0.8), clockwise=TRUE)

pie(x[,1], col=rainbow(length(x[,1]), start=0.1, end=0.8), clockwise=TRUE)

pie(x[,2], col=rainbow(length(x[,2]), start=0.1, end=0.8), clockwise=TRUE)
legend("topleft", legend=row.names(x), cex=1.3, bty="n", pch=15, pt.cex=1.8, col=rainbow(length(x[,2]), start=0.1, end=0.8), ncol=1)

You can export the data: 
write.table(x, " ", "data.txt")
# copy-paste it in SOCR Pie chart to generate another Pie view of data

Line Plots Using ggplot

head(diamonds)

	Carat	Cut	Color	Clarity	Depth	Table	Price	X	Y	Z
1	0.23	Ideal	E	SI2	61.5	55	326	3.95	3.98	2.43
2	0.21	Premium	E	SI1	59.8	61	326	3.89	3.84	2.31
3	0.23	Good	E	VS1	56.9	65	237	4.05	4.07	2.31
4	0.29	Premium	I	VS2	62.4	58	334	4.2	4.23	2.63
5	0.31	Good	J	SI2	63.3	58	335	4.34	4.35	4.75
6	0.24	VeryGood	J	VVS2	62.8	57	336	3.94	3.96	2.48

plot.2 <- ggplot(diamonds, aes(carat, price, group=cut, color=cut)) + geom_line()
print(plot.2)

plot.2 <- ggplot(data1, aes(age, service, group=race, color=race)) + geom_line()
print(plot.2)

# Faceting plot (geometrically, faceting (or facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices)
plot.3 <- ggplot(diamonds, aes(carat, price)) + geom_line(aes(color=cut), size=1) + 
facet_wrap(~cut, ncol=1)
print(plot.3)

Barplots with ggplot

plot.4 <- ggplot(diamonds, aes(cut, fill=cut)) + geom_bar() + facet_grid(. ~ clarity)
print(plot.4)

New_var <- service+rnorm(1000, 0,1)
data1$\$$New_var <- int(New_var)
 plot.4 <- ggplot(data1, aes(race, fill= traumatype)) + geom_bar() + facet_grid(. ~ New_var)
 print(plot.4)


 plot.4a <- ggplot(diamonds, aes(color, price/carat, fill=color)) + geom_boxplot()
 print(plot.4a)

<center>[[Image:SMHS_SciVisualization20.png|500px]] </center>

==='"`UNIQ--h-9--QINU`"'Jitter plot===

 plot.5 <- ggplot(diamonds, aes(color, price/carat)) + geom_jitter(alpha = I(1 / 2), aes(color=color))
 print(plot.5)

<center>[[Image:SMHS_SciVisualization21.png|500px]] </center>

==='"`UNIQ--h-10--QINU`"'Density Plots===

 plot.6 <- ggplot(diamonds, aes(carat, size=2)) + geom_density(aes(color = cut))
 print(plot.6)

<center>[[Image:SMHS_SciVisualization22.png|500px]] </center>

 plot.6 <- ggplot(data1, aes(age, size=2)) + geom_density(aes(color = traumatype))
 print(plot.6)

 plot.7 <- ggplot(diamonds, aes(carat, size=2)) + geom_density(aes(fill = color))
 print(plot.7)

<center>[[Image:SMHS_SciVisualization23.png|500px]] </center>

 plot.8 <- ggplot(diamonds, aes(x=carat, size=1)) + geom_histogram(aes(y = price), binwidth=0.2) + geom_density()
 print(plot.8)

<center>[[Image:SMHS_SciVisualization24.png|500px]] </center>

 plot.8a <- ggplot(diamonds, aes(x=carat, size=1)) + geom_histogram(aes(y = price), stat="identity") + geom_density()
 print(plot.8a)

<center>[[Image:SMHS_SciVisualization25.png|500px]] </center>

==='"`UNIQ--h-11--QINU`"'Heatmaps===

 # Generating Dendogram Association Heatmap Plot (Genotype vs. Imaging phenotype
 # http://stat.ethz.ch/R-manual/R-patched/library/stats/html/heatmap.html
 # http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4005931/ 
	   
 AD_Associations_Data <- read.table("https://umich.instructure.com/files/330387/download?download_frd=1&verifier=gLk2ADgrLhXGeknI6mqIeJugi2ODr8RARsQlBUMe", header=TRUE, row.names=1,  sep=",", dec=".")	   

 MCI_Associations_Data <- read.table("https://umich.instructure.com/files/330390/download?download_frd=1&verifier=FczlJD6ISRPZhu69xvHuoZHx2c7gXX9YEvvPCTBG", header=TRUE, row.names=1,  sep=",", dec=".")	   	   

 NC_Associations_Data <- read.table("https://umich.instructure.com/files/330391/download?download_frd=1&verifier=i2BEtSpmpbrzQUPoA2ST06IzzcaenyVEHRepHSF3", header=TRUE, row.names=1,  sep=",", dec=".")	   	   

 require(graphics)
 require(grDevices)
 library(gplots)

 AD_Data <- AD_Associations_Data 
 MCI_Data <- MCI_Associations_Data 
 NC_Data <- NC_Associations_Data 

 AD_mat  <- as.matrix(AD_Data); class(AD_mat) <- "numeric"
 MCI_mat  <- as.matrix(MCI_Data); class(MCI_mat) <- "numeric"
 NC_mat  <- as.matrix(NC_Data); class(NC_mat) <- "numeric"

 # set up the rol (rc) and column (cc) colors for each cohort
 rcAD <- rainbow(nrow(AD_mat), start = 0, end = 1.0); ccAD<-rainbow(ncol(AD_mat), start = 0, end = 1.0)
 rcMCI <- rainbow(nrow(MCI_mat), start = 0, end=1.0); ccMCI<-rainbow(ncol(MCI_mat),start=0,end=1.0)
 rcNC <- rainbow(nrow(NC_mat), start = 0, end = 1.0); ccNC<-rainbow(ncol(NC_mat), start = 0, end = 1.0)

 # set up 1x3 graph display - par (mfrow=c(1,3)) – does not work with ‘heatmap’
 hvAD <- heatmap(AD_mat, col = cm.colors(256), scale = "column", RowSideColors = rcAD, ColSideColors = ccAD, margins = c(2,2), main="AD Cohort SNP-ROI_volume Association (p_values)")
 hvMCI <- heatmap(MCI_mat, col = cm.colors(256), scale = "column", RowSideColors = rcMCI, ColSideColors = ccMCI, margins = c(2,2), main="MCI Cohort SNP-ROI_volume Association (p_values)")
 hvNC <- heatmap(NC_mat, col = cm.colors(256), scale = "column", RowSideColors = rcNC, ColSideColors = ccNC, margins = c(2,2), main="NC Cohort SNP-ROI_volume Association (p_values)")

<center>[[Image:SMHS_SciVisualization26.png|500px]] </center>

 # Alternatively, we can use the R package gplots
 install.packages("gplots")
 library(gplots)
 ## col dendrogram plotted and col reordering done. 
 # heatmap.2(AD_mat, keysize=2) 
 ## A more decorative heatmap, with z-score scaling along columns 
 heatmap.2(AD_mat, col=cm.colors(255), scale="column", RowSideColors=rcAD, ColSideColors=ccAD, margin=c(8, 7), xlab="Imaging Biomarkers (ROI volume)", ylab= "Genetics Biomarkers (SNPs)", main="AD Associations Heatmap (SNP-Imaging)",     tracecol="green", density="density")

<center>[[Image:SMHS_SciVisualization27.png|500px]] </center>

==='"`UNIQ--h-12--QINU`"'Correlation Plots===

 The <b>corrplot</b> package is a graphical display of a correlation matrix, and confidence intervals, with some tools for matrix reordering. There are seven visualization methods (parameter method) in corrplot package, named   "circle", "square", "ellipse", "number", "shade", "color", "pie".
 # install.packages("corrplot")
 library(corrplot)
 NC_Associations_Data <- read.table("https://umich.instructure.com/files/330391/download?download_frd=1&verifier=i2BEtSpmpbrzQUPoA2ST06IzzcaenyVEHRepHSF3", header=TRUE, row.names=1,  sep=",", dec=".")	   
 M <- cor(NC_Associations_Data)

<center>[[Image:SMHS_SciVisualization28.png|500px]] </center>

==='"`UNIQ--h-13--QINU`"'Hyperbolic Visualization===

•	URL: http://socr.umich.edu/html/Navigators.html  

•	Tools:

<blockquote>o	Java/Jar applet: http://socr.umich.edu/html/navigators/HW/jars/SOCR_HW_Viewer.jar</blockquote>

<blockquote>o	JavaScript: http://socr.umich.edu/html/navigators/D3/SOCR_D3_Viewer.html (JSON)</blockquote>

•	Data Format

<blockquote>o	XML data: http://socr.umich.edu/html/navigators/HW/SOCR_HyperTree.xml</blockquote>

<blockquote>o	JSON data: http://socr.umich.edu/html/navigators/D3/xml/SOCR_HyperTree.json</blockquote> 

•	D3 Visualization

<blockquote>o	E:\Ivo.dir\Research\UMichigan\Education_Teaching_Curricula\2015_2016\HS_853_Fall_2015\Modules_docx\Tools\TreeViewer_JS</blockquote>

<blockquote>	treeJS.json</blockquote>

<blockquote>	flareD3.json</blockquote>

<center>[[Image:SMHS_SciVisualization29.png|500px]] </center>

<center>[[Image:SMHS_SciVisualization30.png|500px]] </center>

•	URL: https://github.com/mbostock/d3/wiki/Gallery

•	Source code: https://github.com/mbostock/d3

<center>[[Image:SMHS_SciVisualization31.png|500px]] </center>

==='"`UNIQ--h-14--QINU`"'Motion Charts===

•	Video: http://www.socr.ucla.edu/SOCR_MotionCharts/SOCR_HTML5_MotionChart_Video2.gif

•	Java: http://www.socr.ucla.edu/SOCR_MotionCharts/ 

•	HTML5: http://socr.umich.edu/HTML5/MotionChart/ 

•	Activities: http://wiki.socr.umich.edu/index.php/SOCR_MotionCharts 


<center>[[Image:SMHS_SciVisualization32.png|500px]] </center>

==='"`UNIQ--h-15--QINU`"'1D/2D/3D signal/area/volume/surface/model/atlas visualization===

• 1D: (See R/SOCR Visualization tools above)

• 2D: http://imagej.nih.gov/ij/ 

• 3D: http://socr.umich.edu/HTML5/BrainViewer/ 

 <b>Supported File Formats:</b>
 Volumes (.nii / .nii.gz / .img&.hdr / .mgh / .mgz / .nrrd)
 Shapes (.dx / .vtk / .stl / FreeSurfer)
 Fibers (.trk)

<center>[[Image:SMHS_SciVisualization33.png|500px]] </center>

==='"`UNIQ--h-16--QINU`"'Trees and Graphs===

• Trees/Hierarchies and general Graphs

 # Install and load the APE package, needed for the phylogenetic tree rendering (as.phylo)
 # install.packages("ape")
 library("ape")

Load data 

 # Data: 02_Nof1_Data.csv
 data.1 <- read.table("https://umich.instructure.com/files/330385/download?download_frd=1&verifier=DwJUGSd6t24dvK7uYmzA2aDyzlmsohyaK6P7jK0Q ", sep=",", header = TRUE)
 head(data.1)

<center>
{| class="wikitable" style="text-align:center; width:35%" border="1"
|-
mydata1
|-		
|||ID||Day||Tx||SelfEff||SelfEff25||WPSS||SocSuppt||PMss||PMss3||PhyAct
|-
|1||1||1||1||33||8||0.97||5.00||4.03||1.03||53
|-
|2||1||2||1||33||8||-0.17||3.87||4.03||1.03||73
|-
|3||1||3||0||33||8||0.81||4.84||4.03||1.03||23
|-
|4||1||4||0||33||8||-0.41||3.62||4.03||1.03||36
|-
|5||1||5||1||33||8||0.59||4.62||4.03||1.03||21
|-
|6||1||6||1||33||8||-1.16||2.87||4.03||1.03||0

|}
</center>


Clustering

 hc = hclust(dist(data.1), 'ave') 
 # the agglomeration method can be specified "ward.D", "ward.D2", "single","complete", "average" (= UPGMA), "mcquitty" (= WPGMA),"median" (= WPGMC) or "centroid" (= UPGMC)

 # (3) Plot clustering diagram
 par (mfrow=c(1,1))
 # very simple dendrogram
 plot(hc)

<center>[[Image:SMHS_SciVisualization34.png|500px]] </center>

 require(graphics)
 (x <- identify(hc)) ##  Terminate with 2nd mouse button !!
 identify(hc, <mark>function(k)</mark> print(table(data.1[k,5])))

You can now cut the tree into branches. You can split the tree into 2 groups, by setting the number of cuts with the k=2 parameter, or by specifying height to cut the tree at (?cutree):

 k	an integer scalar or vector with the desired number of groups
 h	numeric scalar or vector with heights where the tree should be cut

 cutree(hc, k = 2)
 # alternatively specify the height, which is, the value of the criterion associated with the clustering method 
 # for the particular agglomeration.
 cutree(hc, h= 50) # cut at h=50
 table(cutree(hc, h= 50)) # cluster distribution
 # To identify the number of cases for varying number of clusters we can combine calls to cutree and table 
 # in a call to <b>sapply</b> -- to see the sizes of the clusters for 2≤ k≤10 cluster-solutions:
 # numbClusters=5; 
 myClusters = sapply(2:10,function(numbClusters)table(cutree(hc, numbClusters)))
 names(myClusters) <- paste("Number of Clusters=", 2:10, sep = "")
 myClusters
 #To see which SubjectIDs are in which clusters:
 groups.10 <- cutree(hc, k = 10)	
 sapply(unique(groups.10),function(g)data.1$\$$ID[groups.10 == g])
#To see which Treatments (Tx) are in which clusters:
groups.2 <- cutree(hc, k = 2)
sapply(unique(groups.2),function(g)data.1$\$$Tx[groups.2 == g])
 # drill down deeper
 table(groups.2, data.1$\$$Tx)
# For a small number of observations, we can often interpret the cluster solution directly by looking 
# at the labels of the observations that are in each cluster. 
# This is hard for larger data sets. To characterize clusters we can look at cluster summary statistics, 
# like the median, of the variables that were used to perform the cluster analysis broken down 
# by the groups that the cluster analysis identified.

The aggregate function will compute stats (e.g., median) on many variables simultaneously.

To look at the median values for the variables we've used in the cluster analysis, broken up by the cluster groups:

aggregate(data.1, list(groups.10),median) # may have to shrink data.1 prior to clustering! 
# data.2 <- data.1[,-c(1,3)]  # Remove ID and Tx variables?
aggregate(data.2, list(groups.2),median) # for only 2 clusters

	Group	ID	Day	Tx	SelfEff	SelfEff25	WPSS	SocSuppt	PMss	PMss3	PhyAct
1	1	14	16	0	20	-5	-0.040	2.995	3.275	0.275	41
2	2	16	15	1	25	0	0.025	3.280	3.360	0.360	104

table(groups.2, data.1$\$$<u><b>PhyAct</b></u>)

 # library("Hmisc")

 describe(data.1$\$$PhyAct)

# It’s useful to add the numbers of observations in each group (aggregate returns a data frame, 
# that can be manipulated)

df.2 <- aggregate(data.1, list(groups.2),median)

data.frame(Cluster= df.2[,1], Freq=as.vector(table(groups.2)), df.2[,-1])

	Cluster	Freq	ID	Day	Tx	SelfEff	SelfEff25	WPSS	SocSuppt	PMss	PMss3	PhyAct
1	1	570	14	16	0	20	-5	-0.040	2.995	3.275	0.275	41
2	2	330	16	15	1	25	0	0.025	3.280	3.360	0.360	104

Publications

• This paper examines nasal and bronchial tissue cultures as appropriate in vitro models for the assessment of smoking-induced adverse effects in the respiratory system (doi: 10.1177/1091581814551647), using “hclust” package. No data.

• This paper classified subtypes of gastric cancer based on epidemiologic and histologic and gene expression data. These new classifications of gastric cancer have implications for improving our understanding of disease biology and identification of unique molecular drivers for each gastric cancer subtype (doi: 10.1158/1078-0432.CCR-10-2203).

Repeat the clustering

# using centroids and squared Euclidean distance
# cut the tree into 10 clusters and reconstruct the upper part of the tree from the cluster centers.
hc <- hclust(dist(data.1), "cen")
mem <- cutree(hc, k = 10)
cent <- NULL
for(k in 1:10){
 		cent <- rbind(cent, colMeans(data.1[mem == k, , drop = FALSE]))
}

hc1 <- hclust(dist(cent), method = "cen", members = table(mem))

opar <- par(mfrow = c(1, 2))
plot(hc,  labels = FALSE, hang = -1, main = "Original Tree")
plot(hc1, hang = -1, main = "Re-start from 10 clusters")
par(opar)

Identify subjects within each of the 10 classes

rect.hclust(hc, h=10)

# To save the cluster numbers to a new variable in the dataset, use the cutree function.
# data.1$\$$clusterID <- cutree(hc, 10)
 data.1$\$$clusterID <- cutree(hc, 10)
head(data.1)

	ID	Day	Tx	SelfEff	SelfEff25	WPSS	SocSuppt	PMss	PMss3	PhyAct	CluserID
1	1	1	1	33	8	0.97	5.00	4.03	1.03	53	1
2	1	2	1	33	8	-0.17	3.87	4.03	1.03	73	1
3	1	3	0	33	8	0.81	4.84	4.03	1.03	23	2
4	1	4	0	33	8	-0.41	3.62	4.03	1.03	36	2
5	1	5	1	33	8	0.59	4.62	4.03	1.03	21	2
6	1	6	1	33	8	-1.16	2.87	4.03	1.03	0	2

Phylogenetic tree diagram

# library("ape")
plot(as.phylo(hc1), use.edge.length = TRUE, type = "fan")
plot(as.phylo(hc), use.edge.length = TRUE, type = "fan", tip.color = hsv(runif(15, 0.65, 0.95), 1, 1, 0.7), label.offset = 1, cex = log(data.1$\$$ID, 10), col = "red")

<center>[[Image:SMHS_SciVisualization36.png|500px]] </center>

<center>[[Image:SMHS_SciVisualization37.png|500px]] </center>

<b>Hands-on Activity (Health Behavior Risks)</b>

 # load data CaseStudy09_HealthBehaviorRisks_Data
 data.2 <- read.csv("https://umich.instructure.com/files/399182/download?download_frd=1 ", sep=",", header = TRUE)

 # Classify the cases using these variables:  "AGE_G"    "SEX"      "RACEGR3"  "IMPEDUC"  "IMPMRTL"  
 #	"EMPLOY1"  "INCOMG"  "CVDINFR4" "CVDCRHD4" "CVDSTRK3" "DIABETE3" "RFSMOK3"  
 #	"FRTLT1"   "VEGLT1" 
 data.raw <- data.2[,-c(1,14,17)]

 # Does the classification match either of these: 
 #	TOTINDA (Leisure time physical activities per month, 1=Yes, 2=No, 9=Don’t know/Refused/Missing)
 #	RFDRHV4 (Heavy alcohol consumption, 1=No, 2=Yes, 9=Don’t know/Refused/Missing)


 hc = hclust(dist(data.raw), 'ave') 
 # the agglomeration method can be specified "ward.D", "ward.D2", "single", "complete", "average" (= UPGMA), "mcquitty" (= WPGMA), "median" (= WPGMC) or "centroid" (= UPGMC)

 # (3) Plot clustering diagram
 par (mfrow=c(1,1))
 # very simple dendrogram
 plot(hc)
 
 summary(data.2$\$$TOTINDA); summary(data.2$\$$RFDRHV4)

 cutree(hc, k = 2)
 # alternatively specify the height, which is, the value of the criterion associated with the 
 # clustering method for the particular agglomeration -- cutree(hc, h= 10)

 table(cutree(hc, h= 10)) # cluster distribution

 # To identify the number of cases for varying number of clusters we can combine calls to cutree and table 
 # in a call to sapply -- to see the sizes of the clusters for 2≤ k≤10 cluster-solutions:
 # numbClusters=4; 
 myClusters = sapply(2:5,function(numbClusters)table(cutree(hc, numbClusters)))
 names(myClusters) <- paste("Number of Clusters=", 2:5, sep = "")
 myClusters

 #To see which SubjectIDs are in which clusters:
 table(cutree(hc, k=2)) 
 groups.k.2 <- cutree(hc, k = 2)
 sapply(unique(groups.k.2),function(g)data.2$\$$ID[groups.k.2 == g])

#To see which TOTINDA (Leisure time physical activities per month, 1=Yes, 2=No, 9=Don’t 
# 	know/Refused/Missing) & whch RFDRHV4 are in which clusters:
groups.k.3 <- cutree(hc, k = 3)
sapply(unique(groups.k.3),function(g)data.2$\$$TOTINDA [groups.k.3 == g])
 sapply(unique(groups.k.3),function(g)data.2$\$$RFDRHV4[groups.k.3 == g])

# Perhaps there are intrinsically 3 groups here e.g., 1, 2 and 9 …
groups.k.3 <- cutree(hc, k = 3)
sapply(unique(groups.k.3),function(g)data.2$\$$TOTINDA [groups.k.3 == g])
 sapply(unique(groups.k.3),function(g)data.2$\$$RFDRHV4 [groups.k.3 == g])

# Note that there is quite a dependence between the outcome variables …
plot(data.2$\$$RFDRHV4, data.2$\$$TOTINDA)

# drill down deeper
table(groups.k.3, data.2$\$$RFDRHV4)

 # To characterize clusters we can look at cluster summary statistics, 
 # like the median, of the variables that were used to perform the cluster analysis broken down 
 # by the groups that the cluster analysis identified. The aggregate function will compute stats
 # (e.g., median) on many variables simultaneously. To look at the median values for the variables 
 # we've used in the cluster analysis, broken up by the cluster groups:
 aggregate(data.2, list(groups.k.3),median) 

==='"`UNIQ--h-18--QINU`"'Complex Network Visualization===

 # Install package
 # install.packages("igraph")
 library("igraph")

 # build a simple graph
 g <- graph( c(1,2, 1,3, 2,3, 3,4), n=10)
 plot(g)

 summary(g); g; is.igraph(g); is.directed(g); vcount(g); ecount(g)

<center>[[Image:SMHS_SciVisualization38.png|500px]] </center>

<center>[[Image:SMHS_SciVisualization39.png|500px]] </center>

 plot(g, layout=layout.circle)

 plot(g, layout=layout.fruchterman.reingold)
 plot(g, layout=layout.graphopt)
 plot(g, layout=layout.kamada.kawai, vertex.color="cyan")

 # Interactive
 tkplot(g, layout=layout.kamada.kawai)
 # 3D plot
 rglplot(g, layout=layout.kamada.kawai(g))

 # Dataset 1: Coappearance network in the novel “les miserablese”. 
 # D. E. Knuth, The Stanford GraphBase: A Platform for Combinatorial Computing, Addison-Wesley, Reading, 
 # MA (1993).
 # The data contains the weighted network of coappearances of characters in Victor Hugo's novel "Les 
 # Miserables".  Nodes represent characters as indicated by the labels and edges connect any pair of
 # characters that appear in the same chapter of the book.  The values on the edges are the number of 
 # such coappearances.

 # Alternatively, we can use a directed, weighted network representing the neural network of the nematode 
 # C. Elegans. D. Watts and S. Strogatz, Nature 393, 440-442 (1998). The file celegansneural.gml describes a 
 # weighted, directed network where the nodes have been renumbered to be consecutive.
 #  Edge weights are the weights given by Watts.

 install.packages("rgl")
 library("igraph")

 g<-read.graph("C:\\Users\\Dinov\\Desktop\\celegansneural.gml",format=c("gml"))
 g
 plot(g, layout=layout.graphopt)

 data_g <- read.table("https://umich.instructure.com/files/330389/download?download_frd=1&verifier=u1jqCGS8AAU0MsO5ffLCyvVFYXXAflpdLtg8RXhk", sep=" ", header = FALSE)

 data_g_mat <- as.matrix(data_g, byrow=TRUE, nc=2)
 g_miserab <- graph.edgelist(data_g_mat, dir=FALSE)
 summary(g_miserab)
 plot(g_miserab, layout=layout.graphopt)
 # rglplot(g_miserab, layout=layout.kamada.kawai(g_miserab))

 # to name the vertices and and plot the graph  of the first 10 vertices
 V(g_miserab)$name
 g_miserab.1 <- graph.ring(10)
 V(g_miserab.1)$name <- sample(letters, vcount(g_miserab.1))
 plot(g_miserab.1, layout=layout.graphopt)

 # compute the node adjacency matrix
 g <- g_miserab; as_adjacency_matrix(g)
 E(g)$weight <- runif(ecount(g))
 W <- get.adjacency(g, attr="weight")
 W

<b>Social Network Analysis Example</b>

 # free memory
 # rm(list = ls())
 # gc()

 
 # load termDocMatrix dataset
 # These data include Twitter text data of @RDataMining representing a general social network analysis
 # example. The terms represent people and the tweets represent LinkedIn groups.
 # The term-document matrix can be viewed as the group membership of people. 
 # We may want to build a network of terms based on their co-occurrence in the same tweets,
 # similarly to a network of people based on their group membership.
 # https://umich.instructure.com/files/541336/download?download_frd=1 

load("E:\\Ivo.dir\\Research\\UMichigan\\Education_Teaching_Curricula\\2015_2016\\HS_853_Fall_2015\\Modules_docx\\data\\03_GraphNetwork_TermDocMatrix.rdata")

<center><b>Labeled graph</b> [[Image:SMHS_SciVisualization40.png|400px]] </center>

<center><b>Adjacency matrix</b> [[Image:SMHS_SciVisualization41.png|400px]] Coordinates are 1-6.</center>

 # inspect part of the matrix
 termDocMatrix [5:10,1:20]
 # change it to a Boolean matrix == incidence matrix
 termDocMatrix [termDocMatrix >=1] <- 1

 # transform into a term-term adjacency matrix (n×n), where (i,j)th entries correspond to the number of edges 
 # node from xi to node xj.
 # Matrix Multiplication in R: http://www.statmethods.net/advstats/matrix.html, dim(t(termDocMatrix))
 termMatrix <- termDocMatrix %*% t(termDocMatrix)

 # A graph has no loops, when all entries of the adjacency matrix on the main diagonal of are zeroes
 # http://mathonline.wikidot.com/adjacency-matrices 
 diag(termMatrix)

 # The matrix product of incidence matrix (B) and it’s transpose B×B^T represents the degrees of all nodes!
 # inspect terms numbered 5 to 10
 termMatrix[5:10,5:10]

 # library("igraph")
 # build a graph from the adjacency matrix
 g <- graph.adjacency(termMatrix, weighted=T, mode="undirected")
 plot(g)

 # remove loops 
 g <- simplify(g); plot(g)

 # set labels and degrees of  V(g)
 V(g)$\$$label <- V(g)$\$$name
 V(g)$\$$degree <- degree(g)

# set seed to make the layout reproducible
set.seed(1953)
layout1 <- layout.fruchterman.reingold(g)   # Fruchterman-Reingold layout
plot(g, layout=layout1)

# plot(g, layout=layout.kamada.kawai)
# tkplot(g, layout=layout.kamada.kawai)

# Finesse the graph appearance – vertices and edges
V(g)$\$$label.cex <- 2.2 * V(g)$\$$degree / max(V(g)$\$$degree)+ .2
 V(g)$\$$label.color <- rgb(0, 0, .2, .8)
V(g)$\$$frame.color <- rgb(0,0,1)
 egam <- (log(E(g)$\$$weight)+.4) / max(log(E(g)$\$$weight)+.4)
 E(g)$\$$color <- rgb(.5, .5, 0, egam)		# Graph Edges, E(g)
E(g)$\$$width <- egam
 # plot the graph in layout1
 plot(g, layout=layout1)

 V(g)$\$$label <- V(g)$\$$name
 V(g)$\$$label.color <- rgb(0, 0, 0, 0.5)
V(g)$\$$label.dist <- 1.0	# relative distance of labels from node center
 V(g)$\$$label.angle<- 3/8   #in radians
V(g)$\$$label.cex <- 1.4*V(g)$\$$degree/max(V(g)$\$$degree) + 1
 V(g)$\$$color <- rgb(1, 0, 0, .4)
V(g)$\$$size <- 22 * V(g)$\$$degree / max(V(g)$\$$degree)+ 2
 V(g)$\$$shape <- "rectangle"
# V(g)$\$$.size=10*(strwidth(V(g)$\$$label) + strwidth("oo")) * 10
# V(g)$\$$.size2=strheight("I") * 10
 V(g)$\$$frame.color <- NA
# set vertex labels and their colors and sizes
# set edge width and color
E(g)$\$$width <- .3	
 E(g)$\$$color <- rgb(.5, .5, 0, .3)

set.seed(1234)
plot(g, layout=layout.fruchterman.reingold)

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