g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1,2,3)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
#g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.breaks <- g.hist$breaks # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.breaks[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean)/kmin)
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
alpha.LM
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=5)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(yeast)
hist(yeast)
hist(g.vec)
g.pois
g.mean
alpha.LM
alpha.ML
degree(g)
sort(degree(g))
sort(degree(g),decreasing=FALSE)
sort(degree(g),decreasing=F)
sort(degree(g),decreasing=false)
sort(degree(g), decreasing = TRUE)
head(sort(degree(g), decreasing = TRUE))
stddev(degree(g))
sd(degree(g))
tail(sort(degree(g), decreasing = TRUE))
plot(log(g.breaks.clean), log(g.probs.clean))
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(log(g.breaks.clean), log(g.probs.clean))
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
# load gene expression data
load("sense.filtered.cpm.Rdata")
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
# load gene expression data
load("sense.filtered.cpm.Rdata")
dim(sense.filtered.cpm)
colnames(sense.filtered.cpm)
length(sense.filtered.cpm)
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
## 2: Loading Demographic Data
subject.attrs <- read.csv("Demographic_symptom.csv", stringsAsFactors = FALSE)
dim(subject.attrs)  # 160 subjects x 40 attributes
colnames(subject.attrs)  # interested in X (sample ids) and Diag (diagnosis)
subject.attrs$X
subject.attrs$Diag
dim(sense.filtered.cpm)
colnames(sense.filtered.cpm)
rownames(sense.filtered.cpm)
# Matching gene expression samples with their diagnosis
if (!require("dplyr")) install.packages("dplyr")
# Matching gene expression samples with their diagnosis
if (!require("dplyr")) install.packages("dplyr")
# create a phenotype vector
# grab X (subject ids) and Diag (Diagnosis) from subject.attrs that
#   intersect %in% with the RNA-Seq data
phenos.df <- subject.attrs %>%
filter(X %in% colnames(sense.filtered.cpm)) %>%
dplyr::select(X, Diag)
# Matching gene expression samples with their diagnosis
if (!require("dplyr")) install.packages("dplyr")
# create a phenotype vector
# grab X (subject ids) and Diag (Diagnosis) from subject.attrs that
#   intersect %in% with the RNA-Seq data
phenos.df <- subject.attrs %>%
filter(X %in% colnames(sense.filtered.cpm)) %>%
dplyr::select(X, Diag)
library(dplyr)
# create a phenotype vector
# grab X (subject ids) and Diag (Diagnosis) from subject.attrs that
#   intersect %in% with the RNA-Seq data
phenos.df <- subject.attrs %>%
filter(X %in% colnames(sense.filtered.cpm)) %>%
dplyr::select(X, Diag)
colnames(phenos.df) # $Diag is mdd diagnosis
# grab Diag column and convert character to factor
mddPheno <- as.factor(phenos.df$Diag)  # this is our phenotype/class vector
summary(mddPheno) # MDD -- major depressive disorder, HC -- healthy control
#### Part B: Normalization
## 1: log2 transformation
# raw cpm boxplots and histogram of one sample
boxplot(sense.filtered.cpm,range=0,
ylab="raw probe intensity", main="Raw", names=mddPheno)
# log2 transformed boxplots and histogram
boxplot(log2(sense.filtered.cpm), range=0,
ylab="log2 intensity", main="Log2 Transformed", names=mddPheno)
hist(sense.filtered.cpm[,1], freq=F, ylab="density",
xlab="raw probe intensity", main="Raw Data Density for Sample 1")
hist(log2(sense.filtered.cpm[,1]), freq=F, ylab="density",
xlab="log2 probe intensity", main="log2 Data Density for Sample 1")
median(sense.filtered.cpm[,1])
mode(sense.filtered.cpm[,1])
average(sense.filtered.cpm[,1])
mean(sense.filtered.cpm[,1])
getmode <- function(v) {
uniqv <-unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
getmode(sense.filtered.cpm[,1])
median(sense.filtered.cpm[,1])
mean(sense.filtered.cpm[,1])
getmode(sense.filtered.cpm)
median(sense.filtered.cpm)
mean(sense.filtered.cpm)
getmode(log2(sense.filtered.cpm))
median(log2(sense.filtered.cpm))
mean(log2(sense.filtered.cpm))
log2(sense.filtered.cpm)
log2(sense.filtered.cpm[,1])
getmode(log2(sense.filtered.cpm[,1]))
median(log2(sense.filtered.cpm[,1]))
mean(log2(sense.filtered.cpm[,1]))
data <- data.frame(Mean = c(mean(sense.filtered.cpm[,1]),
data <- data.frame(Mean = c(mean(sense.filtered.cpm[,1]),
mean(log2(sense.filtered.cpm[,1]))),
Mode = c(getmode(sense.filtered.cpm[,1]),
getmode(log2(sense.filtered.cpm[,1]))),
Median = c(median(sense.filtered.cpm[,1])),
)
data
data <- data.frame(Mean = c(mean(sense.filtered.cpm[,1]),
mean(log2(sense.filtered.cpm[,1]))),
Mode = c(getmode(sense.filtered.cpm[,1]),
getmode(log2(sense.filtered.cpm[,1]))),
Median = c(median(sense.filtered.cpm[,1])),
)
data <- data.frame(Mean = c(mean(sense.filtered.cpm[,1]),
mean(log2(sense.filtered.cpm[,1]))),
Mode = c(getmode(sense.filtered.cpm[,1]),
getmode(log2(sense.filtered.cpm[,1]))),
Median = c(median(sense.filtered.cpm[,1]))
)
data
rownames(data) = c("Original", "Log2 Transformed")
data
table(data)
data <- data.frame(Mean = c(mean(sense.filtered.cpm[,1]),
mean(log2(sense.filtered.cpm[,1]))),
Mode = c(getmode(sense.filtered.cpm[,1]),
getmode(log2(sense.filtered.cpm[,1]))),
Median = c(median(sense.filtered.cpm[,1]))
)
rownames(data) = c("Original", "Log2 Transformed")
data
## 2: Quantile Normalization
# install quantile normalize
#install.packages("BiocManager")
if (!require("BiocManager")) install.packages("BiocManager")
library(BiocManager)
if (!require("preprocessCore"))
BiocManager::install("preprocessCore")
library(preprocessCore)    # replace with custom function?
# apply quantile normalization
mddExprData_quantile <- normalize.quantiles(sense.filtered.cpm)
boxplot(mddExprData_quantile,range=0,ylab="raw intensity", main="Quantile Normalized")
sapply(mddExprData_quantile, function(x) quantile(x, probs = seq(0, 1, 1/4)))