159 lines
3.1 KiB
Plaintext
159 lines
3.1 KiB
Plaintext
---
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title: "exam2_q4"
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author: "Mark Pearl"
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date: "8/3/2021"
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output: html_document
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---
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```{r setup}
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library(R.matlab)
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library(matlab)
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```
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```{r import data}
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#Read in the matrix files
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random_miss <- read.csv('./RandomMiss.csv',header=FALSE)
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colnames(random_miss) <- c(paste0("X_", 1:100))
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random_miss <- as.matrix(random_miss)
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non_random_miss <- read.csv('./NonRandomMiss.csv',header=FALSE)
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colnames(non_random_miss) <- c(paste0("X_", 1:100))
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non_random_miss <- as.matrix(non_random_miss)
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original <- read.csv('./Original.csv',header=FALSE)
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colnames(original) <- c(paste0("X_", 1:100))
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original <- as.matrix(original)
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```
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```{r run nonrandommiss}
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n1 <- 100
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n2 <- 100
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A <- as.matrix(non_random_miss)
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r <- 2
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decomp <- svd(A)
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U <- decomp$u
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s <- decomp$d
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V <- decomp$v
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s[(r+1): length(s)] <- 0
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S <-diag(s)
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#svd decomp
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X <- U %*% S %*% t(V)
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X0 <- X
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missing_observations <-which(A==0)
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A <- ifelse(A == 0, TRUE, FALSE)
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X[A]<-0
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m <- sum(sum(A==0))
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# Initialization
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Y <- matrix(0,n1,n2)
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delta <- (n1*n2)/m
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lambda <- 5
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tau <- delta*lambda
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# Iterations
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vec <- rep(0,500)
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err <- rep(0,500)
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for (i in 1:500){
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decomp <- svd(Y)
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U <- decomp$u
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S <- decomp$d
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V <- decomp$v
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S_t <- S-tau
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S_t[S_t<0] <- 0
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Z_nonrandom <- U%*%diag(S_t)%*%t(V)
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P <- X-Z_nonrandom
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P[A] <- 0
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Y0 <- Y
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Y <- Z_nonrandom + delta*P
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vec[i] <- sum(sum((Y-Y0)^2))
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err[i] <- sum(sum((X0-Z_nonrandom)^2))/sum(sum((X0)^2))
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}
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plot(vec,type="l")
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plot(err,type="l")
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Ar <- as.vector(A)
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Xr <- as.vector(original)
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Xr_nonrandom <- Xr[Ar]
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Zr <- as.vector(Z_nonrandom)
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Zr_nonrandom <- Zr[Ar]
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#dev.off()
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par(mfrow=c(1,2))
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plot(Xr_nonrandom,type="l")
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lines(Zr_nonrandom, col="red",lty=2)
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plot(Xr_nonrandom-Zr_nonrandom,type="l")
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#dev.off()
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par(mfrow=c(1,2))
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imagesc(Z_nonrandom, main ="M")
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imagesc(original, main ="M0")
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```
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```{r randommiss data}
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n1 <- 100
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n2 <- 100
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A <- as.matrix(random_miss)
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r <- 2
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decomp <- svd(A)
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U <- decomp$u
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s <- decomp$d
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V <- decomp$v
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s[(r+1): length(s)] <- 0
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S <-diag(s)
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#svd decomp
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X <- U %*% S %*% t(V)
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X0 <- X
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missing_observations <-which(A==0)
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A <- ifelse(A == 0, TRUE, FALSE)
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X[A]<-0
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m <- sum(sum(A==0))
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# Initialization
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Y <- matrix(0,n1,n2)
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delta <- (n1*n2)/m
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lambda <- 5
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tau <- delta*lambda
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# Iterations
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vec <- rep(0,500)
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err <- rep(0,500)
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for (i in 1:500){
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decomp <- svd(Y)
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U <- decomp$u
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S <- decomp$d
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V <- decomp$v
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S_t <- S-tau
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S_t[S_t<0] <- 0
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Z_random <- U%*%diag(S_t)%*%t(V)
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P <- X-Z_random
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P[A] <- 0
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Y0 <- Y
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Y <- Z_random + delta*P
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vec[i] <- sum(sum((Y-Y0)^2))
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err[i] <- sum(sum((X0-Z_random)^2))/sum(sum((X0)^2))
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}
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plot(vec,type="l")
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plot(err,type="l")
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Ar <- as.vector(A)
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Xr <- as.vector(original)
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Xr_random <- Xr[Ar]
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Zr <- as.vector(Z_random)
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Zr_random <- Zr[Ar]
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#dev.off()
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par(mfrow=c(1,2))
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plot(Xr_random,type="l")
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lines(Zr_random, col="red",lty=2)
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plot(Xr_random-Zr_random,type="l")
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#dev.off()
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par(mfrow=c(1,2))
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imagesc(Z_random, main ="M")
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imagesc(original, main ="M0")
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```
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```{r original vs other images}
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par(mfrow=c(1,3))
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imagesc(Z_random, main ="Z_random")
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imagesc(Z_nonrandom, main ="Z_nonrandom")
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imagesc(original, main ="Original")
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summary(Zr_random)
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summary(Zr_nonrandom)
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``` |