Lab 3: Started with assignment 2 & 3

lab3/Lab3Block1_2021_SVMs_St.R

@@ -54,16 +54,29 @@ err3
 
 # 3. Implementation of SVM predictions.
 
+gaussian_kernel <- function(x_i, x_star, sigma) {
+  return(exp(-sum((x_i - x_star)^2) / (2 * sigma^2)))
+}
+
 sv<-alphaindex(filter3)[[1]]
 co<-coef(filter3)[[1]]
 inte<- - b(filter3)
 k<-NULL
 for(i in 1:10){ # We produce predictions for just the first 10 points in the dataset.
-  k2<-NULL
+  k2<-0
+  test_point <- spam[i, -58]
   for(j in 1:length(sv)){
-    k2<- # Your code here
+    
+    support_vector <- spam[sv[j], -58]
+    
+    kernel_value <- gaussian_kernel(support_vector, test_point, sigma = 0.05) 
+
+    k2 <- k2 + co[j] * kernel_value
+    
   }
-  k<-c(k, # Your code here)
+  k2 <- k2 + inte
+  k <- c(k, sign(k2))
+  
 }
 k
-predict(filter3,spam[1:10,-58], type = "decision")
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+predict(filter3,spam[1:10,-58], type = "decision")

lab3/assignment2.R

+set.seed(1234567890)
+
+library(geosphere)
+
+stations <- read.csv("stations.csv", fileEncoding = "latin1")
+temps <- read.csv("temps50k.csv")
+
+st <- merge(stations, temps, by = "station_number")
+
+h_distance <- 100000
+h_date <- 15
+h_time <- 4
+
+a <- 58.4274
+b <- 14.826
+date <- "1960-07-11"
+times <- c(
+  "04:00:00",
+  "06:00:00",
+  "08:00:00",
+  "10:00:00",
+  "12:00:00",
+  "14:00:00",
+  "16:00:00",
+  "18:00:00",
+  "20:00:00",
+  "22:00:00",
+  "24:00:00"
+)
+
+
+st <- st[st$date <= date, ] # Filter out posterior dates
+st$time <- strptime(st$time, format = "%H:%M:%S")
+
+dist = seq(0, 300000)
+plot(exp(-abs(dist) ^ 2 / (2 * h_distance ^ 2)),
+     type = 'l',
+     xlab = "Physical distance",
+     ylab = "Kernel")
+
+#choosing appropriate smoothing coefficient for days
+dist = seq(0, 100)
+plot(exp(-abs(dist) ^ 2 / (2 * h_date ^ 2)),
+     type = 'l',
+     xlab = "Distance in days",
+     ylab = "Kernel")
+
+#choosing appropriate smoothing coefficient for hours
+dist = seq(0, 18)
+plot(exp(-abs(dist) ^ 2 / (2 * h_time ^ 2)),
+     type = 'l',
+     xlab = "Distance in hours",
+     ylab = "Kernel")
+
+temp_add <- c()
+temp_mult <- c()
+
+for (time in times) {
+  time <- strptime(time, format = "%H:%M:%S")
+  
+  
+  st_temp <- st[st$date < date |
+                  (st$date == date &
+                     st$time <= time), ]
+  
+  
+  distance_kernels <- mapply(function(lat, lon) {
+    dist <- distHaversine(c(a, b), c(lat, lon))
+    exp(-abs(dist) ^ 2 / (2 * h_distance ^ 2))
+  }, st_temp$latitude, st$longitude)
+  
+  
+  
+  date_kernels <- st_temp$date
+  date_kernels <- sapply(date_kernels, function(x_i) {
+    dist <- as.numeric(as.Date(date) - as.Date(x_i))
+    exp(-abs(dist) ^ 2 / (2 * h_date ^ 2))
+  })
+  
+  
+  time_kernels <- st_temp$time
+  time_kernels <- sapply(time_kernels, function(x_i) {
+    dist <- as.numeric(difftime(time, x_i, units = "hours"))
+    exp(-abs(dist) ^ 2 / (2 * h_time ^ 2))
+  })
+  
+  
+  
+  
+  
+  kernels_add <- distance_kernels + date_kernels + time_kernels
+  kernels_mult <- distance_kernels * date_kernels * time_kernels
+  
+  temp_add <<- c(temp_add,
+                 sum(kernels_add * st_temp$air_temperature) / sum(kernels_add))
+  temp_mult <<- c(temp_mult,
+                   sum(kernels_mult * st_temp$air_temperature) / sum(kernels_mult))
+  
+  
+}
+
+plot(temp_add, type = "o")
+plot(temp_mult, type = "o")
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