From 5bdab9b8ab39093fc4fa263001487caa192c9f7c Mon Sep 17 00:00:00 2001 From: Yandrik Date: Mon, 20 May 2024 16:14:55 +0200 Subject: [PATCH] feat: w3 done --- .gitignore | 1 + w3/README.rmd | 432 +++++++++++++++++++++++++++ w3/data1.txt | 200 +++++++++++++ w3/ea-plot_static-delta.pdf | Bin 0 -> 19409 bytes w3/ea-plot_static-delta_all.pdf | Bin 0 -> 19409 bytes w3/ea-plot_static-delta_one.pdf | Bin 0 -> 17801 bytes w3/ea-plot_static-gaussian_all.pdf | Bin 0 -> 19755 bytes w3/ea-plot_static-gaussian_one.pdf | Bin 0 -> 20129 bytes w3/evoalgs-w3.zip | Bin 0 -> 130435 bytes w3/perceptron-plot.pdf | Bin 0 -> 17368 bytes w3/perceptron-plot_3-adjustments.pdf | Bin 0 -> 18708 bytes w3/w3.Rproj | 13 + 12 files changed, 646 insertions(+) create mode 100644 w3/README.rmd create mode 100644 w3/data1.txt create mode 100644 w3/ea-plot_static-delta.pdf create mode 100644 w3/ea-plot_static-delta_all.pdf create mode 100644 w3/ea-plot_static-delta_one.pdf create mode 100644 w3/ea-plot_static-gaussian_all.pdf create mode 100644 w3/ea-plot_static-gaussian_one.pdf create mode 100644 w3/evoalgs-w3.zip create mode 100644 w3/perceptron-plot.pdf create mode 100644 w3/perceptron-plot_3-adjustments.pdf create mode 100644 w3/w3.Rproj diff --git a/.gitignore b/.gitignore index f19329a..8074216 100644 --- a/.gitignore +++ b/.gitignore @@ -2,3 +2,4 @@ **/.Rhistory **/.RData **/.Ruserdata +.Rproj.user diff --git a/w3/README.rmd b/w3/README.rmd new file mode 100644 index 0000000..ade9d09 --- /dev/null +++ b/w3/README.rmd @@ -0,0 +1,432 @@ +# Übungsblatt 3 - Evolutionary Algorithms (Paul Helstab & Yannik Bretschneider) + +## Loading Data + +```{r setwd} +# Get the current working directory +current_directory <- getwd() + +# Define the folder name to check +folder_name <- "w3" + +# Construct the full path to the folder +folder_path <- file.path(current_directory, folder_name) + +# Check if the folder exists (means most likely in the repo root folder) +if (dir.exists(folder_path)) { + setwd(folder_path) + cat("Changed working directory to:", getwd(), "\n") +} else { + cat("Folder 'w3' does not exist in the current working directory. +Staying where we are\n") +} +``` + + +```{r read_data} +file_path <- "./data1.txt" + +print(paste0("read data from '", file_path, "'")) +data <- read.table( + file_path, + header = FALSE, + sep = " ", + # colClasses = c("numeric", "numeric", "integer", "integer") +) +colnames(data) <- c("x1", "x2", "x_bias", "label") + + +evaluation_set_idx <- c(90:109) +``` + +```r +# possible, but unnecessary here: +# grab first 10 as evaluation set +evaluation_set <- data[evaluation_set_idx, ] + +# grab the rest as training set +training_set <- data[-evaluation_set_idx, ] +``` + +## Aufgabe 1: Perzeptron + +```{r peceptron-impl} +# randomized order +random_order <- sample(nrow(data)) +vecs <- data[random_order, 1:3] +classes <- data[random_order, 4] + +weights <- c(0, 0, 0) + +# matrix for logging weights +wlog <- matrix(weights, ncol = 3) + +infer <- function(x, wghts) { + return(sign(x %*% wghts)) +} + +perceptron_infer <- function(x) { + return(infer(x, weights)) +} + +while (TRUE) { + mispredictions <- 0 + for (i in seq_len(nrow(vecs))) { + vec <- as.numeric(vecs[i, ]) + class <- classes[i] + + # print(vec %*% weights) + + error <- as.numeric(class - perceptron_infer(vec)) + if (error != 0) { + mispredictions <- mispredictions + 1 + + print("adjusting") + weights <- weights + error * vec + wlog <- rbind(wlog, weights) + } + } + + + if (mispredictions == 0) { + print("No more mispredictions") + break + } else { + print(paste0("Misclassifications: ", mispredictions)) + } +} + +print("NOTE: for more interesting plots, run this chunk multiple times until multiple \"adjusting\" can be seen in the output") +``` + +```{r apply-to-data} +perceptron_reinfer <- t(sapply(seq_len(nrow(data)), function(i) { + return(c(as.numeric(data[i, 1:3]), perceptron_infer((as.numeric(data[i, 1:3]))))) +})) + +# perceptron_reinfer +``` + + +### Plots + +The plots show the datapoints on a 2D plot, with the colors showing the classes (`green := 1` and `red := -1`) +The separation plane defined by the normal of the weight vector is shown in increasing opacities, until the final +weights are reached. + +```{r plot-weights} +perceptron_plot <- function() { + plot(data$x1, data$x2, + col = ifelse(data$label == 1, "green", "red"), + pch = 16, xlab = "x1", ylab = "x2", xlim = c(-5, 5), ylim = c(-5, 5) + ) + + legend("topright", + legend = c("Class 1", "Class -1"), + col = c("green", "red"), pch = 16 + ) + + # Plot the separation planes + num_steps <- nrow(wlog) + alpha_step <- 1 / num_steps + + for (i in 1:num_steps) { + a <- wlog[i, 1] + b <- wlog[i, 2] + c <- wlog[i, 3] + + # Calculate the line coordinates + x <- seq(-5, 5, length.out = 100) + y <- -(a * x + c) / b + + # Determine the line color based on the iteration + alpha <- i * alpha_step + line_color <- rgb(0, 0, 1, alpha) + + # Plot the line + lines(x, y, col = line_color) + } + + # Plot the final separation plane + a <- weights[1] + b <- weights[2] + c <- weights[3] + + x <- seq(-5, 5, length.out = 100) + y <- -(a * x + c) / b + + lines(x, y, col = "blue", lwd = 2) +} + +perceptron_plot() +``` + +```{r plot-weights-pdf} +pdf("perceptron-plot.pdf", width = 8, height = 6) +perceptron_plot() +dev.off() +``` + + + +## Aufgabe 2: Perzeptron Evolutionary Algorithm (EA) + + +```{r peceptron-ea-impl} +# randomized order +ea_random_order <- sample(nrow(data)) +ea_vecs <- data[ea_random_order, 1:3] +ea_classes <- data[ea_random_order, 4] + +NUM_INDIVIDUALS <- 3 +MUTATE_ALL_GENES <- FALSE +MUTATE_STEP <- function() { + return(0.5) +} + +# MUTATE_STEP <- function() { +# return(runif(1, min = -1, max = 1)[1]) +# } + +weights <- matrix(0, ncol = 3, nrow = NUM_INDIVIDUALS) + +# matrix for logging weights +ea_wlog <- matrix(0, ncol = 3) + +fittest <- c(0, 0, 0) + + +mutate <- function(genes, step_size_fn, mutate_all) { + if (mutate_all == TRUE) { + for (i in seq_along(genes)) { + step <- step_size_fn() * sample(c(1, -1), size = 1)[1] # mutation in step_size, -step_size or not at all + genes[i] <- genes[i] + step + } + } else { + idx_to_mutate <- sample(seq_along(genes), size = 1)[1] + genes[idx_to_mutate] <- genes[idx_to_mutate] + step_size_fn() * sample(c(1, -1), size = 1)[1] # mutation in step_size or not AT all + } + + return(genes) +} + +infer <- function(x, wghts) { + return(sign(x %*% wghts)) +} + +fitness <- function(wghts) { + mispredictions <- 0 + + + for (i in seq_len(nrow(ea_vecs))) { + vec <- as.numeric(ea_vecs[i, ]) + class <- ea_classes[i] + + # print(vec %*% weights) + + error <- as.numeric(class - infer(vec, wghts)) + if (error != 0) { + mispredictions <- mispredictions + 1 + } + } + + return(mispredictions) +} + +while (TRUE) { + i_fittest <- weights[1, ] + i_fit <- fitness(weights[1, ]) + + for (individual in 2:NUM_INDIVIDUALS) { + this_fitness <- fitness(weights[individual, ]) + if (this_fitness < i_fit) { + i_fittest <- weights[individual, ] + i_fit <- this_fitness + } + } + + # add fittest to weights + ea_wlog <- rbind(ea_wlog, i_fittest) + + if (i_fit == 0) { + print("No more mispredictions") + fittest <- i_fittest + break + } else { + print(paste0("Misclassifications: ", i_fit)) + + for (individual in 1:NUM_INDIVIDUALS) { + weights[individual, ] <- mutate(i_fittest, step_size_fn = MUTATE_STEP, mutate_all = MUTATE_ALL_GENES) + } + } +} +``` + + +```{r ea-apply-to-data} +ea_reinfer <- t(sapply(seq_len(nrow(data)), function(i) { + return(c(as.numeric(data[i, 1:3]), infer((as.numeric(data[i, 1:3])), fittest))) +})) + +# ea_reinfer +``` + +### Plots + +The plots show the datapoints on a 2D plot, with the colors showing the classes (`green := 1` and `red := -1`) +The separation plane defined by the normal of the weight vector is shown in increasing opacities, until the final +weights are reached. + +```{r ea-plot-weights} +ea_plot <- function() { + plot(data$x1, data$x2, + col = ifelse(data$label == 1, "green", "red"), + pch = 16, xlab = "x1", ylab = "x2", xlim = c(-5, 5), ylim = c(-5, 5) + ) + + legend("topright", + legend = c("Class 1", "Class -1"), + col = c("green", "red"), pch = 16 + ) + + # Plot the separation planes + num_steps <- nrow(ea_wlog) + alpha_step <- 1 / num_steps + + for (i in 1:num_steps) { + a <- ea_wlog[i, 1] + b <- ea_wlog[i, 2] + c <- ea_wlog[i, 3] + + # Calculate the line coordinates + x <- seq(-5, 5, length.out = 100) + y <- -(a * x + c) / b + + # Determine the line color based on the iteration + alpha <- i * alpha_step + line_color <- rgb(0, 0, 1, alpha) + + # Plot the line + lines(x, y, col = line_color) + } + + # Plot the final separation plane + a <- fittest[1] + b <- fittest[2] + c <- fittest[3] + + x <- seq(-5, 5, length.out = 100) + y <- -(a * x + c) / b + + lines(x, y, col = "blue", lwd = 2) +} + +ea_plot() +``` + + +```{r plot-weights-pdf} +pdf("ea-plot_static-delta_one.pdf", width = 8, height = 6) +ea_plot() +dev.off() +``` + +### Evaluation + +Gaussian (Mutate All) with a high number of individuals generally acheives a correct result first-try. In our very constrained individuum pool tests with 3 individuals, this also seems to be the best choice for parameters for the EA. Its efficacy seems to increase even more with a larger gene pool. + + +## Aufgabe 3: Exploration vs Exploitation + +```{r setup} +# generate a random binary vector of length 10 +generate_individual <- function() { + sample(c(0, 1), 10, replace = TRUE) +} + +# 1-point crossover +one_point_crossover <- function(parent1, parent2) { + point <- sample(1:9, 1) + child1 <- c(parent1[1:point], parent2[(point + 1):10]) + child2 <- c(parent2[1:point], parent1[(point + 1):10]) + return(list(child1, child2)) +} + +# 2-point crossover +two_point_crossover <- function(parent1, parent2) { + points <- sort(sample(1:9, 2)) + child1 <- c(parent1[1:points[1]], parent2[(points[1] + 1):points[2]], parent1[(points[2] + 1):10]) + child2 <- c(parent2[1:points[1]], parent1[(points[1] + 1):points[2]], parent2[(points[2] + 1):10]) + return(list(child1, child2)) +} + +# uniform crossover +uniform_crossover <- function(parent1, parent2) { + mask <- sample(c(0, 1), 10, replace = TRUE) + child1 <- ifelse(mask == 1, parent1, parent2) + child2 <- ifelse(mask == 1, parent2, parent1) + return(list(child1, child2)) +} + +# Function to convert binary vector to decimal +binary_to_decimal <- function(binary_vector) { + sum(binary_vector * 2^(rev(seq_along(binary_vector) - 1))) +} +``` + + +```{r initialize_parents} +# init parents +parent1 <- generate_individual() +parent2 <- generate_individual() + +print(parent1) +print(parent2) + +# Set num gens +num_generations <- 10000 + +# for tracking unique solutions +unique_solutions <- list() +unique_solutions[[binary_to_decimal(parent1)]] <- TRUE +unique_solutions[[binary_to_decimal(parent2)]] <- TRUE +``` + + +```{r run_genetic_algorithm} +for (generation in 1:num_generations) { + # Choose crossover method + crossover_method <- sample(c("one_point", "two_point", "uniform"), 1) + + if (crossover_method == "one_point") { + children <- one_point_crossover(parent1, parent2) + } else if (crossover_method == "two_point") { + children <- two_point_crossover(parent1, parent2) + } else { + children <- uniform_crossover(parent1, parent2) + } + + + + # Replace + parent1 <- children[[1]] + parent2 <- children[[2]] + + # Track sols + unique_solutions[[binary_to_decimal(parent1)]] <- TRUE + unique_solutions[[binary_to_decimal(parent2)]] <- TRUE +} + +# Calculate number of unique solutions observed +num_unique_solutions <- length(unique_solutions) + +# Calculate number of possible solutions covered +num_possible_solutions <- 2^10 +num_solutions_covered <- length(unique_solutions) + +# Print results +cat("Number of unique solutions observed:", num_unique_solutions, "\n") +cat("Number of possible solutions covered:", num_solutions_covered, "\n") +cat("Percentage of 10-bit numbers covered:", round(num_solutions_covered / num_possible_solutions * 100, 2), "%\n") +``` + diff --git a/w3/data1.txt b/w3/data1.txt new file mode 100644 index 0000000..19eb036 --- /dev/null +++ b/w3/data1.txt @@ -0,0 +1,200 @@ +-1.32897014671217 -2.36785102664075 -1 1 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