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SVMIntuitionPlotter.R
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SVMIntuitionPlotter.R
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#
# This is a Shiny web application to play around with the logic behind Support Vector Machines.
#
#
library(plotly)
library(purrr)
library(shiny)
library(matlib)
library(SVMMaj)
# Define UI for the application
ui <- fluidPage(
titlePanel("SVM intuition plotter"),
fluidRow(
column(8, plotlyOutput("p")),
column(4, textOutput("curr_loss"))
),
br(),
br(),
fluidRow(
column(2, numericInput("marg", "Margin:", 0.1, min = 0.1, max = 10, step = 0.1)),
column(2, numericInput("intercept", "Intercept:", 0, min = -10, max = 10, step = 0.1)),
column(2, numericInput("lambda", "Lambda:", 1, min = 0, max = 1000)),
column(3, actionButton("showproj", "Show/Hide projected points")),
column(3, actionButton("showsol", "Show/Hide optimal solution")),
#,column(2, numericInput("angle", "Angle:", 1, min = 0, max = 1000))
br()
),
fluidRow(
column(2, actionButton("genpoints", "Generate new sample"))
),
br(),
fluidRow(
column(6, HTML(
paste(
h3("Instructions:"),#'<br/>',
h4(tags$b("KNOWN BUG:"), "To make sure everything updates correctly, move the blue dot first."),
h4("Use the mouse to move the blue dot to change the orientation of the axes."),
h4("You can set the lambda, margin and intercept using the input boxes. You can toggle the
optimal solution for this lambda as found by", tags$a(href = 'https://cran.rstudio.com/web/packages/SVMMaj/index.html', 'SVMMaj')," package."),
h4(tags$b("Disclaimer:"), " This was made as a quick proof of concept/experiment and to explore Shiny and plotly. Suggestions and bug reports welcome! ")
)
)
),
column(6, verbatimTextOutput("curr_loss2"))
)
)
# Calculate loss function
loss <- function(xy, type, wx, wy, c_intercept, lambda=1){
sum(pmax(0, (abs(type) - sign(type) * (c_intercept + xy$x * wx + xy$y * wy )))) + lambda * (wx^2 + wy^2)
}
# Generate a new sample of points
generate_points <- function(n=20, meanx=c(-2, 2), meany=c(-1, 1)){
list(x = c(rnorm(n, mean = meanx[1]), rnorm(n, mean = meanx[2])),
y = c(rnorm(n, mean = meany[1]), rnorm(20, mean = meany[2])),
type = c(rep(-1, n), rep(1, n)),
type_color = c(rep(I('red'), n), rep(I('green'), n)))
}
# Project points on axes w1 and w2
proj_points <- function(x, y, w1, w2){
print(w1)
print(w2)
map2_dfr(c(x = x), c(y = y), function(x, y, ...){
output <- Proj(c(x, y), ...);
list(x = output[1], y = output[2])},
X = c(w1, w2))
}
# Calculate new coords for axes
set_axes <- function(new_pos, w, marg, intercept){
ang <- angle(c(0, 1), c(new_pos), degree = FALSE)
ang <- ifelse(new_pos[1] > 0 , ang, -ang)
w$y1 <- c( 2 * sin(ang), -2 * sin(ang)) + intercept * cos(ang)
w$x1 <- c(-2 * cos(ang), 2 * cos(ang)) + intercept * sin(ang)
w$y2 <- c(-2 * cos(ang), 2 * cos(ang))
w$x2 <- c(-2 * sin(ang), 2 * sin(ang))
w$ym1 <- w$y1 + (marg) * cos(ang)
w$ym2 <- w$y1 - (marg) * cos(ang)
w$xm1 <- w$x1 + (marg) * sin(ang)
w$xm2 <- w$x1 - (marg) * sin(ang)
w
}
server <- function(input, output, session) {
# It is necessary to initialise these values to setup projected points
points <- generate_points()
init_x <- points$x
init_y <- points$y
type <- points$type
type_color <- points$type_color
# The original points
xy <- reactiveValues(
x = init_x,
y = init_y
)
# Projected points
proj_xy <- reactiveValues(
x = rep(0, length(init_x)),
y = init_y,
color = type_color,
opacity = 0
)
cursor_coord <- reactiveValues(
x = 0,
y = 3
)
# Axes + margins for plotting
waxes <- reactiveValues(
x1 = c(-2, 2),
y1 = c(0, 0),
x2 = c(0, 0),
y2 = c(-2, 2),
xm1 = c(-2, 2),
ym1 = c(-0.1, -0.1),
xm2 = c(-2, 2),
ym2 = c(0.1, 0.1)
)
# Optimal solution for this lambda
solution <- svmmaj(cbind(init_x, init_y), type, lambda = 1, scale = "none")
# x and y for solution (not normalised)
new_pos <- SVMMaj:::beta.theta(solution$method, solution$theta)
# margin for solution
marg_opt <- sum(new_pos^2)/2
#initialise temp variable for use in reactiveValues
wtemp <- set_axes(new_pos, list(x1 = 0, x2 = 0, y1 = 0, y2 = 0,
xm1 = 0, xm2 = 0, ym1 = 0, ym2 = 0),
marg_opt, solution$theta[1])
# Axes + margins for the solution
wsols <- reactiveValues(
x1 = wtemp$x1,
y1 = wtemp$y1,
x2 = wtemp$x2,
y2 = wtemp$y2,
xm1 = wtemp$xm1,
ym1 = wtemp$ym1,
xm2 = wtemp$xm2,
ym2 = wtemp$ym2,
opacity = 0
)
# Render graph
output$p <- renderPlotly({
# shape for the cursor
cursor <- list(
type = "circle",
xanchor = cursor_coord$x,
yanchor = cursor_coord$y,
# diameter is 2 pixels
x0 = -4, x1 = 4,
y0 = -4, y1 = 4,
xsizemode = "pixel",
ysizemode = "pixel",
fillcolor = "blue",
line = list(color = "transparent")
)
# plot the poinst and lines
p <- plot_ly(type = 'scatter', mode = 'markers') %>%
# plot axes
add_lines(x = waxes$x1, y = waxes$y1, color = I("green"), mode = "lines") %>%
add_lines(x = waxes$x2, y = waxes$y2, color = I("black"), mode = "lines") %>%
# Plot margins
add_lines(x = waxes$xm1, y = waxes$ym1, color = I("gray"), mode = "lines") %>%
add_lines(x = waxes$xm2, y = waxes$ym2, color = I("gray"), mode = "lines") %>%
# Plot axes and margins of the optimal solution
#ldash <- list(dash = 'dash') # Gives error if used in lines below
add_lines(x = wsols$x1, y = wsols$y1, color = I("magenta"), opacity = wsols$opacity, mode = "lines", line = list(dash = 'dash')) %>%
add_lines(x = wsols$x2, y = wsols$y2, color = I("magenta"), opacity = wsols$opacity, mode = "lines", line = list(dash = 'dash')) %>%
add_lines(x = wsols$xm1, y = wsols$ym1, color = I("magenta"), opacity = wsols$opacity, mode = "lines", line = list(dash = 'dash')) %>%
add_lines(x = wsols$xm2, y = wsols$ym2, color = I("magenta"), opacity = wsols$opacity, mode = "lines", line = list(dash = 'dash')) %>%
# Plot the original points
add_trace(x = xy$x, y = xy$y, mode = "markers", marker = list(color = type_color)) %>%
# Plot the points projected on the axes
add_trace(x = proj_xy$x, y = proj_xy$y, mode = 'markers',
marker = list(
color = 'rgba(135, 206, 250, 0)', # Set fill transparent
opacity = proj_xy$opacity,
size = 5,
line = list(
color = type_color,
width = 1
)
)
) %>%
# Plot cursor as shape
layout(shapes = cursor,
xaxis = list(
fixedrange = TRUE, # Needed to prevent zooming
#range = c(-4, 4),
scaleanchor = 'y', # Equal aspect ratio
scaleratio = 1,
constrain = "domain" ),
yaxis = list(
range = c(-4, 4),
fixedrange = TRUE
),
showlegend = FALSE,
autosize = F
) %>%
config(edits = list(shapePosition = TRUE), # No way to disable resize on shapes
displayModeBar = FALSE,
scrollZoom = FALSE
)
})
output$curr_loss <- renderPrint({
cat("Current loss: ", 0)
})
output$curr_loss2 <- renderPrint({
cat("Click Show solution to show the parameters of \n the optimal solution in this window")
})
output$opt_loss <- renderPrint({
cat("Optimal (solution) loss: ", 0)
})
# Switch opacity of solution
observeEvent(input$showsol, {
wsols$opacity = (wsols$opacity + 1) %% 2
})
# Switch opacity of projected points
observeEvent(input$showproj, {
proj_xy$opacity = (proj_xy$opacity + 1) %% 2
})
# Generate new points
observeEvent(input$genpoints, {
points <- generate_points()
xy$x <- points$x
xy$y <- points$y
})
# update all reactive values when cursor is moved
observe({
ed <- event_data("plotly_relayout")
shape_anchors <- ed[grepl("^shapes.*anchor$", names(ed))]
if (length(shape_anchors) != 2) return()
new_pos <- c(shape_anchors[[1]], shape_anchors[[2]])
# Calculate angle from y axis
ang <- angle(c(0, 1), c(new_pos), degree = FALSE)
ang <- ifelse(new_pos[1] > 0 , ang, -ang)
# Sanity check marg
curr_marg <- input$marg
if (is.na(curr_marg) | curr_marg == 0) {
curr_marg <- 0.0001
}
new_pos <- curr_marg * new_pos
cursor_coord$x <- 1.75 * new_pos[1]
cursor_coord$y <- 1.75 * new_pos[2]
set_axes(new_pos, waxes, curr_marg, input$intercept)
# Calculate and set projected points
proj_ax <- proj_points(xy$x, xy$y, waxes$x2[2], waxes$y2[2])
proj_xy$y <- proj_ax$y
proj_xy$x <- proj_ax$x
# Sanity check lambda
curr_lambda <- input$lambda
if (is.na(curr_lambda)) {
curr_lambda <- 0
}
closs <- loss(xy, type, new_pos[1], new_pos[2], input$intercept, lambda = curr_lambda)
output$curr_loss <- renderText(paste("Current loss:", round(closs, digits = 4)))
if (wsols$opacity > 0) {
output$curr_loss2 <- renderText(paste("Optimal model:\n",
"\nLoss:",round(solution$loss, digits = 4),
"\nx,y:", round(new_pos[1], digits = 4), round(new_pos[2], digits = 4),
"\nmargins:", round(marg_opt, digits = 4),
"\nintercept:", round(solution$theta[1], digits = 4) )
)
} else {
output$curr_loss2 <- renderText(paste("Click Show solution to show the parameters of \n the optimal solution in this window"))
}
solution <- svmmaj(cbind(xy$x, xy$y), type, lambda = curr_lambda, scale = "none")
new_pos <- SVMMaj:::beta.theta(solution$method, solution$theta)
marg_opt <- sum(new_pos^2)/2
# Change solution axes
wsols <- set_axes(new_pos, wsols, marg_opt, solution$theta[1])
})
}
# Run the application
shinyApp(ui = ui, server = server)