# Chapter 5
```elixir
Mix.install([
{:nx, "~> 0.6.4"},
{:vega_lite, "~> 0.1.8"},
{:kino_vega_lite, "~> 0.1.11"}
])
alias VegaLite, as: Vl
```
## Data
```elixir
data =
(__DIR__ <> "/data/police.txt")
|> Path.expand()
|> File.read!()
|> String.split()
|> Enum.drop(4)
|> Enum.map(&String.to_integer/1)
|> Enum.chunk_every(4)
|> Nx.tensor()
```
```elixir
{reservations, police} = {data[[.., 0]], data[[.., -1]]}
```
```elixir
plot =
Vl.new(width: 600, height: 600)
|> Vl.data_from_values(%{
"Reservations" => Nx.to_list(reservations),
"Police Call" => Nx.to_list(police)
})
|> Vl.mark(:point)
|> Vl.encode_field(:x, "Reservations", type: :quantitative)
|> Vl.encode_field(:y, "Police Call", type: :quantitative)
```
## Sigmoid
```elixir
defmodule Classifier do
import Nx.Defn
defn sigmoid(z) do
1 / (1 + Nx.exp(-z))
end
defn forward(x, w) do
Nx.dot(x, w)
|> sigmoid()
end
defn classify(x, w) do
forward(x, w)
|> Nx.round()
end
defn loss(x, y, w) do
y_hat = forward(x, w)
first_term = y * Nx.log(y_hat)
second_term = (1 - y) * Nx.log(1 - y_hat)
-Nx.mean(first_term + second_term)
end
defn gradient(x, y, w) do
(forward(x, w) - y)
|> Nx.dot(x)
|> Nx.divide(Nx.axis_size(x, 0))
end
def train(x, y, iterations, lr) do
Enum.reduce(1..iterations, Nx.broadcast(0.0, {Nx.axis_size(x, 1)}), fn i, w ->
IO.puts("Iteration #{i}, loss #{Nx.to_number(loss(x, y, w))}")
Nx.subtract(w, Nx.multiply(gradient(x, y, w), lr))
end)
end
def test(x, y, w) do
Nx.equal(classify(x, w), y)
|> then(&[correct: Nx.sum(&1), total: Nx.size(&1), accuracy: Nx.mean(&1)])
|> Enum.map(fn {k, v} -> {k, Nx.to_number(v)} end)
end
end
```
```elixir
x = Nx.pad(data[[.., 0..2]], 1, [{0, 0, 0}, {1, 0, 0}])
y = data[[.., 3]]
w = Classifier.train(x, y, 10000, 0.001)
```
```elixir
Classifier.test(x, y, w)
```
```elixir
classifications = Classifier.classify(x, w)
Vl.new()
|> Vl.layers([
plot,
Vl.new()
|> Vl.data_from_values(%{
"Reservations" => Nx.to_list(reservations),
"Police Call" => Nx.to_list(classifications)
})
|> Vl.mark(:tick)
|> Vl.encode_field(:x, "Reservations", type: :quantitative)
|> Vl.encode_field(:y, "Police Call", type: :quantitative)
])
```
