To normalize a list of numbers in Elixir, you can calculate the min and max values of the list using the Enum.min and Enum.max functions. Then, for each number in the list, you can normalize it by subtracting the min value and dividing by the range (max - min). This will scale the numbers to a range between 0 and 1. Here is a simple example of how you can normalize a list of numbers in Elixir:

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def normalize_list(numbers) do min = Enum.min(numbers) max = Enum.max(numbers) Enum.map(numbers, fn num -> (num - min) / (max - min) end) end numbers = [1, 2, 3, 4, 5] normalized_numbers = normalize_list(numbers) IO.inspect(normalized_numbers) |

In this example, the `normalize_list`

function takes a list of numbers as input and returns a new list of normalized numbers. You can then call this function with any list of numbers to obtain the normalized values.

## How to implement z-score normalization in Elixir?

Z-score normalization involves standardizing the values of a dataset to have a mean of 0 and a standard deviation of 1.

Here's an implementation of z-score normalization in Elixir:

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defmodule ZScoreNormalization do def normalize(data) do mean = Enum.mean(data) std_dev = :math.sqrt(Enum.reduce(data, 0, fn x, acc -> acc + (x - mean)^2 end) / (length(data) - 1)) normalized_data = data |> Enum.map(fn x -> (x - mean) / std_dev end) normalized_data end end data = [1, 2, 3, 4, 5] normalized_data = ZScoreNormalization.normalize(data) IO.inspect(normalized_data) |

In this implementation, the `normalize/1`

function takes a list of numerical values as input and calculates the mean and standard deviation of the data. It then standardizes each value in the dataset using the z-score formula `(x - mean) / std_dev`

. The normalized dataset is returned as the output.

You can test this implementation by providing a list of numerical values to the `normalize`

function and inspecting the output.

## How to normalize a list of numbers in Elixir using a sliding window approach?

To normalize a list of numbers in Elixir using a sliding window approach, you can follow these steps:

- Define a function that takes a list of numbers and a window size as parameters.
- Iterate through the list of numbers using Enum.chunk_every/2 to create overlapping sublists based on the window size.
- For each sublist, calculate the mean value of the numbers in the sublist.
- Subtract the mean value from each number in the sublist to normalize the values.
- Flatten the normalized sublists into a single list and return the normalized list.

Here is an example implementation of this approach:

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defmodule Normalizer do def normalize(numbers, window_size) do normalized_numbers = Enum.chunk_every(numbers, window_size, window_size - 1, :discard) |> Enum.map(&normalize_sublist(&1)) List.flatten(normalized_numbers) end defp normalize_sublist(sublist) do mean_value = sublist |> Enum.mean() Enum.map(sublist, fn num -> num - mean_value end) end end numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] window_size = 3 normalized_numbers = Normalizer.normalize(numbers, window_size) IO.inspect(normalized_numbers) |

In the example above, the normalize/2 function takes a list of numbers and a window size as input. It uses Enum.chunk_every/2 to create overlapping sublists based on the window size. The normalize_sublist/1 function calculates the mean value of the numbers in each sublist and then normalizes the values by subtracting the mean value from each number. Finally, the normalized sublists are flattened into a single list and returned as the result.

You can adjust the window size parameter and the input list of numbers to test different scenarios and see how the normalization works using the sliding window approach in Elixir.

## How to parallelize the normalization process in Elixir?

To parallelize the normalization process in Elixir, you can leverage the `Task`

module in the Erlang standard library. Here is a general guideline on how to implement parallelization:

**Partition the dataset**: Divide the dataset into smaller chunks to be processed in parallel. Each chunk will be handled by a separate process.**Create tasks**: Create a Task for each chunk of data to be normalized. Each task will be responsible for normalizing its respective chunk.**Start tasks in parallel**: Spawn all tasks concurrently using the Task.async function. This will start the normalization process for each chunk in parallel.**Collect results**: Once all tasks are started, use the Task.await function to collect the normalized results from each task. You can combine the results into a single data structure or process them further as needed.

Here is a simple example demonstrating how to parallelize the normalization process in Elixir:

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# Assume `data` is the dataset to be normalized, and `normalize_chunk/1` is the normalization function data = [...] chunk_size = 100 chunks = Enum.chunk_every(data, chunk_size) tasks = Enum.map(chunks, fn chunk -> Task.async(fn -> normalize_chunk(chunk) end) end) results = Enum.map(tasks, fn task -> Task.await(task) end) # Combine or process the normalized results further |

Keep in mind that the number of tasks created should not exceed the available resources (e.g., CPU cores) to avoid resource contention and inefficient parallelization. Additionally, make sure to handle errors and exceptions that may occur during the normalization process in each task.

## How to apply min-max normalization to a list of numbers in Elixir?

To apply min-max normalization to a list of numbers in Elixir, you can follow these steps:

- Define a function that calculates the minimum and maximum values in the list:

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def min_max(list) do {min, max} = Enum.reduce(list, {hd(list), hd(list)}, fn x, {min_val, max_val} -> {min(min_val, x), max(max_val, x)} end) {min, max} end |

- Define a function that applies min-max normalization to the list using the min and max values:

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def min_max_normalize(list) do {min, max} = min_max(list) Enum.map(list, fn x -> (x - min) / (max - min) end) end |

- Call the min_max_normalize function with your list of numbers to apply min-max normalization:

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list = [10, 20, 30, 40, 50] normalized_list = min_max_normalize(list) IO.inspect(normalized_list) |

This will normalize the values in the list between 0 and 1 based on the minimum and maximum values in the list.