JScience 📊✨

JScience is a JavaScript library designed to provide powerful yet simple tools for scientific computing. Whether you're a data scientist, engineer, or math enthusiast, JScience offers essential functionalities for statistical calculations, data normalization, categorical column encoding, and much more.

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⚠️ Numerical Precision Considerations

JavaScript natively uses the IEEE 754 standard for floating-point numbers, which can lead to small rounding errors in arithmetic operations.

To mitigate this in sensitive calculations (such as probability distributions and combinatorial operations), JScience internally uses the Decimal.js library, which offers arbitrary-precision decimal arithmetic.

However, it's important to be aware that:

• Converting to and from JavaScript's standard Number type when interacting with the library or other parts of your code can introduce precision limitations.
• Operations performed outside of JScience functions that utilize Decimal.js will still be subject to IEEE 754 behavior.

Caution is advised when working with data requiring very high precision, especially when converting between numeric types. For more details on JavaScript's native standard, refer to IEEE 754.

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🚀 Key Features

• Statistics: Calculate mean, standard deviation, correlation, and more.
• Distributions: Binomial and Poisson probabilities.
• Normalization: Techniques like min-max and z-score.
• Data Encoding: One-hot encoding and label encoding.
• Factorial and Combinatorics: Calculate factorials and binomial coefficients.

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🧮 Mathematical Concepts

Pearson Correlation

Pearson correlation measures the linear relationship between two variables. The formula is:

$$ r = \frac{\Sigma((xᵢ - \bar{x})(yᵢ - \bar{y}))}{\sqrt{\Sigma(xᵢ - \bar{x})² \cdot \Sigma(yᵢ - \bar{y})²}} $$

Wheter r is close to 1, it indicates a strong positive linear relationship. If r is close to -1, it indicates a strong negative linear relationship.

Where:

• xᵢ and yᵢ: Data points.
• $\bar{x}$ and $\bar{y}$: Mean of x and y.

Min-Max Normalization

Min-max normalization scales the values of a dataset to the range [0, 1]:

$$ x' = \frac{x - \min(x)}{\max(x) - \min(x)} $$

Where:

• x: Original value.
• x': Normalized value.
• min(x): Minimum value in the dataset.
• max(x): Maximum value in the dataset.

Z-Score

The z-score measures how many standard deviations a value is from the mean:

$$ z = \frac{x - \mu}{\sigma} $$

Where:

• x: Original value.
• μ: Mean of the dataset.
• σ: Standard deviation of the dataset.

Binomial Probability

Binomial probability calculates the chance of k successes in n trials given a probability p:

$$ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} $$

Where:

• n: Number of trials.
• k: Number of successes.
• p: Probability of success on each trial.
• $\binom{n}{k}$: Binomial coefficient.

Poisson Probability

The Poisson distribution estimates the probability of k events in a fixed interval of time given a mean λ:

$$ P(X = k) = \frac{e^{-λ} \cdot λ^k}{k!} $$

Where:

• λ: Mean number of events.
• k: Number of events.
• e: Euler's number.
• k!: Factorial of k.

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📦 Installation

Install the library via npm:

npm install jscience

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🛠️ Getting Started

Import the functions you want to use:

import { mean, std, corr, minMax } from 'jscience';

const data = [1, 2, 3, 4, 5];
console.log(mean(data)); // Mean
console.log(std(data)); // Standard deviation

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📚 Usage Examples

1. Pearson Correlation

import { corr } from 'jscience';

const x = [1, 2, 3, 4];
const y = [2, 4, 6, 8];
console.log(corr(x, y)); // 1 (perfect linear relationship)

2. Min-Max Normalization

import { minMax } from 'jscience';

const data = [10, 20, 30];
console.log(minMax(data)); // [0, 0.5, 1]

3. Binomial Probability

import { binomial } from 'jscience';

console.log(binomial(10, 3, 0.5)); // Probability of 3 successes in 10 trials with p = 0.5

4. Poisson Probability

import { poisson } from 'jscience';

console.log(poisson(2, 3)); // Probability of 3 events with a mean of 2

5. One-Hot Encoding

import { oneHotEncoding } from 'jscience';

const data = [{ color: 'red' }, { color: 'blue' }, { color: 'red' }];
const { rows, columns } = oneHotEncoding(data, ['color']);
console.log(rows); // [{ color_red: 1, color_blue: 0 }, ...]

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📖 Full Documentation

Statistics

• mean(x: number[]): number: Calculates the mean.
• std(x: number[]): number: Calculates the standard deviation.
• corr(x: number[], y: number[]): number: Calculates the Pearson correlation.

Normalization

• minMax(x: number[]): number[]: Normalizes data to the range [0, 1].
• standardize(x: number[]): number[]: Normalizes data using z-score.

Distributions

• binomial(n: number, k: number, p: number): number: Calculates binomial probability.
• poisson(lambda: number, k: number): number: Calculates Poisson probability.

Data Encoding

• oneHotEncoding(rows: any[], columns: string[]): { rows: any[], columns: string[] }: Encodes categorical columns using one-hot encoding.
• labelEncoding(rows: any[], columns: string[]): { rows: any[], mappings: Record<string, Record<any, number>> }: Encodes categorical columns using label encoding.

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🧑‍💻 Contributing

Contributions are welcome! Follow the steps below to contribute:

1. Fork the repository.
2. Create a branch for your feature: git checkout -b my-feature.
3. Commit your changes: git commit -m 'My new feature'.
4. Push to the remote repository: git push origin my-feature.
5. Open a Pull Request.

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📜 License

This project is licensed under the MIT License. See the LICENSE file for more details.

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🌟 Acknowledgments

Thank you for using JScience! If you enjoyed it, don't forget to give the repository a ⭐. 😊