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"Understanding scalars, the fundamental single-number quantities in linear algebra and machine learning." +tags: + [ + scalars, + linear-algebra, + mathematics-for-ml, + data-types, + magnitude, + foundation, + ] +--- + +Before diving into complex structures like vectors and matrices, we must start with the most fundamental concept in Linear Algebra: the **Scalar**. + +Understanding scalars is crucial because they are the building blocks of all mathematical objects used to represent data in Machine Learning. + +## 1. What is a Scalar? + +A **scalar** is simply a single numerical quantity. It is a value that has **magnitude** (size) but no **direction**. + +In the context of data science and machine learning, scalars are single numbers representing an attribute or a quantity. + +### Notation + +Scalars are typically denoted by standard, non-bold, lowercase letters (e.g., $a, x, y, \lambda$). They belong to a specific set of numbers, such as: + +* The set of **Real Numbers** ($\mathbb{R}$). +* The set of **Integers** ($\mathbb{Z}$). + + + + :::info + A scalar is an element of the number field used to define a vector space. For most of ML, this field is the set of **Real Numbers ($\mathbb{R}$)**. + ::: + + + * **Temperature:** $30^\circ C$ + * **Mass:** $5.5\text{ kg}$ + * **Speed:** $100\text{ km/h}$ + * **Time:** $2.5\text{ hours}$ + + + +## 2. Scalars in Machine Learning + +In Machine Learning, almost every single point of data is derived from an initial set of scalars. + +### A. Feature Values +In a dataset, individual feature values are scalars. + +| Feature Name | Example Value (Scalar) | Description | +| :--- | :--- | :--- | +| `House_Size` | $1500$ | The size of the house in square feet. | +| `Bedrooms` | $3$ | The number of bedrooms. | +| `Age` | $12$ | The age of the house in years. | + +### B. Parameters and Hyperparameters +Scalars are used to represent the learned parameters within an ML model and the manually set hyperparameters. + +* **Learning Rate ($\alpha$)**: A scalar value, typically small (e.g., $\alpha = 0.01$), that controls how much the model's parameters are adjusted during training. +* **Bias ($b$)**: A single, learned scalar value added to the output of a neuron. +* **Kernel Size ($k$)**: A scalar defining the size of the kernel in a Convolutional Neural Network (e.g., $k=3$ for a $3\times3$ kernel). + +### C. The Cost/Loss Function Output +The objective of training an ML model is often to minimize a **Cost Function** $J$. The output of this function is always a single scalar value. + +$$ +J(\theta) = \frac{1}{2m} \sum_{i=1}^{m} (h_\theta(x^{(i)}) - y^{(i)})^2 +$$ + +:::tip +The result $J(\theta)$ (the mean squared error) is a single scalar that represents the total error of the model. The training process seeks to find the parameter vector $\theta$ that minimizes this single scalar value. +::: + +## 3. Operations with Scalars + +Scalars follow basic arithmetic rules. They are used to scale (or modify the magnitude of) other mathematical objects, which is where the term **scalar multiplication** comes from. + +If $x$ is a scalar and $\mathbf{v}$ is a vector, then the operation $x\mathbf{v}$ results in a vector where every component of $\mathbf{v}$ is multiplied by the scalar $x$. + +* **Addition:** $a + b$ +* **Multiplication:** $a \cdot b$ + + + + + Let the scalar $a = 5$ and the scalar $b = 10$. + +``` + +a + b = 15 +a * b = 50 + +``` + + + +In Feature Scaling (Normalization), you subtract the mean ($\mu$) and divide by the standard deviation ($\sigma$). Both $\mu$ and $\sigma$ are scalars calculated from the training data. + +$$ +x_{\text{scaled}} = \frac{x - \mu}{\sigma} +$$ + + + +--- + +**Scalars are the fundamental "zero-dimensional" objects. 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-1653,254 +1653,994 @@ const sidebars: SidebarsConfig = { ], ml: [ - "machine-learning/introduction", - "machine-learning/role-of-ml-engineer", - "machine-learning/ml-engineer-vs-ai-engineer", - "machine-learning/skills-and-responsibilities", - "machine-learning/ml-lifecycle", + "machine-learning/index", + { + type: "category", + label: "Introduction", + link: { + type: "generated-index", + title: "Introduction to Machine Learning", + description: + "Get started with Machine Learning. Understand what ML is, the role of an ML engineer, career paths, and the complete ML lifecycle.", + keywords: [ + "machine learning introduction", + "ml engineer", + "ml lifecycle", + "ai vs ml", + ], + }, + items: [ + "machine-learning/introduction/what-is-ml", + "machine-learning/introduction/role-of-ml-engineer", + "machine-learning/introduction/ml-engineer-vs-ai-engineer", + "machine-learning/introduction/skills-and-responsibilities", + "machine-learning/introduction/ml-lifecycle", + ], + }, { type: "category", - label: "ML Fundamentals", + label: "Mathematics for ML", link: { type: "generated-index", - title: "Machine Learning Fundamentals", + title: "Mathematics for Machine Learning", description: - "Understand the core concepts of Machine Learning including types of learning, real-world applications, and essential terminology.", + "Build strong mathematical foundations required for Machine Learning. This section covers Linear Algebra, Calculus, and Discrete Mathematics with ML-focused explanations and examples.", keywords: [ - "machine learning basics", - "ai fundamentals", - "learning types", - "ml introduction", + "mathematics for machine learning", + "math for ML", + "linear algebra for ML", + "calculus for ML", + "discrete mathematics for ML", ], }, items: [ - "machine-learning/fundamentals/what-is-ml", - "machine-learning/fundamentals/types-of-learning", - "machine-learning/fundamentals/ml-workflow", - "machine-learning/fundamentals/data-splitting", + // ========================= + // Linear Algebra + // ========================= + { + type: "category", + label: "Linear Algebra", + link: { + type: "generated-index", + title: "Linear Algebra for Machine Learning", + description: + "Learn core Linear Algebra concepts used in Machine Learning, including vectors, matrices, eigenvalues, and matrix decompositions.", + keywords: [ + "linear algebra for machine learning", + "vectors", + "matrices", + "eigenvalues", + "singular value decomposition", + ], + }, + items: [ + "machine-learning/mathematics-for-ml/linear-algebra/scalars", + "machine-learning/mathematics-for-ml/linear-algebra/vectors", + "machine-learning/mathematics-for-ml/linear-algebra/matrices", + "machine-learning/mathematics-for-ml/linear-algebra/tensors", + "machine-learning/mathematics-for-ml/linear-algebra/matrix-operations", + "machine-learning/mathematics-for-ml/linear-algebra/determinants", + "machine-learning/mathematics-for-ml/linear-algebra/inverse-of-matrix", + "machine-learning/mathematics-for-ml/linear-algebra/eigenvalues-and-eigenvectors", + "machine-learning/mathematics-for-ml/linear-algebra/svd", + "machine-learning/mathematics-for-ml/linear-algebra/diagonalization", + ], + }, + + // ========================= + // Calculus + // ========================= + { + type: "category", + label: "Calculus", + link: { + type: "generated-index", + title: "Calculus for Machine Learning", + description: + "Understand how Calculus powers optimization in Machine Learning, including gradients, Jacobians, Hessians, and backpropagation.", + keywords: [ + "calculus for machine learning", + "derivatives", + "gradients", + "jacobian", + "hessian", + ], + }, + items: [ + "machine-learning/mathematics-for-ml/calculus/derivatives", + "machine-learning/mathematics-for-ml/calculus/partial-derivatives", + "machine-learning/mathematics-for-ml/calculus/chain-rule", + "machine-learning/mathematics-for-ml/calculus/gradients", + "machine-learning/mathematics-for-ml/calculus/jacobian", + "machine-learning/mathematics-for-ml/calculus/hessian", + ], + }, + + // ========================= + // Discrete Mathematics + // ========================= + { + type: "category", + label: "Discrete Mathematics", + link: { + type: "generated-index", + title: "Discrete Mathematics for Machine Learning", + description: + "Explore discrete mathematical concepts essential for ML algorithms, graph-based models, and computational reasoning.", + keywords: [ + "discrete mathematics for machine learning", + "sets and relations", + "logic", + "combinatorics", + "graph theory", + ], + }, + items: [ + "machine-learning/mathematics-for-ml/discrete-mathematics/sets-and-relations", + "machine-learning/mathematics-for-ml/discrete-mathematics/logic", + "machine-learning/mathematics-for-ml/discrete-mathematics/combinatorics", + "machine-learning/mathematics-for-ml/discrete-mathematics/graphs", + ], + }, ], }, - // { - // type: "category", - // label: "Math for ML", - // link: { - // type: "generated-index", - // title: "Essential Math for Machine Learning", - // description: - // "Learn the math behind ML — linear algebra, calculus, statistics, and probability with simplified explanations.", - // keywords: [ - // "math for ml", - // "statistics", - // "probability", - // "linear algebra", - // "calculus in ml", - // ], - // }, - // items: [ - // "machine-learning/math/linear-algebra", - // "machine-learning/math/calculus", - // "machine-learning/math/statistics", - // "machine-learning/math/probability", - // ], - // }, + { + type: "category", + label: "Statistics", + link: { + type: "generated-index", + title: "Statistics for Machine Learning", + description: + "Learn descriptive and inferential statistics, data visualization, and statistical reasoning used in ML models.", + keywords: [ + "statistics", + "descriptive statistics", + "inferential statistics", + ], + }, + items: [ + "machine-learning/statistics/basic-concepts", + "machine-learning/statistics/descriptive-statistics", + "machine-learning/statistics/data-visualization", + "machine-learning/statistics/inferential-statistics", + ], + }, - // { - // type: "category", - // label: "Data Preprocessing", - // link: { - // type: "generated-index", - // title: "Data Cleaning & Preprocessing", - // description: - // "Master the data preparation pipeline — handling missing values, scaling, encoding, feature extraction, and more.", - // keywords: [ - // "ml data preprocessing", - // "data cleaning", - // "feature engineering", - // "ml pipeline", - // ], - // }, - // items: [ - // "machine-learning/data-preprocessing/handling-missing-data", - // "machine-learning/data-preprocessing/feature-scaling", - // "machine-learning/data-preprocessing/encoding", - // "machine-learning/data-preprocessing/feature-engineering", - // ], - // }, + { + type: "category", + label: "Probability", + link: { + type: "generated-index", + title: "Probability for Machine Learning", + description: + "Understand probability theory, Bayes theorem, random variables, and probability distributions used in ML.", + keywords: ["probability", "bayes theorem", "random variables"], + }, + items: [ + "machine-learning/probability/basics-of-probability", + "machine-learning/probability/conditional-probability", + "machine-learning/probability/bayes-theorem", + "machine-learning/probability/random-variables", + "machine-learning/probability/pdf-pmf", + { + type: "category", + label: "Distributions", + link: { + type: "generated-index", + title: "Probability Distributions for Machine Learning", + description: + "Learn the most important probability distributions used in Machine Learning and Data Science. This section explains Normal, Binomial, Poisson, and Uniform distributions with intuition, formulas, and real-world ML examples.", + keywords: [ + "probability distributions", + "probability for machine learning", + "normal distribution", + "binomial distribution", + "poisson distribution", + "uniform distribution", + ], + }, + items: [ + "machine-learning/probability/probability-distributions/normal", + "machine-learning/probability/probability-distributions/binomial", + "machine-learning/probability/probability-distributions/poisson", + "machine-learning/probability/probability-distributions/uniform", + ], + }, + ], + }, - // { - // type: "category", - // label: "Supervised Learning", - // link: { - // type: "generated-index", - // title: "Supervised Machine Learning", - // description: - // "Learn the full set of supervised ML algorithms — regression, classification, trees, SVMs, and ensembles.", - // keywords: [ - // "supervised learning", - // "regression", - // "classification", - // "svm", - // "decision trees", - // "ensemble models", - // ], - // }, - // items: [ - // { - // type: "category", - // label: "Regression", - // items: [ - // "machine-learning/supervised/regression/linear-regression", - // "machine-learning/supervised/regression/polynomial-regression", - // "machine-learning/supervised/regression/ridge-lasso", - // ], - // }, - // { - // type: "category", - // label: "Classification", - // items: [ - // "machine-learning/supervised/classification/logistic-regression", - // "machine-learning/supervised/classification/knn", - // "machine-learning/supervised/classification/svm", - // "machine-learning/supervised/classification/naive-bayes", - // ], - // }, - // { - // type: "category", - // label: "Tree Models", - // items: [ - // "machine-learning/supervised/tree-models/decision-tree", - // "machine-learning/supervised/tree-models/random-forest", - // "machine-learning/supervised/tree-models/gradient-boosting", - // "machine-learning/supervised/tree-models/xgboost", - // ], - // }, - // ], - // }, + { + type: "category", + label: "Programming Fundamentals", + link: { + type: "generated-index", + title: "Programming Fundamentals for ML", + description: + "Learn Python programming fundamentals and essential libraries used in Machine Learning workflows.", + keywords: ["python for ml", "numpy", "pandas", "matplotlib"], + }, + items: [ + "machine-learning/programming-fundamentals/python", + { + type: "category", + label: "Basic Syntax", + link: { + type: "generated-index", + title: "Python Basic Syntax for Machine Learning", + description: + "Learn the core Python syntax required for Machine Learning. This section covers variables, data types, control flow, data structures, functions, and exception handling with ML-focused examples.", + keywords: [ + "python basic syntax", + "python for machine learning", + "variables and data types", + "python data structures", + "loops and conditionals", + "python functions", + "exception handling in python", + ], + }, + items: [ + "machine-learning/programming-fundamentals/basic-syntax/variables-and-data-types", + "machine-learning/programming-fundamentals/basic-syntax/data-structures", + "machine-learning/programming-fundamentals/basic-syntax/loops", + "machine-learning/programming-fundamentals/basic-syntax/conditionals", + "machine-learning/programming-fundamentals/basic-syntax/exceptions", + "machine-learning/programming-fundamentals/basic-syntax/functions", + ], + }, + "machine-learning/programming-fundamentals/object-oriented-programming", + { + type: "category", + label: "Essential Libraries", + link: { + type: "generated-index", + title: "Essential Python Libraries for Machine Learning", + description: + "Master the core Python libraries used in Machine Learning and Data Science. Learn NumPy for numerical computing, Pandas for data manipulation, Matplotlib for visualization, and Seaborn for statistical data exploration.", + keywords: [ + "python libraries for machine learning", + "numpy", + "pandas", + "matplotlib", + "seaborn", + "data science libraries", + "machine learning tools", + "python data analysis", + "data visualization", + ], + }, + items: [ + "machine-learning/programming-fundamentals/essential-libraries/numpy", + "machine-learning/programming-fundamentals/essential-libraries/pandas", + "machine-learning/programming-fundamentals/essential-libraries/matplotlib", + "machine-learning/programming-fundamentals/essential-libraries/seaborn", + ], + }, + ], + }, - // { - // type: "category", - // label: "Unsupervised Learning", - // link: { - // type: "generated-index", - // title: "Unsupervised Machine Learning", - // description: - // "Explore clustering, dimensionality reduction, and anomaly detection techniques used to uncover hidden patterns.", - // keywords: [ - // "unsupervised learning", - // "clustering", - // "k-means", - // "pca", - // "anomaly detection", - // ], - // }, - // items: [ - // "machine-learning/unsupervised/kmeans", - // "machine-learning/unsupervised/hierarchical-clustering", - // "machine-learning/unsupervised/dbscan", - // "machine-learning/unsupervised/pca", - // "machine-learning/unsupervised/anomaly-detection", - // ], - // }, + { + type: "category", + label: "Data Engineering Basics", + link: { + type: "generated-index", + title: "Data Engineering Basics for Machine Learning", + description: + "Learn how real-world data is collected, stored, cleaned, and prepared for Machine Learning. This section covers data sources, formats, and preprocessing techniques essential for building reliable ML pipelines.", + keywords: [ + "data engineering for machine learning", + "data collection", + "data preprocessing", + "data formats", + "feature engineering", + "machine learning pipelines", + ], + }, + items: [ + { + type: "category", + label: "Data Collection", + link: { + type: "generated-index", + title: "Data Collection for Machine Learning", + description: + "Understand where data comes from and how it is collected for Machine Learning systems, including databases, APIs, the internet, mobile apps, and IoT devices.", + keywords: [ + "data collection", + "data sources", + "sql", + "nosql", + "apis", + "iot data", + "machine learning data", + ], + }, + items: [ + "machine-learning/data-engineering-basics/data-collection/data-sources", + "machine-learning/data-engineering-basics/data-collection/databases-sql-nosql", + "machine-learning/data-engineering-basics/data-collection/internet", + "machine-learning/data-engineering-basics/data-collection/apis", + "machine-learning/data-engineering-basics/data-collection/mobile-apps", + "machine-learning/data-engineering-basics/data-collection/iot", + ], + }, - // { - // type: "category", - // label: "Model Evaluation", - // link: { - // type: "generated-index", - // title: "Model Evaluation & Validation", - // description: - // "Learn how to evaluate ML models using metrics, cross-validation, ROC curves, confusion matrices, and more.", - // keywords: [ - // "model evaluation", - // "ml metrics", - // "cross validation", - // "confusion matrix", - // "roc auc", - // ], - // }, - // items: [ - // "machine-learning/evaluation/metrics-regression", - // "machine-learning/evaluation/metrics-classification", - // "machine-learning/evaluation/cross-validation", - // "machine-learning/evaluation/overfitting-underfitting", - // ], - // }, + { + type: "category", + label: "Data Formats", + link: { + type: "generated-index", + title: "Common Data Formats in Machine Learning", + description: + "Learn about the most common data formats used in Machine Learning workflows, including tabular, semi-structured, and columnar formats, and understand when to use each.", + keywords: [ + "data formats", + "csv", + "json", + "parquet", + "xml", + "excel data", + "machine learning datasets", + ], + }, + items: [ + "machine-learning/data-engineering-basics/data-formats/csv", + "machine-learning/data-engineering-basics/data-formats/excel", + "machine-learning/data-engineering-basics/data-formats/json", + "machine-learning/data-engineering-basics/data-formats/parquet", + "machine-learning/data-engineering-basics/data-formats/xml", + ], + }, - // { - // type: "category", - // label: "Neural Networks", - // link: { - // type: "generated-index", - // title: "Neural Networks & Deep Learning", - // description: - // "Understand the foundations of neural networks, activation functions, backpropagation, optimization, and training techniques.", - // keywords: [ - // "neural networks", - // "deep learning", - // "activation functions", - // "backpropagation", - // "optimizers", - // ], - // }, - // items: [ - // "machine-learning/neural-networks/perceptron", - // "machine-learning/neural-networks/activation-functions", - // "machine-learning/neural-networks/loss-functions", - // "machine-learning/neural-networks/backpropagation", - // "machine-learning/neural-networks/optimizers", - // ], - // }, + { + type: "category", + label: "Data Cleaning & Preprocessing", + link: { + type: "generated-index", + title: "Data Cleaning and Preprocessing for ML", + description: + "Prepare raw data for Machine Learning by handling missing values, engineering features, scaling data, reducing dimensionality, and selecting the most relevant features.", + keywords: [ + "data cleaning", + "data preprocessing", + "feature engineering", + "feature scaling", + "normalization", + "dimensionality reduction", + "feature selection", + ], + }, + items: [ + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/handling-missing-data", + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/feature-engineering", + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/feature-scaling", + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/normalization", + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/dimensionality-reduction", + "machine-learning/data-engineering-basics/data-cleaning-and-preprocessing/feature-selection", + ], + }, + ], + }, - // { - // type: "category", - // label: "ML Deployment", - // link: { - // type: "generated-index", - // title: "Deploying Machine Learning Models", - // description: - // "Learn how to serve ML models using Flask, FastAPI, Docker, and cloud platforms. Includes versioning and CI/CD.", - // keywords: [ - // "ml deployment", - // "mlops", - // "fastapi", - // "docker", - // "model serving", - // "ci cd", - // ], - // }, - // items: [ - // "machine-learning/deployment/flask", - // "machine-learning/deployment/fastapi", - // "machine-learning/deployment/docker", - // "machine-learning/deployment/mlflow", - // ], - // }, + { + type: "category", + label: "Machine Learning Core", + link: { + type: "generated-index", + title: "Machine Learning Core Concepts", + description: + "Dive into the core concepts of Machine Learning. Learn how ML works, explore different learning paradigms, implement models using Scikit-learn, and understand evaluation techniques used in real-world ML systems.", + keywords: [ + "machine learning core", + "introduction to machine learning", + "types of machine learning", + "scikit-learn", + "ml algorithms", + "model evaluation", + ], + }, + items: [ + "machine-learning/machine-learning-core/introduction-to-ml", - // { - // type: "category", - // label: "Project Practicals", - // link: { - // type: "generated-index", - // title: "Machine Learning Project Practicals", - // description: - // "Hands-on ML projects for real-world learning — from EDA to model training, tuning, and deployment.", - // keywords: [ - // "ml projects", - // "ml practicals", - // "machine learning hands on", - // "real world ml", - // ], - // }, - // items: [ - // "machine-learning/projects/eda-project", - // "machine-learning/projects/regression-project", - // "machine-learning/projects/classification-project", - // "machine-learning/projects/clustering-project", - // "machine-learning/projects/deployment-project", - // ], - // }, + { + type: "category", + label: "Types of Machine Learning", + link: { + type: "generated-index", + title: "Types of Machine Learning", + description: + "Understand the different learning paradigms in Machine Learning, including supervised, unsupervised, semi-supervised, self-supervised, and reinforcement learning.", + keywords: [ + "types of machine learning", + "supervised learning", + "unsupervised learning", + "reinforcement learning", + "semi-supervised learning", + "self-supervised learning", + ], + }, + items: [ + "machine-learning/machine-learning-core/types-of-machine-learning/supervised-learning", + "machine-learning/machine-learning-core/types-of-machine-learning/unsupervised-learning", + "machine-learning/machine-learning-core/types-of-machine-learning/semi-supervised-learning", + "machine-learning/machine-learning-core/types-of-machine-learning/self-supervised-learning", + "machine-learning/machine-learning-core/types-of-machine-learning/reinforcement-learning", + ], + }, + + { + type: "category", + label: "Scikit-learn", + link: { + type: "generated-index", + title: "Scikit-learn for Machine Learning", + description: + "Learn how to build end-to-end Machine Learning workflows using Scikit-learn, from data loading and preprocessing to model selection, tuning, and making predictions.", + keywords: [ + "scikit-learn", + "machine learning pipelines", + "data preparation", + "model selection", + "hyperparameter tuning", + ], + }, + items: [ + "machine-learning/machine-learning-core/scikit-learn/data-loading", + "machine-learning/machine-learning-core/scikit-learn/text-data", + "machine-learning/machine-learning-core/scikit-learn/data-preparation", + "machine-learning/machine-learning-core/scikit-learn/model-selection", + "machine-learning/machine-learning-core/scikit-learn/hyperparameter-tuning", + "machine-learning/machine-learning-core/scikit-learn/predictions", + ], + }, + + { + type: "category", + label: "Supervised Learning", + link: { + type: "generated-index", + title: "Supervised Learning Algorithms", + description: + "Learn supervised learning techniques where models are trained using labeled data. Explore classification and regression algorithms widely used in industry.", + keywords: [ + "supervised learning", + "classification algorithms", + "regression algorithms", + "labeled data", + ], + }, + items: [ + { + type: "category", + label: "Classification", + link: { + type: "generated-index", + title: "Classification Algorithms", + description: + "Explore classification algorithms used to predict discrete class labels, including distance-based, probabilistic, margin-based, and tree-based methods.", + keywords: [ + "classification", + "knn", + "logistic regression", + "svm", + "decision trees", + "random forest", + "gradient boosting", + ], + }, + items: [ + "machine-learning/machine-learning-core/supervised-learning/classification/knn", + "machine-learning/machine-learning-core/supervised-learning/classification/logistic-regression", + "machine-learning/machine-learning-core/supervised-learning/classification/svm", + "machine-learning/machine-learning-core/supervised-learning/classification/decision-trees", + "machine-learning/machine-learning-core/supervised-learning/classification/random-forest", + "machine-learning/machine-learning-core/supervised-learning/classification/gradient-boosting", + ], + }, + + { + type: "category", + label: "Regression", + link: { + type: "generated-index", + title: "Regression Algorithms", + description: + "Learn regression techniques used to predict continuous values. Understand linear and regularized regression models and their practical applications.", + keywords: [ + "regression", + "linear regression", + "lasso", + "ridge", + "elastic net", + "polynomial regression", + ], + }, + items: [ + "machine-learning/machine-learning-core/supervised-learning/regression/linear-regression", + "machine-learning/machine-learning-core/supervised-learning/regression/polynomial-regression", + "machine-learning/machine-learning-core/supervised-learning/regression/lasso", + "machine-learning/machine-learning-core/supervised-learning/regression/ridge", + "machine-learning/machine-learning-core/supervised-learning/regression/elastic-net", + ], + }, + ], + }, + + { + type: "category", + label: "Unsupervised Learning", + link: { + type: "generated-index", + title: "Unsupervised Learning Algorithms", + description: + "Discover unsupervised learning methods used to uncover hidden patterns in unlabeled data, including clustering and dimensionality reduction techniques.", + keywords: [ + "unsupervised learning", + "clustering", + "dimensionality reduction", + "kmeans", + "pca", + ], + }, + items: [ + { + type: "category", + label: "Clustering", + link: { + type: "generated-index", + title: "Clustering Algorithms", + description: + "Learn clustering techniques that group similar data points together, helping in customer segmentation, anomaly detection, and exploratory analysis.", + keywords: [ + "clustering", + "kmeans", + "hierarchical clustering", + "dbscan", + "gaussian mixture models", + ], + }, + items: [ + "machine-learning/machine-learning-core/unsupervised-learning/clustering/kmeans", + "machine-learning/machine-learning-core/unsupervised-learning/clustering/hierarchical", + "machine-learning/machine-learning-core/unsupervised-learning/clustering/dbscan", + "machine-learning/machine-learning-core/unsupervised-learning/clustering/gaussian-mixtures", + ], + }, + + { + type: "category", + label: "Dimensionality Reduction", + link: { + type: "generated-index", + title: "Dimensionality Reduction Techniques", + description: + "Reduce feature space complexity while preserving important information using techniques like PCA and Autoencoders.", + keywords: [ + "dimensionality reduction", + "pca", + "autoencoders", + "feature reduction", + ], + }, + items: [ + "machine-learning/machine-learning-core/unsupervised-learning/dimensionality-reduction/pca", + "machine-learning/machine-learning-core/unsupervised-learning/dimensionality-reduction/autoencoders", + ], + }, + ], + }, + + { + type: "category", + label: "Reinforcement Learning", + link: { + type: "generated-index", + title: "Reinforcement Learning Fundamentals", + description: + "Learn how agents interact with environments to make sequential decisions using reward-based learning strategies.", + keywords: [ + "reinforcement learning", + "q-learning", + "policy gradients", + "actor critic", + "deep q networks", + ], + }, + items: [ + "machine-learning/machine-learning-core/reinforcement-learning/q-learning", + "machine-learning/machine-learning-core/reinforcement-learning/policy-gradients", + "machine-learning/machine-learning-core/reinforcement-learning/actor-critic", + "machine-learning/machine-learning-core/reinforcement-learning/deep-q-networks", + ], + }, + + { + type: "category", + label: "Model Evaluation", + link: { + type: "generated-index", + title: "Model Evaluation and Validation", + description: + "Learn how to evaluate Machine Learning models using appropriate metrics and validation strategies to ensure reliability and generalization.", + keywords: [ + "model evaluation", + "ml metrics", + "cross validation", + "train test split", + "model performance", + ], + }, + items: [ + "machine-learning/machine-learning-core/model-evaluation/why-evaluation-matters", + + { + type: "category", + label: "Metrics", + link: { + type: "generated-index", + title: "Machine Learning Evaluation Metrics", + description: + 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