📖 Computational Problems Dictionary

A structured overview of fundamental problems in computation and the techniques used to solve them in real-world applications.

Anomaly Detection

Identifies rare or unexpected items in datasets, often used in fraud, system health monitoring, or security breaches.

Techniques: Isolation Forests, One-Class SVM, Autoencoders, Z-score, DBSCAN

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Computer Vision

Extracting, analyzing, and generating meaningful information from digital images or video streams.

Techniques: CNNs, YOLO, U-Net, Haar Cascades, GANs

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Data Reduction & Transformation

Dimensionality Reduction

Reduces feature space to make data easier to visualize or process while preserving structure.

Techniques: PCA, t-SNE, UMAP, LDA

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Interpolation and Curve Fitting

Fills missing data or smooths values across a range using known reference points.

Techniques: Linear, Spline, Polynomial, Bezier

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Learning Problems

Classification

Sorting input into labeled categories (e.g., spam vs. non-spam).

Techniques: Logistic Regression, SVM, Decision Trees, CNNs, k-NN

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Regression

Predicting continuous values based on one or more input features.

Techniques: Linear, Polynomial, Ridge, Lasso, GPR, Neural Nets

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Clustering

Grouping data by similarity without predefined categories.

Techniques: k-Means, DBSCAN, GMM, SOM

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Reinforcement Learning

Learning optimal actions via environment feedback—used in robotics, games, and autonomous systems.

Techniques: Q-Learning, DQN, Actor-Critic, MCTS

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Natural Language Processing

Analyzing and generating human language for applications like sentiment analysis, translation, or chatbots.

Techniques: Transformers, TF-IDF, Word2Vec, RNNs, Topic Modeling

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Optimization & Simulation

Optimization

Finding the best solution from many, often under constraints (e.g., cost, speed, efficiency).

Techniques: Linear/Integer Programming, Gradient Descent, Genetic Algorithms, Constraint Programming

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Simulation and Modeling

Creating digital models to explore system behavior, often used in physics, economics, logistics.

Techniques: Monte Carlo, Agent-Based Modeling, Markov Chains, FEA

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Graph Theory

Analyzing connected data like social networks, routing, knowledge graphs.

Techniques: Dijkstra's, BFS, DFS, GNNs, PageRank

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Time-Based Analysis

Predicting future values using historical trends (e.g., stock forecasting, weather prediction).

Techniques: ARIMA, RNNs, Prophet, Holt-Winters, State Space Models

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