Essential Big Data Algorithms

Why This Matters

Big data algorithms aren't just tools—they're the foundation of how we extract meaning from massive datasets. You're being tested on understanding when to apply which algorithm, why certain approaches work better for specific problems, and how these algorithms scale to handle data that traditional methods can't touch. The concepts here connect directly to core themes: distributed computing, machine learning paradigms, dimensionality challenges, and the trade-offs between accuracy, interpretability, and computational cost.

Don't just memorize algorithm names and definitions. Know what problem each algorithm solves, what assumptions it makes, and how it compares to alternatives. When you see an FRQ asking you to recommend an approach for a given scenario, you need to think in categories: Is this a clustering problem or classification? Do I need distributed processing or can a single machine handle it? Is interpretability more important than raw accuracy? Master these distinctions, and you'll handle any question thrown at you.

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Distributed Processing Frameworks

These algorithms and systems solve the fundamental challenge of processing data too large for a single machine. The key principle is dividing work across multiple nodes while managing communication overhead and fault tolerance.

MapReduce

• Two-phase processing model—the Map function transforms input into key-value pairs, then Reduce aggregates results by key
• Parallel execution enables horizontal scaling across commodity hardware clusters without rewriting application logic
• Disk-based processing makes it reliable but slower than in-memory alternatives; best for batch processing where latency isn't critical

Hadoop Distributed File System (HDFS)

• Block-based storage splits large files across multiple machines, typically in 128MB chunks for efficient parallel access
• Replication factor (default 3 copies) ensures fault tolerance—if a node fails, data remains accessible from replicas
• Write-once, read-many design optimizes for throughput over random access, making it ideal for batch analytics workloads

Apache Spark

• In-memory processing keeps intermediate results in RAM, delivering up to 100x speed improvements over disk-based MapReduce
• Resilient Distributed Datasets (RDDs) provide fault tolerance through lineage tracking rather than replication
• Unified engine supports SQL, streaming, ML, and graph processing through consistent APIs in Python, Scala, Java, and R

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Clustering and Pattern Discovery

These algorithms find structure in unlabeled data. They identify natural groupings or associations without being told what to look for—the essence of unsupervised learning.

K-means Clustering

• Iterative centroid optimization—assigns points to nearest centroid, recalculates centroids, repeats until convergence
• Requires pre-specifying K (number of clusters), making the elbow method or silhouette analysis essential for choosing optimal values
• Assumes spherical clusters of similar size; struggles with irregular shapes or varying densities

Apriori Algorithm

• Frequent itemset mining discovers combinations of items that appear together above a minimum support threshold
• Pruning principle—if an itemset is infrequent, all its supersets must also be infrequent, dramatically reducing search space
• Market basket analysis is the classic application: "customers who buy X often buy Y"

Association Rule Mining

• Generates if-then rules from frequent itemsets using metrics like confidence ($P(Y|X)$) and lift (how much better than random)
• Support, confidence, and lift are the three key metrics for evaluating rule quality and business relevance
• Beyond retail—applies to medical diagnosis patterns, web navigation paths, and fraud detection sequences

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Classification Algorithms

These supervised learning methods predict categorical outcomes from labeled training data. The core challenge is learning decision boundaries that generalize well to unseen examples.

Naive Bayes

• Bayes' theorem application—calculates $P(\text{class}|\text{features})$ by assuming features are conditionally independent
• Independence assumption is often violated in practice but the algorithm still performs surprisingly well, especially with text
• Highly scalable with minimal training time, making it the go-to baseline for text classification and spam filtering

Decision Trees

• Recursive partitioning splits data on feature values that maximize information gain or minimize Gini impurity
• Interpretable structure produces human-readable rules ("if income > 50K and age > 30, then approve loan")
• Prone to overfitting without pruning or depth limits; individual trees rarely used alone in production

Support Vector Machines (SVM)

• Maximum margin classifier finds the hyperplane that maximizes distance to nearest points of each class
• Kernel trick enables nonlinear classification by mapping data to higher-dimensional spaces without explicit computation
• Effective in high dimensions where number of features exceeds number of samples; less suited for very large datasets

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Ensemble Methods

These algorithms combine multiple models to achieve better performance than any single model. The principle: diverse models make different errors, and aggregating their predictions cancels out individual weaknesses.

Random Forest

• Bootstrap aggregating (bagging) trains each tree on a random sample of data with replacement
• Feature randomization at each split ensures trees are decorrelated, improving ensemble diversity
• Robust to overfitting and handles missing values well; provides built-in feature importance rankings

Gradient Boosting

• Sequential error correction—each new tree specifically targets the residual errors of the combined previous trees
• Loss function minimization through gradient descent in function space, hence the name "gradient" boosting
• State-of-the-art performance on structured data; XGBoost and LightGBM implementations dominate Kaggle competitions

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Regression and Dimensionality Reduction

These algorithms handle continuous prediction and the challenge of high-dimensional data. They address the fundamental tension between model complexity and interpretability.

Linear Regression

• Models linear relationships between features and target: $y = \beta_0 + \beta_1x_1 + \beta_2x_2 + ... + \epsilon$
• Least squares estimation minimizes the sum of squared residuals to find optimal coefficients
• Interpretable coefficients tell you exactly how much each feature contributes; the baseline for all regression tasks

Principal Component Analysis (PCA)

• Variance maximization finds orthogonal directions (principal components) that capture the most data variation
• Dimensionality reduction projects high-dimensional data to fewer dimensions while preserving essential structure
• Preprocessing powerhouse—reduces noise, speeds up downstream algorithms, and enables visualization of complex datasets

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Recommendation and Ranking Systems

These algorithms power personalization at scale. They solve the problem of predicting preferences from sparse, implicit feedback data.

Collaborative Filtering

• User-based approach finds users with similar rating patterns and recommends what they liked
• Item-based approach identifies items frequently rated similarly and recommends related items (more scalable)
• Cold start problem is the key limitation—new users or items have no history to base recommendations on

PageRank

• Link analysis algorithm treats hyperlinks as votes, with links from important pages counting more
• Iterative probability calculation—models a random web surfer and computes steady-state visit probabilities
• Beyond search—applies to citation networks, social influence measurement, and any graph-based importance ranking

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Quick Reference Table

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Self-Check Questions

1. Which two algorithms both use tree structures but differ fundamentally in how they combine multiple trees—and when would you choose one over the other?

2. A company needs to process 10TB of log files daily for batch reporting. Compare MapReduce and Spark for this use case, explaining which factors would influence your recommendation.

3. You're building a system to classify customer support tickets into categories. Which algorithm would you prototype with first, and why might you switch to a different algorithm for production?

4. Explain how PCA and K-means might be used together in a data pipeline. What problem does each solve, and why is their order of application important?

5. Compare collaborative filtering and association rule mining for an e-commerce recommendation system. What type of insight does each provide, and how might you use both in a single platform?