## 3 Challenges in Big Data for Machine Learning
### Scalability of Algorithms  
One of the most significant challenges in applying ML to big data is the scalability of algorithms. Traditional ML algorithms, many of which were developed when data volumes were orders of magnitude smaller, struggle to scale effectively in the face of today's massive datasets. As the size of data increases, both in terms of the number of samples and the dimensionality of features, the computational cost and memory requirements of these algorithms grow exponentially. This challenge is particularly pronounced in real-time applications, such as high-frequency trading or autonomous vehicles, where quick decision making is critical [200, 201]. Many conventional ML algorithms, such as support vector machines (SVMs) and k-nearest neighbors (k-NN), are inherently limited by their reliance on operations like pairwise comparisons or matrix computations, which become computationally prohibitive as dataset sizes increase. Additionally, these algorithms are typically designed for static and structured datasets, making them ill-suited for the dynamic, heterogeneous, and unstructured nature of big data. For instance, big data environments often include continuous \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Topic** & **References** & **Description** \\ \hline Agriculture \& Environmental Monitoring & [86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101] & ML for precision farming, environmental monitoring, disaster prediction, and resource management. \\ \hline Telecommunications & [102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113] & ML for network optimization, customer retention, fraud detection, and service quality improvement. \\ \hline Manufacturing \& Industry 4.0 & [114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125] & ML applications in predictive maintenance, quality control, supply chain optimization, and automation in manufacturing. \\ \hline Education \& learning & [126; 127; 128; 129; 130; 131; 132; 133; 134; 135; 136; 137] & ML applications in personalized learning, intelligent tutoring systems, predictive analytics for student success, and automated grading. \\ \hline Media \& Entertainment & [138; 139; 140; 141; 142; 143; 144; 145; 146; 147; 148; 149; 150] & ML for content recommendation, media production, distribution, and social media analytics. \\ \hline Legal \& Compliance & [151; 152; 153; 154; 155; 156; 157; 158; 159; 160; 161; 162] & ML applications in legal research, contract analysis, compliance monitoring, and e-discovery. \\ \hline HR \& Talent Management & [163; 164; 165; 166; 167; 168; 169; 170; 171; 172; 173; 174] & ML applications in recruitment, employee engagement, workforce planning, and performance management. \\ \hline Aerospace \& Defense & [175; 176; 177; 178] & ML for predictive maintenance, mission planning, autonomous systems, and cybersecurity in aerospace and defense. \\ \hline Government \& Public Policy & [188; 189; 190; 191; 192; 193; 194; 195; 196; 197; 198; 199] & ML applications in predictive analytics, public safety, law enforcement, and public health monitoring. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._streams of diverse data types, such as text, images, and sensor readings, which require flexible and adaptive approaches [202; 203; 204; 205]. To address these limitations, significant advancements have been made in distributed computing frameworks, such as Apache Hadoop and Apache Spark, which allow data to be processed in parallel across clusters of machines. Techniques like stochastic gradient descent (SGD) and mini-batch processing have also emerged, enabling scalable training of large models while reducing computational overhead. Furthermore, edge computing and federated learning are gaining traction as paradigms for the decentralization of computation, bringing data processing closer to its source and alleviating the bottlenecks of centralized processing [206; 207; 208]. Despite these advancements, achieving true scalability remains an ongoing challenge.