Support Vector Machines (SVM)

Understanding machine learning algorithms isn't as implausible as it may seem. Most novices set the ball rolling with the concept of regression, a simple yet effective tool. However, machine learning is more versatile than just regression. Think of machine learning algorithms like a toolbox full of varied tools - swords, knives, arrows, daggers, and the like. You need to comprehend their purpose and effective use.

Regression: The Initial Dive

Consider 'Regression' as a swift blade, efficient for chopping down data, albeit suffering when dealing with data complexities. Conversely, 'Support Vector Machines' are akin to a sharp dagger which thrives on crunching smaller datasets but also capable of handling bigger ones with strength and power.

Demystifying Support Vector Machines (SVM)

'SVM' is a supervised learning method, often used for tackling classification and regression issues. More often than not, it's used to decipher classification problems. It maps each data instance as a point in multi-dimensional space where each attribute becomes a value for a particular coordinate. Classification is executed by identifying the hyper-plane which distinctly differentiates the two classes. Essentially, support vectors correspond to coordinates of individual observations. The SVM classifier is like a boundary that segregates the two classes effectively.

Hyperplanes and Dimensionality

The foundational concept of SVMs revolves around creating a hyperplane that segregates a dataset into two parts as optimally as possible. The points from the dataset that lie closest to the hyperplane or such points whose removal would alter the position of the dividing hyperplane are termed as 'support vectors'. Thus, these points are fundamental to the dataset.

For a classification task with two features, a hyperplane can be visualized as a line that segregates and classifies a set of data linearly. The further the data points lie from the hyperplane, the more confident we are about their correct categorization. Consequently, we strive to keep the data points as distant as possible from the hyperplane while staying on the correct side. Consequently, when new validation data is fed, its classification depends on the side of the hyperplane it lands on.

But what if a clear hyperplane is absent? That's where the challenge begins. More often than not, a dataset is quite mixed, making it linearly non separable. In such cases, it becomes necessary to transform our perspective from 2d to 3d. Of course, with the jump to three dimensions, our separating hyperplane evolves from a simple line to a planar surface. To facilitate this process of 'lifting' the data into higher dimensions, a technique called 'Kerneling' is deployed. Ultimately, our aim is to keep raising the dimensionality of the data until a separating hyperplane can be identified.

Strengths and Limitations of SVM

Advantages and disadvantages of SVM are clear - it performs well on small, easily distinguishable datasets and is efficient as it uses just a subset of training points. However, it is time-consuming for larger datasets and lacks effectiveness on noisy datasets where classes overlap.

Applications in the Real World

SVM is widely used for text classification tasks like topic assignment, spam detection, and sentiment analysis. It is particularly favored for image recognition tasks excelling at feature-based recognition and color categorization. SVM even finds its applications in recognizing handwritten digits, serving industries like postal automation.