As we have seen in the previous section, reducing the dimensions of the datasets increases the efficiency of the model generation, without sacrificing the amount of knowledge contained in the data. As a result, the data is compressed and easy to visualize in fewer dimensions. SVD is a fundamental mathematical tool that can be easily leveraged for dimensionality reduction.
Before we try to understand SVD, here is a quick overview of linear algebra and matrix theory concepts. Although a comprehensive discussion on these topics is outside the scope of this book, a brief discussion is definitely in order:
- Scalar: A single number is termed a scalar. A scalar represents the magnitude of an entity. For example, the speed of a car is 60 miles/hour. Here, the number 60 is a scalar.
- Vectors: An array of multiple scalars arranged in an order is called a vector. Typically, vectors define magnitude as well as direction, and are considered...