Singular value decomposition
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.
Matrix theory and linear algebra overview
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...
