Sparse Arrays

Introduction

Sparse data occurs when the data is predominantly empty or contains a small number of non-zero values compared to the overall size of the data set. Here are some examples of sparse data occurring in real-world scenarios:

• Image and video processing: Images and videos often contain a significant amount of empty or black pixels. Sparse matrices or compressed formats, such as Compressed Sparse Column (CSC) or Compressed Sparse Row (CSR) representations, are employed to store and process these visual data efficiently.

• Natural language processing (NLP): In NLP, text data can be represented using sparse vectors where each dimension corresponds to a unique word in a vocabulary. Since most documents contain only a small fraction of the vocabulary, sparse representations (e.g., the Term Frequency-Inverse Document Frequency model) are used.

• Recommender systems: Sparse matrices are commonly used to model user-item interactions in recommender systems. Users typically interact with only a small subset of items in a large catalog. Therefore, sparse representations are employed to store and process this data efficiently.

Note: Sparse doesn’t necessarily refer to zero values only. It can also refer to other values, such as np.nan for floats and None for other data types.

Instead of storing all the data points, which will be inefficient and consume excessive memory, sparse datasets are typically represented using specialized data structures that can effectively handle and exploit the sparsity. This leads to significant savings in memory ...