Hotvector

Hotvector refers to a vector of numbers where most of the elements are zero. The non-zero elements are typically positive and their sum is large. Hotvectors are commonly used in machine learning, particularly in natural language processing and recommendation systems. For example, in a document classification task, a document might be represented as a hotvector where each dimension corresponds to a word in the vocabulary. If a word appears in the document, the corresponding dimension in the hotvector is set to 1, otherwise it's 0. This is also known as a sparse vector. The term "hot" implies that many dimensions are activated or "on" with non-zero values.

The efficiency of working with hotvectors stems from the fact that algorithms can be optimized to only process the non-zero elements, ignoring the vast majority of zeros. This significantly reduces computational cost and memory requirements, especially when dealing with very high-dimensional data. Specialized data structures and algorithms exist to handle hotvectors effectively. In contrast, a dense vector would have non-zero values in most or all of its dimensions. The concept of hotvectors is fundamental to understanding how large-scale datasets are represented and manipulated in various data-driven applications.