I saw an impressive news recently. It was about matrices and vectors being removed from some curricula. If you look closely, it is not that they are being completely removed, but rather that they are being made selective so that you can avoid geometry and vectors altogether. I also studied vectors properly in college, when I was forced to(?) learn discrete mathematics and engineering mathematics, but I think that learning without any basic knowledge is somewhat different from learning with an understanding of the concepts.
Vectors and vector databases have become increasingly important in recent years, especially with the advent of Large Language Models (LLMs). These technologies offer new ways to process and analyze data, and are particularly valuable in the fields of artificial intelligence and machine learning. In this article, we will explain the concepts of vectors and vector databases, explore how they are used, and why they are important.
What is a vector?
The best vector expert I know...
A vector is a geometric object that has length (magnitude) and direction. For example, it is used to express movement from one point to another in two-dimensional space. Vectors can be defined in various dimensions, and each dimension represents one element of the direction the vector points. These properties of vectors are built on a mathematical foundation called vector algebra, which allows us to accurately analyze the relationships between vectors.
Code representation of vector
In mathematics, a vector is a quantity that has magnitude and direction, and is used to express concepts such as movement in geometric space or force in physics. These mathematical vectors can be defined in multiple dimensions, with each dimension representing one element of the direction in which the vector points.
In the artificial intelligence, especially machine learning and deep learning industries, vectors are used as a way to represent data numerically. For example, when processing text data, each word or sentence is converted into a vector so that the computer can understand and process it. The vector thus converted numerically encodes the semantic and contextual characteristics of the word.
Vectors can be represented in code in several ways. The simplest form is as an object, where the coordinates of the start and end points are stored. However, since the important parts of a vector are its length and direction, it is also possible to represent it by normalizing all vectors to start from the origin (0,0). In this case, the data can be simplified by storing only the coordinates of the end point.
Practical examples of vectors (what to use?)
Computer Graphics: Computer graphics uses vectors to represent points in 2D or 3D space. These vectors are essential for determining the location of pixels on a screen or for defining the position and orientation of objects in 3D modeling.
Recommendation Engine: In a recommender system, the characteristics of an item (e.g., the genre of the movie, its length, etc.) are represented as a multidimensional vector and compared to the user's preferences to recommend items that are suitable for the user. This involves calculating the similarity between vectors to find the most relevant items.
Machine Learning: In the field of machine learning, various forms of data such as images, text, and sound are converted into vectors and processed. These converted vectors are analyzed by algorithms and used for tasks such as classification, prediction, and recommendation.
In fact, the potential uses are endless, but recently, the concept of vectors is becoming more important as techniques utilizing VectorDB for optimizing or personalizing artificial intelligence are emerging.
The Role of Vector Databases
Vector databases are databases optimized for storing and retrieving vectors and their associated metadata. These databases are designed to quickly find similar vectors using the Approximate Nearest Neighbor (ANN) algorithm. This allows for efficient retrieval of similar items from large data sets.
The Impact of Vector Databases on LLM
Models like LLM have limitations in their inputs and outputs, so using a vector database can overcome these limitations by converting text or other data into vectors and storing them. This allows the model to query and process only relevant parts of the data, greatly improving efficiency and performance.
In summary, vectors and vector databases are essential tools in modern software development, especially in the fields of artificial intelligence and machine learning. They provide powerful ways to effectively model and process data, and the results can be seen in a variety of applications and systems. Therefore, understanding vectors and vector databases is essential for using or studying these technologies.
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