— MAKING A HIGH-DIMENSIONAL CONCEPT VISIBLE —
While taking an online course at the University of the Arts London, I started learning about word vectors and embeddings. I do not have a background in mathematics or programming; my closest reference was the elementary physics I learned in secondary school, where vectors could be understood visually through position, magnitude and direction.
As I studied the concept, I found that most of the diagrams available explained the mathematics of vectors, but none of them quite represented the way I was beginning to understand embeddings.
These were the two reference images that most closely matched the way I was trying to understand the problem. One (view) helped clarify vector addition and displacement, while the other (view) suggested how consistent relationships could appear as repeated directional patterns between words.
Both references clarified part of the problem, but neither fully described what I wanted to understand: a word embedding is not only about isolated vectors, but about words existing inside a much larger relational space.
I became interested in using space itself as an explanatory device. If a word can be represented as a vector, could that vector appear to move through an environment? Could the displacement between words become something visible? And could a sequence of words — eventually even a sentence — be perceived as tracing a path through that space?
That question became the starting point for this project. Rather than approaching embeddings as a mathematical or programming exercise, I approached them as a visual communication problem: how could an abstract computational concept be translated into something spatial, intuitive and explorable?
The project became an opportunity to combine data visualization, infographics, interaction and AI-assisted vibe coding, while applying creative direction to the construction of a complete visual system.
The result is an interactive 3D interpretation built from real word-vector data. It is not intended to reproduce the full mathematical structure of an embedding. Compressing a high-dimensional space into three dimensions necessarily removes information. Instead, the visualization uses that simplification deliberately, allowing the user to explore the difference between the data that exists mathematically and the portion of it that can be made visible.
The visualization can be explored in three different ways:
The 3D space can be rotated, zoomed and filtered using the viewer controls. Labels, vectors, word chains, the grid and semantic groups can be shown or hidden independently.
In this project, every word is represented by a 50-dimensional vector from GloVe 6B, a pretrained model built from approximately 6 billion tokens of text.
A word is therefore not stored as a point with X, Y and Z coordinates. It is represented by a list of 50 numerical values:
Those values describe the word's position within a much larger statistical space. Words that occur in similar linguistic contexts tend to develop related vector representations.
FROM 50 DIMENSIONS TO 3
A 50-dimensional space cannot be directly displayed on a screen, so the complete vocabulary is reduced to three dimensions using Principal Component Analysis (PCA):
The same transformation is applied to every word, producing the X, Y and Z coordinates visible in the interactive visualization.
The first three principal components preserve approximately 19.3% of the variance contained in the processed vocabulary. The 3D space is therefore a real projection of the original data, but not a complete representation of it.
This distinction is important: two words that appear close together on screen are not necessarily the closest words in the original embedding.
TWO SPACES, TWO TYPES OF MEASUREMENT
Cosine similarity is calculated from the original 50-dimensional GloVe vectors. It measures how closely two vectors point in the same direction and is used to examine semantic relationships and find neighboring words.
Euclidean distance in 3D describes the distance between the positions produced by PCA. It tells us what is happening in the visible projection, rather than in the complete embedding.
This makes it possible to compare what the model contains with what the visualization is able to show.
MOVEMENT THROUGH THE SPACE
Vectors can also describe displacement.
The difference between two words can be expressed as:
Some linguistic relationships produce similar displacements. This is the idea behind well-known examples such as:
In this visualization, vector arithmetic is calculated first in the original 50-dimensional space. The resulting vector is then projected into 3D, where it can be compared with the actual position of the closest matching word.
The Semantic Neighbors mode works in a similar way: neighboring words are ranked using cosine similarity in the original 50D embedding, while their existing PCA coordinates are used only to display them in the 3D environment.
WHAT THE SPACE MEANS
The positions are not manually arranged, and semantic categories do not determine where words appear. Colors and categories are an editorial layer added to make the vocabulary easier to read.
GloVe derives its vectors statistically from patterns of word co-occurrence in large collections of text. Because of this, the space can reveal meaningful linguistic relationships, but it can also reproduce biases, associations and distortions present in the language used to train it.
The visualization should therefore not be read as an objective map of meaning.
The 50-dimensional vectors are the data. The 3D space is a projection designed to make part of their structure visible.
