NISHIO Hirokazu

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Visualizing High-Dimensional Vectors

In graduate school I studied the visualization of high-dimensional vectors: projecting data with thousands of dimensions onto a two- or three-dimensional map a human can look at. That single technical thread has run through the center of my work for over twenty years, changing only its subject — from gene-expression data (my doctoral research), to words (word2vec), to people's opinions (broad listening).

After my Ph.D. I did not stay in academia; I became a software engineer, and I never followed what you would call a researcher's path. Even so, the idea I picked up in graduate school — turning high-dimensional data into a map — kept coming back to the center of my work, each time with a different subject.

One and the same line

Visualizing high-dimensional vectors has a property that holds no matter what the subject is: in the resulting 2-D scatter plot, the axes themselves mean nothing. A point's position encodes only the relative closeness of the vectors; reading "upper-right, therefore good" is simply wrong. This is something I always caution about in broad listening — and it is exactly what I was saying twenty years ago when I projected gene-expression data onto a spherical SOM (self-organizing map). Build a map where similar things cluster, and let a human read the clusters. The subject changed from molecules to words to voices, but the skeleton of the work did not.

Record of practice

In other words, the high-dimensional vector visualization I studied in graduate school came back to the center of my work twenty years later, in the completely different application domain of broad listening.

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Related stories: Broad Listening in Practice / Intellectual Production / Plurality / Nurturing the Next Generation

This page is a record as of 2026-07-29. The subject of visualization may keep widening, so this page may continue to grow.