# dimension Published articles for dimension. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## The Two-Dimensional Fourier Transform and Digital Watermarking DevFeed: [The Two-Dimensional Fourier Transform and Digital Watermarking]() Original publisher: [Read original article]() Published: 2013-12-30T19:24:05Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [fourier transform](), [watermarking](), [Algorithm](), [Code]() Tags: [algorithm](), [animations](), [big-o-notation](), [calculus](), [dimension](), [fft](), [fourier-analysis](), [fourier-transform](), [github](), [graphics](), [image-manipulation](), [images](), [james-hance](), [mathematics](), [matrices](), [programming](), [python](), [star-wars](), [up](), [watermarking]() ### AI overview This tutorial introduces the multidimensional Fourier transform, explains its relationship to the one-dimensional transform, describes an FFT-style algorithm for computing it, and applies it to digitally watermarking images. ### Source excerpt We've studied the Fourier transform quite a bit on this blog: with four primers and the Fast Fourier Transform algorithm under our belt, it's about time we opened up our eyes to higher dimensions. Indeed, in the decades since Cooley & Tukey's landmark paper, the most interesting applications of the discrete Fourier transform have occurred in dimensions greater than 1. But for all our work we haven't yet discussed what it means to take an "n-dimensional" Fourier transform. ## Constructing Topological Spaces -- A Primer DevFeed: [Constructing Topological Spaces -- A Primer]() Original publisher: [Read original article]() Published: 2012-11-11T18:13:58Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [spaces]() Tags: [building](), [complex](), [dimension](), [quotients](), [spaces](), [topology]() ### AI overview This primer explains how to construct more complex topological spaces from simpler ones using subspaces and quotients. It introduces the subspace topology and defines spheres, including the circle, as topological spaces. ### Source excerpt Last time we investigated the (very unintuitive) concept of a topological space as a set of "points" endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up into more complex ones. This will take the form of subspaces and quotients, and through these we will make rigorous the notion of "gluing" and "building" spaces. ## K-Nearest-Neighbors and Handwritten Digit Classification DevFeed: [K-Nearest-Neighbors and Handwritten Digit Classification]() Original publisher: [Read original article]() Published: 2012-08-26T12:19:43Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Machine Learning & Artificial Intelligence](), [Data Science](), [Math and Logic]() Tags: [dimension](), [linear-algebra](), [machine-learning](), [mathematics](), [metric](), [process](), [programming](), [supervised-learning]() ### AI overview This tutorial introduces supervised classification in machine learning and explains how labeled data, training algorithms, models, and classification algorithms work together. It then examines the assumption that data points in the same class are close under an appropriate metric. ### Source excerpt The Recipe for Classification One important task in machine learning is to classify data into one of a fixed number of classes. For instance, one might want to discriminate between useful email and unsolicited spam. Or one might wish to determine the species of a beetle based on its physical attributes, such as weight, color, and mandible length. These "attributes" are often called "features" in the world of machine learning, and they often correspond to dimensions when interpreted in the framework of linear algebra.