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high-dimensional_data

Visual Analytics Course

High-dimensional data

The main difficulty in handling high-dimensional data is its … high dimension. A data sample is high-dimensional if its elements may be seen as tuples with a usually high value for . Note however that may be considered high already when or since in these cases the data cannot be directly plotted on a screen. In the sequel, will denote the size of the .

Go have a look at the 'zoo', as Jeffrey Heer calls it (Heer is the creator of prefuse and Vizster). The zoo contains lots of images of layouts for high-dimensional data.

Scatterplots

Scatterplots are basic graphical devices. They are nonetheless extremely relevant, useful and well understood.

Projecting onto 2D space

We shall look at two different strategies to project high-dimensional data onto 2D space.

  • The first one is a classical (statistical) data analysis approach: Principal Components Analysis (PCA)
  • A second and different approach is quite well known and used in Information Visualization and uses different start ingredients. Because it is concerned with the dimension reduction problem, it is known as Multidimensional Scaling (MDS).

Parallel coordinates

Parallel coordinates offer an alternative to scatterplot matrix by allowing the simultaneous visualization of multiple variables of a same dataset using polylines. In a nutshell: imagine the data has been laid out in an p-dimensional space, positioning an element e = (x_1, …, x_p) at this precise position in Euclidean space. Now, project each of the unit axis onto parallel lines in the 2D planes. What you get is a parallel coordinates view of your data.

Put differently, parallel coordinates view can be realized by using parallel vertical axis (positioned at x = i) each ranging over the range of the ith variable. For each element e = (x_1, …, x_p) we draw a polyline crossing the ith axis at y = x_i.

/net/html/perso/melancon/Visual_Analytics_Course/data/pages/high-dimensional_data.txt · Last modified: 2015/10/22 09:58 by melancon