Friday, July 26, 2013

Visualization Friday: 14 dimensions represented in 2D using MDS, Colors, and Shapes

For the last three years I've been building an Agent-based Model (ABM) of innovation ecosystems to explore how agent value systems and histories mutually influence each other.  The focus to this point has been on Producer-Consumer relationships and the Products they produce and consume.

One of my key challenges has been how to visualize changes in agent value systems as new products are introduced.  Products have surface characteristics defined as a 10-element vector of real numbers between 0 and 1.  Consumers make valuation decisions based on their perception of these 10 dimensions compared to their current "ideal type".  But they realize utility after consuming based on three "hidden" dimensions.  Adding on the dimension of consumption volume, this means I need to somehow visualize 14 dimensions in a 2D dynamic display.

The figures below show my solution.  Products are represented by black squares, while Consumer ideal points are represented by blue dots.  (There are about 200 Consumers in this simulation.)  Products that are not yet introduced are represented by hollow dark red squares.  The 10 dimensions of Product surface characteristics are reduced to 2D coordinates through Multi-Dimensional Scaling (MDS).  Therefore the 2D space is a dimensionless projection where 2D distances between points is roughly proportional to distances in the original 10 dimensions.

The three utility dimensions are represented by colored "spikes" coming off of each Product.  The length of each spike is proportional to the utility offered by that Product on that dimension.

Finally, the proportion of the Product population is represented by a dark red circle around each product (black filled square).

These two plots show the same simulation at different points in time, about 300 ticks apart, showing the effect of the introduction of several new products.  What we are looking for is patterns and trajectories of Consumer ideal points (blue dots).

Putting these all together:

  • Dots are close or distant in 2D space according to how they are perceived by Consumers based on surface characteristics.
  • Products that are close to each other in 2D space may or may not have similar utility characteristics (spikes).  This reveals the "ruggedness" of the "landscape", and thus the search difficulty faced by Consumers.
  • The circles around each product allow easy identification of popular vs unpopular products.
Initial Consumer ideal points (blue dots) after 1000 ticks, given 5 initial Products (black filled squares in center), plus one new Product (far left).  Red arrow points to a product with low utility on 3 dimensions.  -- click to see larger image.
Consumer ideal points (blue dots) after 1367 ticks, showing influence of new Product (black dot on far left).  Notice large increase in popularity of product pointed to by red arrow.  Though it has relatively low utility on all three dimensions, it is a "bridge" between products on right side and new (high utility) product on left side. -- click to see larger image.

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