Opinion to ponder… “ Since we are a visual species (especially the American culture), because of our educational system. Many of the tools currently used to educate children are graphic in nature. We teach them words by showing them pictures of things. We teach them to count by showing them the order that numbers fall. Therefore, our visual receptors are heightened at the expense of other cognitive functions. I have also found that business people respond better to graphs and charts than they do to numbers.” by Professor Hossein Arsham from University of Baltimore

“ MultiDimensional Detective” Alfred Inselberg, Multidimensional Graphs Ltd A presentation by Margaret Ellis

“ do not let the picture intimidate you ”

Parallel Coordinates multi-dimensional information equally spaced parallel axes varying scales on axes Point  Line duality

DEMO

The Point Line Duality Taken from: Process Improvement Laboratory’s Overview Of Parallel Coordinates (University of Florida)

Inselberg’s Data VLSI chip production –yield (% of useful chips) –quality –10 types of defects –4 physical parameters Objective: Raise the yield and maintain quality. Conclusion: Small amounts of certain defects actually helped accomplish the objective!

Inselberg’s Data Demonstrating Interior Point Algorithm Outputs of a country’s economic sectors –output of 5 industries –output of the government –output of miscellaneous spending –resulting GNP A feasible economic policy can be visualized by interactively varying the chosen first variable, points interior to the region satisfy the constraints.

Advantages Multi-dimensional data can be visualized in two dimensions with low complexity. Each variable is treated uniformly. Relations within multi-dimensional data can be discovered (“data mining”). Because of its visual cues, can serve as a preprocessor to other methods.

Disadvantages Close axes as dimensions increase. Clutter can reduce information perceived. Varying axes scale, although indicating relationships, may cause confusion. Connecting the data points can be misleading.

DISADVANTAGE: LEVEL OF CLUTTER Taken from: “Hierarchical Parallel Coordinates” Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward 16,384 records in 5 dimensions causes over-plotting.

DISADVANTAGE: Connecting Data Points TAKEN FROM: “THE ANALYSIS OF T48 LOW PRESSURE TURBINE INLET TEMPERATURES USING PARALLEL COORDINATES” By Frank S. Budny X-longitude Y-latitude Z- height

User Tasks and Metrics User performance for discovering relations among multiple variables should be increased. User performance for discovering relations between two variables may be decreased. Learnability can be low without proper geometrical understanding. Error rate for the experienced user is probably similar to other representations.

Do use parallel coordinates With multidimensional data! When looking for relationships! If occlusion would occur in 3-D. For geometrical structures such as a Convex Hypersurface in 20-D.

Do use parallel coordinates With an interior point algorithm to –analyze trade-off –discover sensitivities –understand the impact of constraints –optimize

Do not use parallel coordinates when… the user doesn’t understand them. querying multidimensional data. other methods are better for user objective –Glyphs? –Chernoff faces? –Star Coordinates? –Worlds within Worlds? –Table Lens?

DEALING WITH CLUTTER: “ The deepest opacity is a function of the density of a cluster, defined as the ratio.” Improvement: SUMMARIZATION Taken from: “Hierarchical Parallel Coordinates” Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward.

Which is better? A.B.

Improvement: MANIPULATION Taken from: “Hierarchical Parallel Coordinates” Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward Extent Scaling –the thickness of the bands is varied Structure-Based Brushing –localizing a subspace Drill-down and Roll-up – increasing and decreasing detail Dimension zooming – magnification or distortion Dynamic masking –interactively fade out nodes

Goals of development Low representational complexity Works for any N(number of dimensions) Every variable is treated uniformly Displayed object can be recognized under projective transformations(i.e. rotation, translation, scaling, perspective) Easily/intuitively conveys information Methodology is based on rigourous mathematical and algorithmic results