Reading
Inselberg (Inselberg 1997) made a full review of how to visually read out parallel coords' relational patterns. When most lines between two parallel axis are somewhat parallel to each others, that suggests a positive relationship between these two dimensions. When lines cross in a kind of superposition of X-shapes, that's negative relationship. When lines cross randomly or are parallel, that show there is no particular relationship.
Read more about this topic: Parallel Coordinates
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