Reading through this reminded me of a WoB that seemed relavant. When looking for it I found another one along the same lines.
Though not conclusive, these suggest to me that Shards, like Allomantic metals, can be categorized into groups of four, but that isn't something inherent about the Shattering. Instead, these groupings are more what a scholar (like Khriss) would assign afterwards.
Commenting on the "opposites" idea. Using the Allomantic metals as an example, metals like iron and steel form a perfectly opposing pair (Pushing and Pulling on the same anchor will have a net zero effect), while its hard to see how tin and pewter are "opposites" (one enhances senses, the other physical strength). So analogously, some Shards, like Ruin and Preservation, are complete opposites, while others may only be "opposites" in the way that tin and pewter are.
On that note, I found an interesting tidbit in Arcanum Unbounded. In Khriss's article on the Selish System, she says:
Dominion and Devotion are opposites.