Sign is related to Nod. Nod is a type of Gesture. Gesture is related to Raise. Raise is related to Increased. 
Improved is similar to Better. Best is etymologically related to Better. Best is related to Achievement. 
Sign <--RelatedTo--> Nod --IsA--> Gesture <--RelatedTo--> Raise <--RelatedTo--> Increased 
Improved <--SimilarTo--> Better <--EtymologicallyRelatedTo-- Best <--RelatedTo--> Achievement 