Sparse Data Analysis Strategy for Neural Spike Classification

Table 1

Criteria of arrangement used within the framework of the clustering one-mode.

Type	Criterion to optimize depending on the dissimilarity matrix 𝐷={𝑑𝑖𝑗}𝑖,𝑗∈{1,…,𝑛}
Structural criteria	𝐶1=^𝑛𝑛𝑖=1𝑗=1𝑑𝑖𝑗|𝑖−𝑗|^2
	𝐶2=^𝑛𝑛𝑖=1𝑗=1(𝑑𝑖𝑗−𝛼|𝑖−𝑗|^2)
	𝐶3=^𝑛−2𝑖=1^𝑛−1𝑛𝑗=𝑖+1𝑘=𝑗+1(𝑑𝑖𝑗−𝛼|𝑖−𝑗|^2)
	𝐶4=1≤𝑖<𝑗<𝑘≤𝑛𝑓(𝑑𝑖𝑘,𝑑𝑖𝑗)+1≤𝑖<𝑗<𝑘≤𝑛𝑓(𝑑𝑘𝑗,𝑑𝑖𝑗) with
	𝑓(𝑥,𝑦)=sign(𝑥−𝑦)
	𝑓(𝑥,𝑦)==|𝑥−𝑦|sign(𝑥−𝑦)
	𝑓(𝑥,𝑦)=𝕀𝑥>𝑦
	𝑓(𝑥,𝑦)=|𝑥−𝑦|𝕀𝑥>𝑦
	𝐶5=^𝑛−1𝑛𝑗=𝑖+1𝑘=𝑗+1|𝑑𝑖𝑗−𝑑𝑖,𝑗+1|
Similarity criteria	𝐶6=^𝑛𝑖,𝑗=1𝑑𝑖𝑗(𝑑𝑖,𝑗−1+𝑑𝑖,𝑗+1+𝑑𝑖+1,𝑗+𝑑𝑖−1,𝑗)
	𝐶7=^𝑛𝑖,𝑗=1𝑓𝑖𝑗 with
	𝑓𝑖,𝑗=^min(𝑛,𝑖+1)𝑘=max(1,𝑖−1)^min(𝑛,𝑗+1)=max(𝑖,𝑗−1)(𝑑𝑖𝑗−𝑑𝑘)^2
	𝑓𝑖,𝑗=^min(𝑛,𝑖+1)𝑘=max(1,𝑖−1)(𝑑𝑖𝑗−𝑑𝑘𝑗)^2+^min(𝑛,𝑗+1)=max(𝑖,𝑗−1)(𝑑𝑖𝑗−𝑑𝑖)^2