  An operator tuple $\mathbf{T}=(T_{1},\ldots,T_{n})$ is called strongly
irreducible (SI), if the joint commutant of $\mathbf{T}$ does not any
nontrivial idempotent operator. In this paper, we study the uniqueness of
finitely strong irreducible decomposition of operator tuples up to similarity
by $K$-theory of operator algebra, and give the algebraically similarity
invariants of the Cowen-Douglas tuple with index 1 by using $K_{0}$-group of
the commutant of operator tuples. As an application, we calculate
$K_{0}$-groups of some multiplier algebras, and describe the similarity of
backwards multishifts on Drury-Arveson space by means of inflation theory.
