  We consider a problem of multiclass classification, where the training sample
$S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb P(Y = m | X
= x) = \eta_m(x)$, $1 \leq m \leq M$, and $\eta_1(x), \dots, \eta_M(x)$ are
unknown $\alpha$-Holder continuous functions.Given a test point $X$, our goal
is to predict its label. A widely used $\mathsf k$-nearest-neighbors classifier
constructs estimates of $\eta_1(X), \dots, \eta_M(X)$ and uses a plug-in rule
for the prediction. However, it requires a proper choice of the smoothing
parameter $\mathsf k$, which may become tricky in some situations. In our
solution, we fix several integers $n_1, \dots, n_K$, compute corresponding
$n_k$-nearest-neighbor estimates for each $m$ and each $n_k$ and apply an
aggregation procedure. We study an algorithm, which constructs a convex
combination of these estimates such that the aggregated estimate behaves
approximately as well as an oracle choice. We also provide a non-asymptotic
analysis of the procedure, prove its adaptation to the unknown smoothness
parameter $\alpha$ and to the margin and establish rates of convergence under
mild assumptions.
