Clustered Data Distribution

The dataset consists of clusters with means µ(1),..., µ(k) and the examples in the j-th cluster are labeled by y(j). The clusters are generated as follows: we draw j ∼ U[0, 1] and x ∼ N(µ(j), σ2Id), and set y(i) = y(j). Moreover, we assume the following: µ(j) = √d for all j ∈ [k], 0 < σ ≤ maxi |h µ(i), µ(j)| ≤ 4σ√d ln(d) + 1, and k ≤ 4σ√d ln(d)+1.