components only contain noise variables. Then, whether those variables are grouped correctly or kept in one big component does not affect the performance of the component lasso as long as the noisy components are excluded.]{} In order to focus on how the signal variables are split, we use the misclassification measure from on the signal variables only: $$M(C,T)=\frac{ \sum_{i>i'}|I_C(i,i')-I_T(i,i')| }{{n \choose 2}} ,$$ where C is the partition of points, T corresponds to the true clustering, and $I()$ is an indicator function for whether the clustering places i and i’ in the same cluster. The measure quantifies the misclassification of signal variables over all signal pairs. It can be seen from the tables that the component lasso method favors splitting the predictors into clusters with low misclassification rate. The true number of components, which corresponds to the number of diagonal blocks in the covariance matrix used to generate the data, is indicated by a \*.

  **Number of Components**   1\*   3      5      7
  -------------------------- ----- ------ ------ ----
  **Number of Datasets**     38    26     21     15
  **Mis. Rate**              0     0.60   0.86   1

  : ***Example 1:** Optimal NOC and misclassification rate of the signal variables.*

  **N. of Components**   1      2\*   3      4      5      