Monitoring high-dimensional data streams has become increasingly important for real-time detection of abnormal activities in many applications. The challenges associated with designing an efficient change-detection scheme for high-dimensional processes when clustering or spatial information exists are yet to be well addressed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the traditional detection procedure. We propose a design-adaptive testing procedure to utilize the clustering information when only a limited number of variables can be accessed or observed at each time. Under mild conditions, we derive an optimal sampling strategy with which the proposed test possesses asymptotically and locally best power under alternatives. Then, a sequential change-detection procedure is proposed by integrating this test with the generalized likelihood ratio approach. Benefiting from dynamically estimating the optimal design, the proposed procedure is able to improve the detection sensitivity of existing procedures. Its advantages are demonstrated in numerical simulations and a real data example.