Nowadays, most streaming data sources are becoming high dimensional. Accordingly, subspace stream clustering, which aims at finding evolving clusters within subgroups of dimensions, has gained a significant importance. However, in spite of the rich literature of subspace and projected clustering algorithms on static data, only three stream projected algorithms are available. Additionally, existing subspace clustering evaluation measures are mainly designed for static data, and cannot reflect the quality of the evolving nature of data streams. On the other hand, available stream clustering evaluation measures care only about the errors of the full-space clustering but not the quality of subspace clustering. In this article we present a method for designing new stream subspace and projected algorithms. We propose also, to the first of our knowledge, the first subspace clustering measure that is designed for streaming data, called SubCMM: Subspace Cluster Mapping Measure. SubCMM is an effective evaluation measure for stream subspace clustering that is able to handle errors caused by emerging, moving, or splitting subspace clusters. Additionally, we propose a novel method for using available offline subspace clustering measures for data streams over the suggested new algorithms within the Subspace MOA framework.