Discovering Subdimensional Motifs of Different Lengths in LargeScale Multivariate Time Series Detecting repeating patterns of different lengths in time series, also called variablelength motifs, has received a great amount of attention by researchers and practitioners. Despite the significant progress that has been made in recent single dimensional variablelength motif discovery work, detecting variablelength sub dimensional motifs xe2x80x94patterns that are simultaneously occurring only in a subset of dimensions in multivariate time seriesxe2x80x94remains a difficult task. The main challenge is scalability. On the one hand, the bruteforce enumeration solution, which searches for motifs of all possible lengths, is very time consuming even in single dimensional time series. On the other hand, previous work show that indexbased fixedlength approximate motif discovery algorithms such as random projection are not suitable for detecting variablelength motifs due to memory requirement. In this paper, we introduce an approximate variablelength subdimensional motif discovery algorithm called Collaborative HIerarchy based Motif Enumeration (CHIME) to efficiently detect variablelength subdimensional motifs given a minimum motif length in largescale multivariate time series. We show that the memory cost of the approach is significantly smaller than that of random projection. Moreover, the speed of the proposed algorithm is significantly faster than that of the stateoftheart algorithms. We demonstrate that CHIME can efficiently detect meaningful variablelength subdimensional motifs in large real world multivariate time series datasets.

Matrix Profile XV: Exploiting Time Series Consensus Motifs to Find Structure in Time Series Sets In recent years the data mining community has largely coalesced around the idea that many problems in time series analytics essentially reduce to finding and then reasoning about repeated structure in time series. Existing tools can find conserved structure within a single time series (motifs) and between pairs of time series (joins). However, to date there are no tools to find repeated structure in sets of time series, an idea we call time series consensus motifs in recognition of their similarity to their discrete analogs in DNA strings. In this work we introduce a definition of time series consensus motifs and a scalable algorithm to discover them in large data collections. We further show that given this new primitive, we can solve multiple higherlevel problems in time series data mining. We demonstrate the utility of our ideas with case studies in diverse domains.