RESUMEN
In machine learning, it is common to interpret each data sample as a multivariate vector disregarding the correlations among covariates. However, the data may actually be functional, i.e., each data point is a function of some variable, such as time, and the function is discretely sampled. The naive treatment of functional data as traditional multivariate data can lead to poor performance due to the correlations. In this article, we focus on subspace clustering for functional data or curves and propose a new method robust to shift and rotation. The idea is to define a function or curve and all its versions generated by shift and rotation as an equivalent class and then to find the subspace structure among all equivalent classes as the surrogate for all curves. Experimental evaluation on synthetic and real data reveals that this method massively outperforms prior clustering methods in both speed and accuracy when clustering functional data.
RESUMEN
BACKGROUND: In response to increases in methamphatemine-associated sexually transmitted diseases, the San Francisco Department of Public Health implemented a contingency management (CM) field program called the Positive Reinforcement Opportunity Project (PROP). METHODS: Methamphetamine-using men who have sex with men (MSM) in San Francisco qualified for PROP following expressed interest in the program, provision of an observed urine sample that tested positive for methamphetamine metabolites and self-report of recent methamphetamine use. For 12 weeks, PROP participants provided observed urine samples on Mondays, Wednesdays and Fridays and received vouchers of increasing value for each consecutive sample that tested negative to metabolites of methamphetamine. Vouchers were exchanged for goods and services that promoted a healthy lifestyle. No cash was provided. Primary outcomes included acceptability (number of enrollments/time), impact (clinical response to treatment and cost-effectiveness as cost per patient treated). RESULTS: Enrollment in PROP was brisk indicating its acceptability. During the first 10 months of operation, 143 men sought treatment and of these 77.6% were HIV-infected. Of those screened, 111 began CM treatment and averaged 15 (42%) methamphetamine-free urine samples out of a possible 36 samples during the 12-week treatment period; 60% completed 4 weeks of treatment; 48% 8 weeks and 30% 12 weeks. Across all participants, an average of $159 (SD = $165) in vouchers or 35.1% of the maximum possible ($453) was provided for these participants. The average cost per participant of the 143 treated was $800. CONCLUSION: Clinical responses to CM in PROP were similar to CM delivered in drug treatment programs, supporting the adaptability and effectiveness of CM to non-traditional drug treatment settings. Costs were reasonable and less than or comparable to other methamphetamine outpatient treatment programs. Further expansion of programs like PROP could address the increasing need for acceptable, feasible and cost-effective methamphetamine treatment in this group with exceptionally high rates of HIV-infection.