How intrusive does a life-saving user-monitoring application really need to be? While most previous research was focused on analyzing mental state of users from social media and smartphones, there is little effort towards protecting user privacy in these analyses. A challenge in analyzing user behaviors is that not only is the data multi-dimensional with a myriad of user activities but these activities occur at varying temporal rates. The overarching question of our work is: Given a set of sensitive user features, what is the minimum amount of information required to group users with similar behavior? Furthermore, does this user behavior correlate with their mental state? Towards answering those questions, our contributions are two fold: we introduce the concept of privacy surfaces that combine sensitive user data at different levels of intrusiveness. As our second contribution, we introduce MIMiS, an unsupervised privacy-aware framework that clusters users in a given privacy surface configuration to homogeneous groups with respect to their temporal signature. In addition, we explore the trade-off between intrusiveness and prediction accuracy. MIMiS employs multi-set decomposition in order to deal with incompatible temporal granularities in user activities. We extensively evaluate MIMiS on real data. Across a variety of privacy surfaces, MIMiS identified groups that are highly homogeneous with respect to self-reported mental health scores. Finally, we conduct an in-depth exploration of the discovered clusters, identifying groups whose behavior is consistent with academic deadlines.
@cite_14 presented the most recent survey of tensors, algorithms and its applications. The most efficient algorithm for PARAFAC2 appeared in @cite_28 . @cite_31 used CP decomposition to discover low-dimensional structures in smartphone data and found studying, partying and academic deadline patterns in college students. Multi-set analysis and PARAFAC2 have been used very successfully in Chemometrics @cite_16 because it allows the joint analysis of chemical measurements that may contain time shifts. @cite_13 used PARAFAC2 to analyze a set of term-document matrices of the same documents for different languages; Because each language has a different set of terms used, it is beneficial to jointly analyze the data into a common reduced dimension. Most recent work uses multi-set mining @cite_25 to for mining electronic health records of patients and deriving time-evolving phenotypes.
@cite_14 @cite_28 @cite_31 @cite_16 @cite_13 @cite_25
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Tensors and tensor decompositions are very powerful and versatile tools that can model a wide variety of heterogeneous, multiaspect data. As a result, tensor decompositions, which extract useful latent information out of multiaspect data tensors, have witnessed increasing popularity and adoption by the data mining community. In this survey, we present some of the most widely used tensor decompositions, providing the key insights behind them, and summarizing them from a practitioner’s point of view. We then provide an overview of a very broad spectrum of applications where tensors have been instrumental in achieving state-of-the-art performance, ranging from social network analysis to brain data analysis, and from web mining to healthcare. Subsequently, we present recent algorithmic advances in scaling tensor decompositions up to today’s big data, outlining the existing systems and summarizing the key ideas behind them. Finally, we conclude with a list of challenges and open problems that outline exciting future research directions. In recent years, the rapid growth in technology has increased the opportunity for longitudinal human behavioral studies. Rich multimodal data, from wearables like Fitbit, online social networks, mobile phones etc. can be collected in natural environments. Uncovering the underlying low-dimensional structure of noisy multi-way data in an unsupervised setting is a challenging problem. Tensor factorization has been successful in extracting the interconnected low-dimensional descriptions of multi-way data. In this paper, we apply non-negative tensor factorization on a real-word wearable sensor data, StudentLife, to find latent temporal factors and group of similar individuals. Meta data is available for the semester schedule, as well as the individuals' performance and personality. We demonstrate that non-negative tensor factorization can successfully discover clusters of individuals who exhibit higher academic performance, as well as those who frequently engage in leisure activities. The recovered latent temporal patterns associated with these groups are validated against ground truth data to demonstrate the accuracy of our framework. SUMMARY This paper offers an approach for handling retention time shifts in resolving chromatographic data using the PARAFAC2 model. In Part I of this series an algorithm for PARAFAC2 was developed and extended toN-way arrays. It was discussed that the PARAFAC2 model has a number of attractive features. It is unique under mild conditions though it puts fewer restrictions on the data than the well-known PARAFAC1 model. This has important implications for the modeling of chromatographic data in which retention time shifts can be regarded as a violation of the assumption of parallel proportional profiles underlying the PARAFAC1 model. The PARAFAC2 model does not assume parallel proportional elution profiles, but only that the matrix of elution profiles preserve its ‘inner-product structure’ from sample to sample. This means that the cross-products of the matrix holding the elution profiles in its columns remain constant. Here an application using chromatographic separation based on the molecular size of thick juice samples from the beet sugar industry illustrates the benefit of using the PARAFAC2 model. Copyright © 1999 John Wiley & Sons, Ltd. A standard approach to cross-language information retrieval (CLIR) uses Latent Semantic Analysis (LSA) in conjunction with a multilingual parallel aligned corpus. This approach has been shown to be successful in identifying similar documents across languages - or more precisely, retrieving the most similar document in one language to a query in another language. However, the approach has severe drawbacks when applied to a related task, that of clustering documents "language-independently", so that documents about similar topics end up closest to one another in the semantic space regardless of their language. The problem is that documents are generally more similar to other documents in the same language than they are to documents in a different language, but on the same topic. As a result, when using multilingual LSA, documents will in practice cluster by language, not by topic. We propose a novel application of PARAFAC2 (which is a variant of PARAFAC, a multi-way generalization of the singular value decomposition [SVD]) to overcome this problem. Instead of forming a single multilingual term-by-document matrix which, under LSA, is subjected to SVD, we form an irregular three-way array, each slice of which is a separate term-by-document matrix for a single language in the parallel corpus. The goal is to compute an SVD for each language such that V (the matrix of right singular vectors) is the same across all languages. Effectively, PARAFAC2 imposes the constraint, not present in standard LSA, that the "concepts" in all documents in the parallel corpus are the same regardless of language. Intuitively, this constraint makes sense, since the whole purpose of using a parallel corpus is that exactly the same concepts are expressed in the translations. We tested this approach by comparing the performance of PARAFAC2 with standard LSA in solving a particular CLIR problem. From our results, we conclude that PARAFAC2 offers a very promising alternative to LSA not only for multilingual document clustering, but also for solving other problems in cross-language information retrieval. In exploratory tensor mining, a common problem is how to analyze a set of variables across a set of subjects whose observations do not align naturally. For example, when modeling medical features across a set of patients, the number and duration of treatments may vary widely in time, meaning there is no meaningful way to align their clinical records across time points for analysis purposes. To handle such data, the state-of-the-art tensor model is the so-called PARAFAC2, which yields interpretable and robust output and can naturally handle sparse data. However, its main limitation up to now has been the lack of efficient algorithms that can handle large-scale datasets. In this work, we fill this gap by developing a scalable method to compute the PARAFAC2 decomposition of large and sparse datasets, called SPARTan. Our method exploits special structure within PARAFAC2, leading to a novel algorithmic reformulation that is both faster (in absolute time) and more memory-efficient than prior work. We evaluate SPARTan on both synthetic and real datasets, showing 22X performance gains over the best previous implementation and also handling larger problem instances for which the baseline fails. Furthermore, we are able to apply SPARTan to the mining of temporally-evolving phenotypes on data taken from real and medically complex pediatric patients. The clinical meaningfulness of the phenotypes identified in this process, as well as their temporal evolution over time for several patients, have been endorsed by clinical experts.