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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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. Tensor CANDECOMP PARAFAC (CP) decomposition is a powerful but computationally challenging tool in modern data analytics. In this paper, we show ways of sampling intermediate steps of alternating minimization algorithms for computing low rank tensor CP decompositions, leading to the sparse alternating least squares (SPALS) method. Specifically, we sample the the Khatri-Rao product, which arises as an intermediate object during the iterations of alternating least squares. This product captures the interactions between different tensor modes, and form the main computational bottleneck for solving many tensor related tasks. By exploiting the spectral structures of the matrix Khatri-Rao product, we provide efficient access to its statistical leverage scores. When applied to the tensor CP decomposition, our method leads to the first algorithm that runs in sublinear time per-iteration and approximates the output of deterministic alternating least squares algorithms. Empirical evaluations of this approach show significantly speedups over existing randomized and deterministic routines for performing CP decomposition. On a tensor of the size 2.4m by 6.6m by 92k with over 2 billion nonzeros formed by Amazon product reviews, our routine converges in two minutes to the same error as deterministic ALS. Tensor CANDECOMP PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results. Abstract This paper explains the multi-way decomposition method PARAFAC and its use in chemometrics. PARAFAC is a generalization of PCA to higher order arrays, but some of the characteristics of the method are quite different from the ordinary two-way case. There is no rotation problem in PARAFAC, and e.g., pure spectra can be recovered from multi-way spectral data. One cannot as in PCA estimate components successively as this will give a model with poorer fit, than if the simultaneous solution is estimated. Finally scaling and centering is not as straightforward in the multi-way case as in the two-way case. An important advantage of using multi-way methods instead of unfolding methods is that the estimated models are very simple in a mathematical sense, and therefore more robust and easier to interpret. All these aspects plus more are explained in this tutorial and an implementation in Matlab code is available, that contains most of the features explained in the text. Three examples show how PARAFAC can be used for specific problems. The applications include subjects as: Analysis of variance by PARAFAC, a five-way application of PARAFAC, PARAFAC with half the elements missing, PARAFAC constrained to positive solutions and PARAFAC for regression as in principal component regression.