Fast DTT

Tensors are higher order generalizations of matrices to model multi-aspect data, e.g., a set of purchase records with the schema (user_id, product_id, timestamp, feedback). Tensor factorization is a powerful technique for generating a model from a tensor, just like matrix factorization generates a model from a matrix, but with higher accuracy and richer information as more attributes are available in a higher- order tensor than a matrix. The data model obtained by tensor factorization can be used for classification, recommendation, anomaly detection, and so on. Though having a broad range of applications, tensor factorization has not been popularly applied compared with matrix factorization that has been widely used in recommender systems, mainly due to the high computational cost and poor scalability of existing tensor factorization methods. Efficient and scalable tensor factorization is particularly challenging because real world tensor data are mostly sparse and massive. In this paper, we propose a novel distributed algorithm, called Lock-Free Tensor Factorization (LFTF), which significantly improves the efficiency and scalability of distributed tensor factorization by exploiting asynchronous execution in a re-formulated problem. Our experiments show that LFTF achieves much higher CPU and network throughput than existing methods, converges at least 17 times faster and scales to much larger datasets.

In the recent years, researchers have developed a surge of interest in the identification and analysis of the communities in complex heterogeneous social networks. Mining latent community structure in such networks is an arduous task owing to the multiple relations among the users. In this article, a multi-relational network is modeled as a tensor and then tensor factorization is performed to obtain the hidden features of the data. Based on the revealed inherent features of the data, clustering is applied to discover topically meaningful communities. The purpose of this study is to comparatively investigate the performance of various tensor factorization and clustering techniques. Experimental evaluation is conducted on synthetic as well as real world datasets and statistical tests are conducted to further validate the results.

With the development of Service-Oriented technologies, the amount of Web services grows rapidly. QoS-Aware Web service recommendation can help service users to design more efficient service-oriented systems. However, existing methods assume the QoS information for service users are all known and accurate, but in real case, there are always many missing QoS values in history records, which increase the difficulty of the missing QoS value prediction. By considering the user-service-time three dimension context information, we study a Temporal QoS-Aware Web Service Recommendation Framework which aims to recommend best candidates to service user's requirements and meanwhile improve the QoS prediction accuracy. We propose to envision such QoS value data as a tensor which is known as multi-way array, and formalize this problem as a tensor factorization model and propose a Tucker decomposition (TD)algorithm which is able to deal with the triadic relations of user-service-time model. However, one major challenge is that how to deal with the dynamic incoming service QoS value data streams. Thus, we introduce the incremental tensor factorization (ITF)method which is (a) scalable, (b) space efficient (it does not need to store the past data). Extensive experiments are conductedbasedc on our real-world QoS dataset collected on Planet-Lab, comprised of service invocation response-time values from 408 users on 5,473 Web services at 240 time periods. Comprehensive empirical studies demonstrate that our approach is faster and more accuracy than other approaches.

Facial images change appearance due to multiple factors such as poses, lighting variations, facial expressions, etc. Tensor approach, an extension of conventional matrix, is appropriate to analyze facial factors since tensors make it possible to construct multilinear models using a multiple factor structure. We use higher-order tensors to model multiple factors of facial variations, but this provides some difficulty in use. First, it is difficult to decompose the multiple factors of a test image, especially when the factor parameters are unknown or are not in the training set. Second, for face recognition and face synthesis tasks, it is also difficult to construct reliable multilinear models which have more than two factors. In this paper, we propose a novel tensor factorization method to decompose mixing factors for unseen test images. We set up tensor factorization problem as a least squares problems with a quadratic equality constraint, and solve it using numerical optimization techniques. The novelty in our approach compared to previous work is that our tensor factorization method does not require any knowledge or assumption of test images; we can attain parameters of facial factors by our tensor factorization method. We have conducted several experiments to show the versatility of the method for both face recognition and synthesis tasks. Thus, we demonstrate the proposed method produces reliable results for trilinear models as well as bilinear models.

Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stacking the spectral responses of the pixels into an observed matrix. Therefore, various constrained NMF methods are developed to impose spectral structure, spatial structure, and spectral-spatial joint structure into NMF to enforce the estimated endmembers and abundances preserve these structures. Compared with matrix format, the third-order tensor is more natural to represent a hyperspectral data cube as a whole, by which the intrinsic structure of hyperspectral imagery can be losslessly retained. Extended from NMF-based methods, a matrix-vector nonnegative tensor factorization (NTF) model is proposed in this paper for spectral unmixing. Different from widely used tensor factorization models, such as canonical polyadic decomposition CPD) and Tucker decomposition, the proposed method is derived from block term decomposition, which is a combination of CPD and Tucker decomposition. This leads to a more flexible frame to model various application-dependent problems. The matrix-vector NTF decomposes a third-order tensor into the sum of several component tensors, with each component tensor being the outer product of a vector (endmember) and a matrix (corresponding abundances). From a formal perspective, this tensor decomposition is consistent with linear spectral mixture model. From an informative perspective, the structures within spatial domain, within spectral domain, and cross spectral-spatial domain are retreated interdependently. Experiments demonstrate that the proposed method has outperformed several state-of-the-art NMF-based unmixing methods.

In this paper, we introduce a novel approach based on Tucker Decomposition and quasi-periodic nature of ECG signal for fetal ECG extraction from abdominal ECG mixture. We adapt variable periodicity constraint of the ECG components to main objective function of the Tucker Decomposition and shape it to matrix form in order to simply optimize the objective function. We form a 3rd order tensor by stacking the mixed multichannel ECG and reconstructed fetal and maternal subspaces using BSS methods in order to have the benefit of further artificial observations, and apply our proposed penalized decomposition on it. The proposed method is evaluated on synthetic and real datasets using the criteria Signal to Interference plus Noise Ratio (SINR) for fetal component considering mother component as interference. Results and evaluations show a superior SINR improvement of 1 to 4 dB compared to other state of the art methods.

Tensor dynamic neighborhood preserving embedding algorithm for fault diagnosis of batch process

Coupled tensor factorization methods are useful for sensor fusion, combining information from several related datasets by simultaneously approximating them by products of latent tensors. In these methods, the choice of a suitable optimization criteria becomes difficult as observed datasets may have different statistical characteristics and their relative importance for the task at hand can vary. In this paper, we present an algorithmic framework for coupled factorization that, while estimating a latent factorization also estimates a specific ß-divergence for each dataset as well as the relative weights in an overall additive cost function. We evaluate the proposed method on both synthetical and real datasets, where we apply our methods on a link prediction problem. The results show that our method outperforms the state-of-the-art by a significant margin.

The low-rank tensor factorization (LRTF) technique has received increasing attention in many computer vision applications. Compared with the traditional matrix factorization technique, it can better preserve the intrinsic structure information and thus has a better low-dimensional subspace recovery performance. Basically, the desired low-rank tensor is recovered by minimizing the least square loss between the input data and its factorized representation. Since the least square loss is most optimal when the noise follows a Gaussian distribution, -norm-based methods are designed to deal with outliers. Unfortunately, they may lose their effectiveness when dealing with real data, which are often contaminated by complex noise. In this paper, we consider integrating the noise modeling technique into a generalized weighted LRTF (GWLRTF) procedure. This procedure treats the original issue as an LRTF problem and models the noise using a mixture of Gaussians (MoG), a procedure called MoG GWLRTF. To extend the applicability of the model, two typical tensor factorization operations, i.e., CANDECOMP/PARAFAC factorization and Tucker factorization, are incorporated into the LRTF procedure. Its parameters are updated under the expectation-maximization framework. Extensive experiments indicate the respective advantages of these two versions of MoG GWLRTF in various applications and also demonstrate their effectiveness compared with other competing methods.

Given a high-dimensional large-scale tensor, how can we decompose it into latent factors? Can we process it on commodity computers with limited memory? These questions are closely related to recommender systems, which have modeled rating data not as a matrix but as a tensor to utilize contextual information such as time and location. This increase in the dimension requires tensor factorization methods scalable with both the dimension and size of a tensor. In this paper, we propose two distributed tensor factorization methods, SALS and CDTF. Both methods are scalable with all aspects of data, and they show an interesting trade-off between convergence speed and memory requirements. SALS updates a subset of the columns of a factor matrix at a time, and CDTF, a special case of SALS, updates one column at a time. In our experiments, only our methods factorize a 5-dimensional tensor with 1 billion observable entries, 10M mode length, and 1K rank, while all other state-of-the-art methods fail. Moreover, our methods require several orders of magnitude less memory than our competitors. We implement our methods on MapReduce with two widely-applicable optimization techniques: local disk caching and greedy row assignment. They speed up our methods up to 98.2X and also the competitors up to 5.9X.

Many kinds of real-world multi-way signal, like color images, videos, etc., are represented in tensor form and may often be corrupted by outliers. To recover an unknown signal tensor corrupted by outliers, tensor robust principal component analysis (TRPCA) serves as a robust tensorial modification of the fundamental PCA. Recently, a successful TRPCA model based on the tubal nuclear norm (TNN) (Lu et al. in IEEE Trans Pattern Anal Mach Intell 42:925–938, 2019) has attracted much attention thanks to its superiority in many applications. However, TNN is computationally expensive due to the requirement of full singular value decompositions, seriously limiting its scalability to large tensors. To address this issue, we propose a new TRPCA model which adopts a factorization strategy. Algorithmically, an algorithm based on the non-convex augmented Lagrangian method is developed with convergence guarantee. Theoretically, we rigorously establish the sub-optimality of the proposed algorithm. We also extend the proposed model to the robust tensor completion problem. Both the effectiveness and efficiency of the proposed algorithm is demonstrated through extensive experiments on both synthetic and real data sets.

Tensor Ring decomposition for context-aware recommendation

Big data produced in our life implies rich information and can help us better understand the world when used correctly. However, the data collected is always too sparse to be directly applied. Tensor factorization as an extension of matrix factorization has been more and more popular on data mining. The classical methods for tensor factorization are all for dense tensors, which is no longer efficient for sparse data tensor. The most-used factorization method for sparse tensor also exists some problems, such as long convergence time, low fitting precision, complex parameter settings and so on. In this paper, we propose an adaptive stochastic gradient descent method, called RMSGD for N-dimensional tensor factorization to deal with data sparsity problem and predict the missing values in a sparse tensor precisely. We evaluate our method based on two real data sets, i.e., the GPS trajectories generated by 2000 taxis in Beijing and the 311 complaint data collected from New York City (NYC). The results demonstrate that the effectiveness and efficiency of our method are better than the baseline approaches.

In recommender systems user preferences can be fairly dynamic, as users tend to exploit a wide range of items and modify their tastes accordingly over time. In this paper, we model user-item interactions over time using a tensor that has time as a dimension (mode). To account for the fact that user preferences change individually, we propose a new measure of user-preference dynamics (UPD) that captures the rate with which the current preferences of each user have been shifted. UPD shows the variability in how users interact with items in recommender systems. We generate recommendations based on a tensor factorization technique, where the importance of past user preferences are weighted according to their UPD values, that is, higher UPD values downweigh more past user preferences. Additionally, we exploit users’ side data, such as demographics, which improve the accuracy of recommendations based on a coupled tensor-matrix factorization scheme. Our empirical evaluation uses two real benchmark datasets from the social media platforms Last.fm and MovieLens, containing users’ history records pertaining to listening to songs and viewing movies, respectively. We demonstrate that in both datasets, there are users with a varying level of dynamics, expressed by the UPD metric. Our experimental results show that the proposed method outperforms several baselines, by taking into account both dynamics and side data of users.

In order to achieve best neutron flux-mapping within nuclear research reactors, we investigate in this paper, the application of blind source separation algorithms to extract different independent components that form the fission chamber output signals. More specifically, we simulated the fission chamber using python-based of Fission Chambers (pyFC) code suite. The resulting simulated signals are considered observation vectors. They are then, processed via nonnegative matrix and tensor factorization (NMF&NTF) methods to isolate the independent components that form a neutron signal. Thus, in order to select the most efficient one to analyze our set of data, various algorithms have been tested and classified according to their performance index of separability (PI). The extracted independent components have been used to characterize neutron signal through spectrogram time-frequency representation. Obtained results will be illustrated and discussed.