Matrix-Vector Nonnegative Tensor Factorization for Blind Unmixing of Hyperspectral Imagery

We have studied the feature extraction from sea ice SAR images based on non-negative factorization methods. The methods reported here are the sparseness-constrained non-negative matrix factorization (SC-NMF) and Non-negative tensor factorization (NTF). The studies performed show that these methods can be used to extract meaningful features from SAR images and that they can be used in sea ice SAR classification.

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.

This paper proposes parallel method of non-negative large sparse matrix factorization - very popular technique in computational linguistics. Proposed blocks factorization approach using Latent Dirichlet allocation, for speedup of non-negative sparse extra-large linguistic matrix and tensor factorization. The proposed method also supports the scalability of the model.

Non-negative Tensor Factorization (NTF) is a widely used technique for decomposing a non-negative value tensor into sparse and reasonably interpretable factors. However, NTF performs poorly when the tensor is extremely sparse, which is often the case with real-world data and higher-order tensors. In this paper, we propose Non-negative Multiple Tensor Factorization (NMTF), which factorizes the target tensor and auxiliary tensors simultaneously. Auxiliary data tensors compensate for the sparseness of the target data tensor. The factors of the auxiliary tensors also allow us to examine the target data from several different aspects. We experimentally confirm that NMTF performs better than NTF in terms of reconstructing the given data. Furthermore, we demonstrate that the proposed NMTF can successfully extract spatio-temporal patterns of people's daily life such as leisure, drinking, and shopping activity by analyzing several tensors extracted from online review data sets.

Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis

In recent years, multidimensional data is becoming increasingly popular in recommender systems. For example, social tagging systems encourage users to employ user-defined keywords to help manage content in a personalized way. Recommender systems built upon social tagging systems utilize social tagging data to improve recommendation accuracy. Context-aware recommender systems incorporate context information (e.g. time, location, weather, etc.) into recommendation models to make recommendations more personalized. User profiles play a crucial role in recommender systems because user profiles provide the information about users’ information needs based on which personalized recommendations can be generated. Existing user profiling techniques for collaborative filtering (CF) recommender systems based on multidimensional data mostly analyze data through splitting the multidimensional relations into lower-dimensional relations. However, this leads to the loss of multidimensionality in user-item interactions. A different type of methods for addressing multidimensional data is factorization techniques such as tensor factorization (TF), which discover holistic latent relations between all dimensions in multidimensional data. However, TF models are not constructed to analyze any particular dimension of multidimensional data. But for many application domains, certain dimensions are of particular interest such as the user dimension in recommender systems. However, user profiles are not explicitly reflected in TF models. In this paper, we propose a unified approach to profile any particular dimension in multidimensional data based on partially-decomposed Tucker models (TM). We prove that the proposed profiling approach is a compatible higher-order extension of the matrix factorization based approaches. Moreover, we prove that the proposed TM-based profiles can be updated incrementally with new data without reconstructing the entire profiles. We integrate the proposed TF-based user/item profiling approach into neighborhood-based collaborative filtering recommenders for making top-N item recommendations. Extensive experiments have been conducted using real-world social tagging datasets to demonstrate that the CF recommenders integrated with the proposed user/item profiles outperform state-of-the-art CF recommendation approaches in terms of recommendation accuracy.

The main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions.

This paper proposes a hybrid model of aspect-oriented sentiment prediction which integrates tensor factorization (TF) and sentiment utility logistic model (SULM). First, using sentiment dictionary words as seeds, the aspect or opinion words can be extended iteratively through double propagation. Accordingly, the users’ reviews could be represented as the features in user-item-aspect space, in which prediction model could be built. Various combinations of the hybrid model were proposed and evaluated on the Chinese reviews on places of interest from Trip Advisor. Experimental results show that the hybrid model can achieve better prediction performance than TF or SULM. The hybrid model also outperforms either TF or SULM while handling cold-start problem.

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.

Many real-life datasets exhibit structure in the form of physically meaningful clusters - e.g., news documents can be categorized as sports, politics, entertainment, and so on. Taking these clusters into account together with low-rank structure may yield parsimonious matrix and tensor factorization models and more powerful data analytics. Prior works made use of data-domain similarity to improve nonnegative matrix factorization. Here we are instead interested in joint low-rank factorization and latent-domain clustering; that is, in clustering the latent reduced-dimension representations of the observed entities. A unified algorithmic framework that can deal with both matrix and tensor factorization and latent clustering is proposed. Numerical results obtained from synthetic and real document data show that the proposed approach can significantly improve factor analysis and clustering accuracy.

Hyperspectral unmixing refers to a source separation problem of decomposing a hyperspectral imagery (HSI) to estimate endmembers, and their corresponding abundances. Recently, matrix-vector nonnegative tensor factorization (MV-NTF) was proposed for unmixing to avoid structure information loss, which is caused by the HSI cube unfolding in nonnegative matrix factorization (NMF)-based methods. However, MV-NTF ignores local spatial information due to directly dealing with data as a whole, meanwhile, the forceful rank constraint in low-rank tensor decomposition loses some detailed structures. Unlike MV-NTF works at the original data, the pixel-based NMF is more adaptive to learn local spatial variations. Hence, from the perspective of multi-view, itis significant to utilize the complementary advantages of MV-NTF and NMF to fully preserve the intrinsic structure information, and exploit more detailed spatial information. In this article, we propose a sparsity-constrained coupled nonnegative matrix-tensor factorization (SCNMTF) model for unmixing, wherein MV-NTF and NMF are subtly coupled by sharing endmembers and abundances. Since the representations for abundances in MV-NTF and NMF are distinct, abundance sharing is achieved indirectly by introducing an auxiliary constraint. Furthermore, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> regularizer is adopted to promote the sparsity of abundances. A series of experiments on synthetic and real hyperspectral data demonstrate the effectiveness of the proposed SCNMTF method.

Non-negative tensor factorization (NTF) is a technique for computing a parts-based representation of high-dimensional data. NTF excels at exposing latent structures in datasets, and at finding good low-rank approximations to the data. We describe an approach for computing the NTF of a dataset that relies only on iterative linear-algebra techniques and that is comparable in cost to the non-negative matrix factorization (NMF). (The better-known NMF is a special case of NTF and is also handled by our implementation.) Some important features of our implementation include mechanisms for encouraging sparse factors and for ensuring that they are equilibrated in norm. The complete MATLAB software package is available under the GPL license.

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention, as it is more challenging compared to more classical tensor models such as canonical polyadic decomposition (CPD) and Tucker decomposition (TD). This paper reports our recent results on this topic, which are based on an appropriate extension to the BTD model of our earlier rank-revealing work on low-rank matrix approximation. The idea is to impose column sparsity jointly on the factors and successively estimate the ranks as the numbers of factor columns of non-negligible magnitude, with the aid of alternating iteratively reweighted least squares (IRLS). Simulation results are reported that demonstrate the effectiveness of our method in accurately estimating both the ranks and the factors of the least squares BTD approximation.

The vehicle recognition consists of two steps; the vehicle region detection step and vehicle identification step based on the feature extracted from the detected region. Among the linear transformations, the non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) can be used in part-based representation. So we can utilize the local features of a car as a basis vector. In this paper, we propose a feature extraction using NMF and NTF suitable for the vehicle recognition, and verify the recognition rate. We show that the proposed feature is robust in the urban scene where occlusions are frequently occur.

Modeling user preferences using neural networks and tensor factorization model