In this letter, we propose a new blind source separation method, independent low-rank matrix analysis based on generalized Kullback-Leibler divergence. This method assumes a time-frequency-varying complex Poisson distribution as the source generative model, which yields convex optimization in the spectrogram estimation. The experimental evaluation confirms the proposed method's efficacy.

In 2017, Shirase proposed a variant of Elliptic Curve Method combined with Complex Multiplication method for generating certain special kinds of elliptic curves. His algorithm can efficiently factorize a given composite integer when it has a prime factor p of the form 4p=1+Dv2 for some integer v, where -D is an auxiliary input integer called a discriminant. However, there is a disadvantage that the previous method works only for restricted cases where the class polynomial associated to -D has degree at most two. In this paper, we propose a generalization of the previous algorithm to the cases of class polynomials having arbitrary degrees, which enlarges the class of composite integers factorizable by our algorithm. We also extend the algorithm to more various cases where we have 4p=t2+Dv2 and p+1-t is a smooth integer.

A light field, which is often understood as a set of dense multi-view images, has been utilized in various 2D/3D applications. Efficient light field acquisition using a coded aperture camera is the target problem considered in this paper. Specifically, the entire light field, which consists of many images, should be reconstructed from only a few images that are captured through different aperture patterns. In previous work, this problem has often been discussed from the context of compressed sensing (CS), where sparse representations on a pre-trained dictionary or basis are explored to reconstruct the light field. In contrast, we formulated this problem from the perspective of principal component analysis (PCA) and non-negative matrix factorization (NMF), where only a small number of basis vectors are selected in advance based on the analysis of the training dataset. From this formulation, we derived optimal non-negative aperture patterns and a straight-forward reconstruction algorithm. Even though our method is based on conventional techniques, it has proven to be more accurate and much faster than a state-of-the-art CS-based method.

Recommender systems (RS) exploit user ratings on items and side information to make personalized recommendations. In order to recommend the right products to users, RS must accurately model the implicit preferences of each user and the properties of each product. In reality, both user preferences and item properties are changing dynamically over time, so treating the historical decisions of a user or the received comments of an item as static is inappropriate. Besides, the review text accompanied with a rating score can help us to understand why a user likes or dislikes an item, so temporal dynamics and text information in reviews are important side information for recommender systems. Moreover, compared with the large number of available items, the number of items a user can buy is very limited, which is called the sparsity problem. In order to solve this problem, utilizing item correlation provides a promising solution. Although famous methods like TimeSVD++, TopicMF and CoFactor partially take temporal dynamics, reviews and correlation into consideration, none of them combine these information together for accurate recommendation. Therefore, in this paper we propose a novel combined model called TmRevCo which is based on matrix factorization. Our model combines the dynamic user factor of TimeSVD++ with the hidden topic of each review text mined by the topic model of TopicMF through a new transformation function. Meanwhile, to support our five-scoring datasets, we use a more appropriate item correlation measure in CoFactor and associate the item factors of CoFactor with that of matrix factorization. Our model comprehensively combines the temporal dynamics, review information and item correlation simultaneously. Experimental results on three real-world datasets show that our proposed model leads to significant improvement compared with the baseline methods.

We prove generalization error bounds of classes of low-rank matrices with some norm constraints for collaborative filtering tasks. Our bounds are tighter, compared to known bounds using rank or the related quantity only, by taking the additional L1 and L∞ constraints into account. Also, we show that our bounds on the Rademacher complexity of the classes are optimal.

Existing trajectory prediction methods suffer from the “data sparsity” and neglect “time awareness”, which leads to low accuracy. Aiming to the problem, we propose a fast time-aware sparse trajectories prediction with tensor factorization method (TSTP-TF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the original trajectory space. It resolves the sparse problem of trajectory data and makes the new trajectory space more reliable. Then, we introduce multidimensional tensor modeling into Markov model to add the time dimension. Tensor factorization is adopted to infer the missing regions transition probabilities to further solve the problem of data sparsity. Due to the scale of the tensor, we design a divide and conquer tensor factorization model to reduce memory consumption and speed up decomposition. Experiments with real dataset show that TSTP-TF improves prediction accuracy generally by as much as 9% and 2% compared to the Baseline algorithm and ESTP-MF algorithm, respectively.

This paper proposes a semi-supervised source separation method for stereophonic music signals containing multiple recorded or processed signals, where synthesized music is focused on the stereophonic music. As the synthesized music signals are often generated as linear combinations of many individual source signals and their respective mixing gains, phase or phase difference information between inter-channel signals, which represent spatial characteristics of recording environments, cannot be utilized as acoustic clues for source separation. Non-negative Tensor Factorization (NTF) is an effective technique which can be used to resolve this problem by decomposing amplitude spectrograms of stereo channel music signals into basis vectors and activations of individual music source signals, along with their corresponding mixing gains. However, it is difficult to achieve sufficient separation performance using this method alone, as the acoustic clues available for separation are limited. To address this issue, this paper proposes a Cepstral Distance Regularization (CDR) method for NTF-based stereo channel separation, which involves making the cepstrum of the separated source signals follow Gaussian Mixture Models (GMMs) of the corresponding the music source signal. These GMMs are trained in advance using available samples. Experimental evaluations separating three and four sound sources are conducted to investigate the effectiveness of the proposed method in both supervised and semi-supervised separation frameworks, and performance is also compared with that of a conventional NTF method. Experimental results demonstrate that the proposed method yields significant improvements within both separation frameworks, and that cepstral distance regularization provides better separation parameters.

In this paper, operator-based reset control for a class of nonlinear systems with unknown bounded disturbance is considered using right coprime factorization approach. In detail, firstly, for dealing with the unknown bounded disturbance of the nonlinear systems, operator-based reset control framework is proposed based on right coprime factorization. By the proposed framework, robust stability of the nonlinear systems with unknown bounded disturbance is guaranteed by using the proposed reset controller. Secondly, under the reset control framework, an optimal design scheme is discussed for minimizing the error norm based on the proposed operator-based reset controller. Finally, for conforming effectiveness of the proposed design scheme, a simulation example is given.

In this work, two new proposed NMF models are developed for facial expression recognition. They are called maximum volume constrained nonnegative matrix factorization (MV_NMF) and maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). They achieve sparseness from a larger simplicial cone constraint and the extracted features preserve the topological structure of the original images.

Nonnegative Matrix Factorization (NMF) with sparseness and smoothness constraints has attracted increasing attention. When these properties are considered, NMF is usually formulated as an optimization problem in which a linear combination of an approximation error term and some regularization terms must be minimized under the constraint that the factor matrices are nonnegative. In this paper, we focus our attention on the error measure based on the Euclidean distance and propose a new iterative method for solving those optimization problems. The proposed method is based on the Hierarchical Alternating Least Squares (HALS) algorithm developed by Cichocki et al. We first present an example to show that the original HALS algorithm can increase the objective value. We then propose a new algorithm called the Gauss-Seidel HALS algorithm that decreases the objective value monotonically. We also prove that it has the global convergence property in the sense of Zangwill. We finally verify the effectiveness of the proposed algorithm through numerical experiments using synthetic and real data.

This work presents a new approach which derives a learned data representation method through matrix factorization on the complex domain. In particular, we introduce an encoding matrix-a new representation of data-that satisfies the simplicial constraint of the projective basis matrix on the field of complex numbers. A complex optimization framework is provided. It employs the gradient descent method and computes the derivative of the cost function based on Wirtinger's calculus.

Community detection is an important task in the social network analysis field. Many detection methods have been developed; however, they provide little semantic interpretation for the discovered communities. We develop a framework based on joint matrix factorization to integrate network topology and node content information, such that the communities and their semantic labels are derived simultaneously. Moreover, to improve the detection accuracy, we attempt to make the community relationships derived from two types of information consistent. Experimental results on real-world networks show the superior performance of the proposed method and demonstrate its ability to semantically annotate communities.

Network equipment, such as routers, switches, and RADIUS servers, generate various log messages induced by network events such as hardware failures and protocol flaps. In large production networks, analyzing the log messages is crucial for diagnosing network anomalies; however, it has become challenging due to the following two reasons. First, the log messages are composed of unstructured text messages generated in accordance with vendor-specific rules. Second, network events that induce the log messages span several geographical locations, network layers, protocols, and services. We developed a method to tackle these obstacles consisting of two techniques: statistical template extraction (STE) and log tensor factorization (LTF). The former leverages a statistical clustering technique to automatically extract primary templates from unstructured log messages. The latter builds a statistical model that collects spatial-temporal patterns of log messages. Such spatial-temporal patterns provide useful insights into understanding the impact and patterns of hidden network events. We evaluate our techniques using a massive amount of network log messages collected from a large operating network and confirm that our model fits the data well. We also investigate several case studies that validate the usefulness of our method.

Existing moving object's trajectory prediction algorithms suffer from the data sparsity problem, which affects the accuracy of the trajectory prediction. Aiming to the problem, we present an Entropy-based Sparse Trajectories Prediction method enhanced by Matrix Factorization (ESTP-MF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the trajectory space. It can resolve the sparse problem of trajectory data and make the new trajectory space more reliable. Secondly, under the new trajectory space, we introduce matrix factorization into Markov models to improve the sparse trajectory prediction. It uses matrix factorization to infer transition probabilities of the missing regions in terms of corresponding existing elements in the transition probability matrix. It aims to further solve the problem of data sparsity. Experiments with a real trajectory dataset show that ESTP-MF generally improves prediction accuracy by as much as 6% and 4% compared to the SubSyn algorithm and STP-EE algorithm respectively.

Nonnegative matrix factorization (NMF) is one of the most popular machine learning tools for speech enhancement. The supervised NMF-based speech enhancement is accomplished by updating iteratively with the prior knowledge of the clean speech and noise spectra bases. However, in many real-world scenarios, it is not always possible for conducting any prior training. The traditional semi-supervised NMF (SNMF) version overcomes this shortcoming while the performance degrades. In this letter, without any prior knowledge of the speech and noise, we present an improved semi-supervised NMF-based speech enhancement algorithm combining techniques of NMF and robust principal component analysis (RPCA). In this approach, fixed speech bases are obtained from the training samples chosen from public dateset offline. The noise samples used for noise bases training, instead of characterizing a priori as usual, can be obtained via RPCA algorithm on the fly. This letter also conducts a study on the assumption whether the time length of the estimated noise samples may have an effect on the performance of the algorithm. Three metrics, including PESQ, SDR and SNR are applied to evaluate the performance of the algorithms by making experiments on TIMIT with 20 noise types at various signal-to-noise ratio levels. Extensive experimental results demonstrate the superiority of the proposed algorithm over the competing speech enhancement algorithm.

Collaborative filtering with only implicit feedbacks has become a quite common scenario (e.g. purchase history, click-through log, and page visitation). This kind of feedback data only has a small portion of positive instances reflecting the user's interaction. Such characteristics pose great challenges to dealing with implicit recommendation problems. In this letter, we take full advantage of matrix factorization and relative preference to make the recommendation model more scalable and flexible. In addition, we propose to take into consideration the concept of covisitation which captures the underlying relationships between items or users. To this end, we propose the algorithm Integrated Collaborative Filtering for Implicit Feedback incorporating Covisitation (ICFIF-C) to integrate matrix factorization and collaborative ranking incorporating the covisitation of users and items simultaneously to model recommendation with implicit feedback. The experimental results show that the proposed model outperforms state-of-the-art algorithms on three standard datasets.

In multi-view social networks field, a flexible Nonnegative Matrix Factorization (NMF) based framework is proposed which integrates multi-view relation data and feature data for community discovery. Benefit with a relaxed pairwise regularization and a novel orthogonal regularization, it outperforms the-state-of-art algorithms on five real-world datasets in terms of accuracy and NMI.

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm is developed to approximate the RLS-based online NMF algorithm with low complexity. The proposed algorithm is evaluated in terms of audio source separation, and the results show that the performance of the proposed algorithms are superior to that of the conventional online NMF algorithm with significantly reduced complexity.

In tutoring systems, students are more likely to utilize hints to assist their decisions about difficult or confusing problems. In the meanwhile, students with weaker knowledge mastery tend to choose more hints than others with stronger knowledge mastery. Hints are important assistances to help students deal with questions. Students can learn from hints and enhance their knowledge about questions. In this paper we firstly use hints alone to build a model named Hints-Model to predict student performance. In addition, matrix factorization (MF) has been prevalent in educational fields to predict student performance, which is derived from their success in collaborative filtering (CF) for recommender systems (RS). While there is another factorization method named non-negative matrix factorization (NMF) which has been developed over one decade, and has additional non-negative constrains on the factorization matrices. Considering the sparseness of the original matrix and the efficiency, we can utilize an element-based matrix factorization called regularized single-element-based NMF (RSNMF). We compared the results of different factorization methods to their combination with Hints-Model. From the experiment results on two datasets, we can find the combination of RSNMF with Hints-Model has achieved significant improvement and obtains the best result. We have also compared the Hints-Model with the pioneer approach performance factor analysis (PFA), and the outcomes show that the former method exceeds the later one.

In this paper, robust stability of nonlinear feedback systems with unknown disturbance is considered by using the operator-based right coprime factorization method. For dealing with the unknown disturbance, a new design scheme and a nonlinear controller are given. That is, robust stability of the nonlinear systems with unknown disturbance is guaranteed by combining right coprime factorization with the proposed controller. Simultaneously, adverse effects resulting from the disturbance are removed by using the proposed nonlinear operator controller. Finally, a simulation example is given to show the effectiveness of the proposed design scheme of this paper.