Mode-by-mode impulse responses, or spectral transfer matrix (STM) of birefringent fibers are measured by using linear optical sampling, with assist of polarization multiplexed probe pulse. By using the eigenvalue analysis of the STM, the differential mode delay and PMD vector of polarization-maintaining fiber are analyzed as a function of optical frequency over 1THz. We show that the amplitude averaging of the complex impulse responses is effective for enhancing the signal-to-noise ratio of the measurement, resulting in improving the accuracy and expanding the bandwidth of the measurement.

A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).

In the age of big data, recommendation systems provide users with fast access to interesting information, resulting to a significant commercial value. However, the extreme sparseness of user assessment data is one of the key factors that lead to the poor performance of recommendation algorithms. To address this problem, we propose a spectral clustering recommendation scheme with low-rank matrix completion and spectral clustering. Our scheme exploits spectral clustering to achieve the division of a similar user group. Meanwhile, the low-rank matrix completion is used to effectively predict un-rated items in the sub-matrix of the spectral clustering. With the real dataset experiment, the results show that our proposed scheme can effectively improve the prediction accuracy of un-rated items.

For the blind estimation of short-code direct sequence spread spectrum (DSSS) signal pseudo-noise (PN) sequences, the eigenvalue decomposition (EVD) algorithm, the singular value decomposition (SVD) algorithm and the double-periodic projection approximation subspace tracking with deflation (DPASTd) algorithm are often used to estimate the PN sequence. However, when the asynchronous time delay is unknown, the largest eigenvalue and the second largest eigenvalue may be very close, resulting in the estimated largest eigenvector being any non-zero linear combination of the really required largest eigenvector and the really required second largest eigenvector. In other words, the estimated largest eigenvector exhibits unitary ambiguity. This degrades the performance of any algorithm estimating the PN sequence from the estimated largest eigenvector. To tackle this problem, this paper proposes a spreading sequence blind estimation algorithm based on the rotation matrix. First of all, the received signal is divided into two-information-period-length temporal vectors overlapped by one-information-period. The SVD or DPASTd algorithm can then be applied to obtain the largest eigenvector and the second largest eigenvector. The matrix composed of the largest eigenvector and the second largest eigenvector can be rotated by the rotation matrix to eliminate any unitary ambiguity. In this way, the best estimation of the PN sequence can be obtained. Simulation results show that the proposed algorithm not only solves the problem of estimating the PN sequence when the largest eigenvalue and the second largest eigenvalue are close, but also performs well at low signal-to-noise ratio (SNR) values.

Link prediction, the computational problem of determining whether there is a link between two objects, is important in machine learning and data mining. Feature-based link prediction, in which the feature vectors of the two objects are given, is of particular interest because it can also be used for various identification-related problems. Although the factorization machine and the higher-order factorization machine (HOFM) are widely used for feature-based link prediction, they use feature combinations not only across the two objects but also from the same object. Feature combinations from the same object are irrelevant to major link prediction problems such as predicting identity because using them increases computational cost and degrades accuracy. In this paper, we present novel models that use higher-order feature combinations only across the two objects. Since there were no algorithms for efficiently computing higher-order feature combinations only across two objects, we derive one by leveraging reported and newly obtained results of calculating the ANOVA kernel. We present an efficient coordinate descent algorithm for proposed models. We also improve the effectiveness of the existing one for the HOFM. Furthermore, we extend proposed models to a deep neural network. Experimental results demonstrated the effectiveness of our proposed models.

Embedding efficiency is an important issue in steganography methods. Matrix embedding (1, n, h) steganography was proposed by Crandall to achieve high embedding efficiency for palette images. This paper proposes a steganography method based on multilayer matrix embedding for palette images. First, a parity assignment is provided to increase the image quality. Then, a multilayer matrix embedding (k, 1, n, h) is presented to achieve high embedding efficiency and capacity. Without modifying the color palette, hk secret bits can be embedded into n pixels by changing at most k pixels. Under the same capacity, the embedding efficiency of the proposed method is compared with that of pixel-based steganography methods. The comparison indicates that the proposed method has higher embedding efficiency than pixel-based steganography methods. The experimental results also suggest that the proposed method provides higher image quality than some existing methods under the same embedding efficiency and capacity.

Web service users are overwhelmed by the amount of information presented to them and have difficulties in finding the information that they need. Therefore, a recommendation system that predicts users' taste is an essential factor for the success of businesses. However, recommendation systems require users' personal information and can thus lead to serious privacy violations. To solve this problem, many research has been conducted about protecting personal information in recommendation systems and implementing differential privacy, a privacy protection technique that inserts noise into the original data. However, previous studies did not examine the following factors in applying differential privacy to recommendation systems. First, they did not consider the sparsity of user rating information. The total number of items is much more than the number of user-rated items. Therefore, a rating matrix created for users and items will be very sparse. This characteristic renders the identification of user patterns in rating matrixes difficult. Therefore, the sparsity issue should be considered in the application of differential privacy to recommendation systems. Second, previous studies focused on protecting user rating information but did not aim to protect the lists of user-rated items. Recommendation systems should protect these item lists because they also disclose user preferences. In this study, we propose a differentially private recommendation scheme that bases on a grouping method to solve the sparsity issue and to protect user-rated item lists and user rating information. The proposed technique shows better performance and privacy protection on actual movie rating data in comparison with an existing technique.

Time-sequence data is high dimensional and contains a lot of information, which can be utilized in various fields, such as insurance, finance, and advertising. Personal data including time-sequence data is converted to anonymized datasets, which need to strike a balance between both privacy and utility. In this paper, we consider low-rank matrix factorization as one of anonymization methods and evaluate its efficiency. We convert time-sequence datasets to matrices and evaluate both privacy and utility. The record IDs in time-sequence data are changed at regular intervals to reduce re-identification risk. However, since individuals tend to behave in a similar fashion over periods of time, there remains a risk of record linkage even if record IDs are different. Hence, we evaluate the re-identification and linkage risks as privacy risks of time-sequence data. Our experimental results show that matrix factorization is a viable anonymization method and it can achieve better utility than existing anonymization methods.

We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achieve input-output mappings with a given data set. In this paper, we propose the non-negative task matrix decomposition method, which applies non-negative matrix factorization to a trained layered neural network. This enables us to decompose the inference mechanism of a trained layered neural network into multiple principal tasks of input-output mapping, and reveal the roles of hidden units in terms of their contribution to each principal task.

A novel matrix completion ESPRIT (MC-ESPRIT) algorithm is proposed to estimate the direction of arrival (DOA) with nonuniform linear arrays (NLA). By exploiting the matrix completion theory and the characters of Hankel matrix, the received data matrix of an NLA is tranformed into a two-fold Hankel matrix, which is a treatable for matrix completion. Then the decision variable can be reconstructed by the inexact augmented Lagrange multiplier method. This approach yields a completed data matrix, which is the same as the data matrix of uniform linear array (ULA). Thus the ESPRIT-type algorithm can be used to estimate the DOA. The MC-ESPRIT could resolve more signals than the MUSIC-type algorithms with NLA. Furthermore, the proposed algorithm does not need to divide the field of view of the array compared to the existing virtual interpolated array ESPRIT (VIA-ESPRIT). Simulation results confirm the effectiveness of MC-ESPRIT.

The natural gradient descent is an optimization method for real-valued neural networks that was proposed from the viewpoint of information geometry. Here, we present an extension of the natural gradient descent to complex-valued neural networks. Our idea is to use the Hermitian extension of the Fisher information matrix. Moreover, we generalize the projected natural gradient (PRONG), which is a fast natural gradient descent algorithm, to complex-valued neural networks. We also consider the advantage of complex-valued neural networks over real-valued neural networks. A useful property of complex numbers in the complex plane is that the rotation is simply expressed by the multiplication. By focusing on this property, we construct the output function of complex-valued neural networks, which is invariant even if the input is changed to its rotated value. Then, our complex-valued neural network can learn rotated data without data augmentation. Finally, through simulation of online character recognition, we demonstrate the effectiveness of the proposed approach.

A travel route recommendation service that recommends a sequence of points of interest for tourists traveling in an unfamiliar city is a very useful tool in the field of location-based social networks. Although there are many web services and mobile applications that can help tourists to plan their trips by providing information about sightseeing attractions, travel route recommendation services are still not widely applied. One reason could be that most of the previous studies that addressed this task were based on the orienteering problem model, which mainly focuses on the estimation of a user-location relation (for example, a user preference). This assumes that a user receives a reward by visiting a point of interest and the travel route is recommended by maximizing the total rewards from visiting those locations. However, a location-location relation, which we introduce as a transition pattern in this paper, implies useful information such as visiting order and can help to improve the quality of travel route recommendations. To this end, we propose a travel route recommendation method by combining location and transition knowledge, which assigns rewards for both locations and transitions.

Detecting community structures and analyzing temporal evolution in dynamic networks are challenging tasks to explore the inherent characteristics of the complex networks. In this paper, we propose a semi-supervised evolutionary clustering model based on symmetric nonnegative matrix factorization to detect communities in dynamic networks, named sEC-SNMF. We use the results of community partition at the previous time step as the priori information to modify the current network topology, then smooth-out the evolution of the communities and reduce the impact of noise. Furthermore, we introduce a community transition probability matrix to track and analyze the temporal evolutions. Different from previous algorithms, our approach does not need to know the number of communities in advance and can deal with the situation in which the number of communities and nodes varies over time. Extensive experiments on synthetic datasets demonstrate that the proposed method is competitive and has a superior performance.

Hadamard matrix is defined as a square matrix where any components are -1 or +1, and where any pairs of rows are mutually orthogonal. In this work, we consider the similar matrix on finite field GF(p) where p is an odd prime. In such a matrix, every component is one of the integers on GF(p){0}, that is, {1,2,...,p-1}. Any additions and multiplications should be executed under modulo p. In this paper, a method to generate such matrices is proposed. In addition, the paper includes the applications to generate n-shift orthogonal sequences and complete complementary codes. The generated complete complementary code is a family of multi-valued sequences on GF(p){0}, where the number of sequence sets, the number of sequences in each sequence set and the sequence length depend on the various divisors of p-1. Such complete complementary codes with various parameters have not been proposed in previous studies.

In this letter, a construction of sparse measurement matrices is presented. Based on finite fields, a base matrix is obtained. Then a Hadamard matrix or a discrete Fourier transform (DFT) matrix is nested in the base matrix, which eventually formes a new deterministic measurement matrix. The coherence of the proposed matrices is low, which meets the Welch bound asymptotically. Thus these matrices could satisfy the restricted isometry property (RIP). Simulation results demonstrate that the proposed matrices give better performance than Gaussian counterparts.

The estimation of the matrix rank of harmonic components of a music spectrogram provides some useful information, e.g., the determination of the number of basis vectors of the matrix-factorization-based algorithms, which is required for the automatic music transcription or in post-processing. In this work, we develop an algorithm based on Stein's unbiased risk estimator (SURE) algorithm with the matrix factorization model. The noise variance required for the SURE algorithm is estimated by suppressing the harmonic component via median filtering. An evaluation performed using the MIDI-aligned piano sounds (MAPS) database revealed an average estimation error of -0.26 (standard deviation: 4.4) for the proposed algorithm.

In this letter, we investigate the separating redundancy of binary linear codes. Using analytical techniques, we provide a general lower bound on the first separating redundancy of binary linear codes and show the bound is tight for a particular family of binary linear codes, i.e., cycle codes. In other words, the first separating redundancy of cycle codes can be determined. We also derive a deterministic and constructive upper bound on the second separating redundancy of cycle codes, which is shown to be better than the general deterministic and constructive upper bounds for the codes.

This paper addresses the association problem of tracking closely spaced targets in group or formation. In the Labeled Multi-Bernoulli Filter (LMB), the weight of a hypothesis is directly affected by the distance between prediction and measurement. This may generate false associations when dealing with the closely spaced multiple targets. Thus we consider utilizing structure information among the group or formation. Since, the relative position relation of the targets in group or formation varies slightly within a short time, the targets are considered as nodes of a topological structure. Then the position relation among the targets is modeled as a hypergraph. The hypergraph matching method is used to resolve the association matrix. At last, with the structure prior information introduced, the new joint cost matrix is re-derived to generate hypotheses, and the filtering recursion is implemented in a Gaussian mixture way. The simulation results show that the proposed algorithm can effectively deal with group targets and is superior to the LMB filter in tracking precision and accuracy.

The traditional recommendation system (RS) can learn the potential personal preferences of users and potential attribute characteristics of items through the rating records between users and items to make recommendations.However, for the new items with no historical rating records,the traditional RS usually suffers from the typical cold start problem. Additional auxiliary information has usually been used in the item cold start recommendation,we further bring temporal dynamics,text and relevance in our models to release item cold start.Two new cold start recommendation models TmTx(Time,Text) and TmTI(Time,Text,Item correlation) proposed to solve the item cold start problem for different cold start scenarios.While well-known methods like TimeSVD++ and CoFactor partially take temporal dynamics,comments,and item correlations into consideration to solve the cold start problem but none of them combines these information together.Two models proposed in this paper fused features such as time,text,and relevance can effectively improve the performance under item cold start.We select the convolutional neural network (CNN) to extract features from item description text which provides the model the ability to deal with cold start items.Both proposed models can effectively improve the performance with item cold start.Experimental results on three real-world data set show that our proposed models lead to significant improvement compared with the baseline methods.