A matrix factorization framework for jointly analyzing multiple nonnegative data source

Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this paper, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications–improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources.

Blind Source Separation by Nonnegative Matrix Factorization with Minimum-Volume Constraint

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method.

Nonnegative Matrix Factorization Applied to Nonlinear Speech and Image Cryptosystems

Nonnegative matrix factorization (NMF) is widely used in signal separation and image compression. Motivated by its successful applications, we propose a new cryptosystem based on NMF, where the nonlinear mixing (NLM) model with a strong noise is introduced for encryption and NMF is used for decryption. The security of the cryptosystem relies on following two facts: 1) the constructed multivariable nonlinear function is not invertible; 2) the process of NMF is unilateral, if the inverse matrix of the constructed linear mixing matrix is not nonnegative. Comparing with Lin's method (2006) that is a theoretical scheme using one-time padding in the cryptosystem, our cipher can be used repeatedly for the practical request, i.e., multitme padding is used in our cryptosystem. Also, there is no restriction on statistical characteristics of the ciphers and the plaintexts. Thus, more signals can be processed (successfully encrypted and decrypted), no matter they are correlative, sparse, or Gaussian. Furthermore, instead of the number of zero-crossing-based method that is often unstable in encryption and decryption, an improved method based on the kurtosis of the signals is introduced to solve permutation ambiguities in waveform reconstruction. Simulations are given to illustrate security and availability of our cryptosystem.

Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.

Online blind source separation using incremental nonnegative matrix factorization with volume constraint

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Spectral unmixing based on nonnegative matrix factorization with local smoothness constraint

Spectral unmixing (SU) is an emerging problem in the remote sensing image processing. Since both the endmember signatures and their abundances have nonnegative values, it is a natural choice to employ the attractive nonnegative matrix factorization (NMF) methods to solve this problem. Motivated by that the abundances are sparse, the NMF with local smoothness constraint (NMF-LSC) is proposed in this paper. In the proposed method, the smoothness constraint is utilized to impose the sparseness, instead of the traditional L1-norm which is restricted by the underlying column-sum-to-one requirement of the to the abundance matrix. Simulations show the advantages of our algorithm over the compared methods.

A matrix factorization framework for jointly analyzing multiple nonnegative data sources

Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this chapter, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications—improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources.

A fast non-smooth nonnegative matrix factorization for learning sparse representation

Nonnegative matrix factorization (NMF) is a hot topic in machine learning and data processing. Recently, a constrained version, non-smooth NMF (NsNMF), shows a great potential in learning meaningful sparse representation of the observed data. However, it suffers from a slow linear convergence rate, discouraging its applications to large-scale data representation. In this paper, a fast NsNMF (FNsNMF) algorithm is proposed to speed up NsNMF. In the proposed method, it first shows that the cost function of the derived sub-problem is convex and the corresponding gradient is Lipschitz continuous. Then, the optimization to this function is replaced by solving a proximal function, which is designed based on the Lipschitz constant and can be solved through utilizing a constructed fast convergent sequence. Due to the usage of the proximal function and its efficient optimization, our method can achieve a nonlinear convergence rate, much faster than NsNMF. Simulations in both computer generated data and the real-world data show the advantages of our algorithm over the compared methods.

Information sharing between heterogeneous uncertain reasoning models in a multi-agent environment : a case study

The issue of information sharing and exchanging is one of the most important issues in the areas of artificial intelligence and knowledge-based systems (KBSs), or even in the broader areas of computer and information technology. This paper deals with a special case of this issue by carrying out a case study of information sharing between two well-known heterogeneous uncertain reasoning models: the certainty factor model and the subjective Bayesian method. More precisely, this paper discovers a family of exactly isomorphic transformations between these two uncertain reasoning models. More interestingly, among isomorphic transformation functions in this family, different ones can handle different degrees to which a domain expert is positive or negative when performing such a transformation task. The direct motivation of the investigation lies in a realistic consideration. In the past, expert systems exploited mainly these two models to deal with uncertainties. In other words, a lot of stand-alone expert systems which use the two uncertain reasoning models are available. If there is a reasonable transformation mechanism between these two uncertain reasoning models, we can use the Internet to couple these pre-existing expert systems together so that the integrated systems are able to exchange and share useful information with each other, thereby improving their performance through cooperation. Also, the issue of transformation between heterogeneous uncertain reasoning models is significant in the research area of multi-agent systems because different agents in a multi-agent system could employ different expert systems with heterogeneous uncertain reasonings for their action selections and the information sharing and exchanging is unavoidable between different agents. In addition, we make clear the relationship between the certainty factor model and probability theory.

Variation in gametophyte dominance in populations of Chondrus verrucosus (Gigartinaceae, Rhodophyta)

We describe the abundance, including spatial and temporal variability, of phases of the isomorphic Chondrus verrucosus Mikami from Japan. Chondrus verrucosus occurred in a dense (∼90% cover) and temporally stable bed on a small, isolated rocky outcrop (Oyakoiwa) in Shizuoka Prefecture. Small vegetative fronds were always much more abundant than large vegetative and fertile fronds over the spring to late summer periods in 1999 and 2000. Over the same period, fertile carposporophytic fronds were generally more abundant than fertile tetrasporophytic fronds, and fertile male fronds appeared infrequently at low densities. Using the resorcinol-acetal test, we determined the proportion of gametophytes and tetrasporophytes in three populations of C. verrucosus: Oyakoiwa and Noroshi (Shizuoka) in the summers of 1999 and 2000 and Kamehana Point (Miyagi) in autumn 2000. All populations had a significantly higher proportion of gametophytes than tetrasporophytes in both years, although gametophytic proportions were lower at Noroshi (∼70%) than at Oyakoiwa (∼80%) and Kamehana Point (∼97%). However, examination of all isolated individuals sampled on Noroshi showed equal proportions of each phase in 1999, but gametophyte dominance (74%) in 2000. Differences in dispersal and spore production between phases are discussed as mechanisms potentially contributing to variation in gametophyte dominance.

Faster CRT-RSA Decryption towards RFID applications

In this paper we present a strategy to design the RSA parameters in such a manner so that the CRT-RSA decryption becomes more efficient than the existing methods. We achieve around 21% improvement in speed over the currently best known implementation strategy for CRT-RSA decryption with our properly chosen parameters that also helps in terms of less memory requirement. Moreover, we argue in detail the cryptographic security regarding our choice of the secret parameters.

Today's university : mimicry versus creativity

There are significant dilemmas associated with the contemporary way in which convergence to neo-liberal ideology and norms coheres to support an economic view of ‘development’ and ‘modernization’ that seriously threatens values integrity in what Samir Amin refers to as ‘peripheral’ societies. Recognizing this issue leads us to look more deeply at the problems of convergence and divergence from neo-liberal hegemony and norms when we engage issues of institutional reform and to what extent we can map out an alternative way of engaging globalization that allows the maintenance of creative values integrity and dignity. The core argument of this paper is that the problem of creativity in higher education is related to our struggle against isomorphic mimicry. If we are to challenge or ameliorate the influences of convergent isomorphism in higher education, upon what theoretical basis can we begin our discussion?