Discrete Hashing Based Supervised Matrix Factorization for Cross-Modal Retrieval

The learning-based hashing has recently made encouraging progress in face recognition. However, most existing hashing methods disregard the discrete constraint during optimization, inducing the accumulated quantization errors. In this work, we develop an effective learning-based hashing model, namely local feature hashing with binary auto-encoder (LFH-BAE), to directly learn local binary descriptors in the Hamming space. It attempts to exploit structure factors to well reconstruct the face image from binary codes. Specifically, we first introduce a binary auto-encoder to learn a hashing function to project each face region into high-quality binary codes. Since the original problem is a tricky combinational function, we then present a softened version to decompose it into separate tractable sub-problems. Next, we propose an effective alternating algorithm based on the augmented Lagrange method (ALM) to solve these sub-problems, which helps to generate strong discriminative and excellent robust binary codes. Moreover, we utilize the discrete cyclic coordinate descent (DCC) method to optimize binary codes to reduce the loss of useful information. Lastly, we cluster and pool the obtained binary codes, and construct a histogram feature as the final face representation for each image. Extensive experimental results on four public datasets including FERET, CAS-PEAL-R1, LFW and PaSC show that our LFH-BAE is superior to most state-of-the-art face recognition algorithms.

A zero-one linear program is a global discrete optimization problem. Namely, it is a linear programming problem with zero-one variables. The real relaxation of a zero-one program is again a continuous linear programming problem. Simply, the zero-one variables are replaced by continuous variables varying between zero and one independently of each other. If the real relaxation, as a continuous problem, solved with the simplex method happens to have a zero-one optimal solution, then this particular solution is also an optimal solution of the original zero-one programming problem. Suppose that x1,…,xn are all the variables of a given zero-one linear programming problem. For convenience we introduce further variables y1,…,yn defined by y1=1−x1,…, yn=1−xn respectively. For a unified notation the variables x1,…,xn and y1,…, yn together will be denoted by z1,…,z2n. These variables will play the roles the nodes of the conflict graph Г associated with the given zero-one linear programming problem. Fixing the variables zi and zj both to be equal to one simultaneously reduces the number of variables in the problem. If the new smaller optimization problem does not have any feasible solution, then the nodes zi and zj will be connected by an edge in the graph Γ. The graph Γ simply records that there is a conflict between the assignments zi =1 and zj =1 which explains the name conflict graph. In other words the non-directed edge between the nodes zi and zj codes the fact that the inequality zi+zj≤1holds. The conflict graph was designed to generate additional constraints the so-called valid inequalities or cuts in order to expedite the solution of the zero-one linear program via its real relaxation. This particular solution strategy is aptly named the branch and cut method. It will be shown that the conflict graph besides its intended use can also be applied in another solution technique the method of implicit enumeration. We will illustrate by examples that the conflict graph provides us with rules to prune the search tree that are not offered by the commonly applied pruning rules. In addition the computations involved can easily be organized into a highly parallel computational scheme.

This article is dedicated to unifying the framework used to derive the Wiener–Hopf equations arising from some discrete and continuous wave diffraction problems. The main tools are the discrete Green’s identity and the appropriate notion of discrete normal derivative. The resulting formal analogy between the Wiener–Hopf equations allows one to effortlessly move between the discrete and continuous formulations. The validity is illustrated through several famous two-dimensional canonical diffraction problems and extended to three-dimensional problems. It is shown that the analogy preserves kernels of the Chebotarev–Daniele–Khrapkov class, which allows the solution of certain discrete problems.

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrangement-invariant class of functions; in the second one we find extremal values for the expectation of a random process with monotone trajectories at a random time. In both cases we reduce the continuous problems to their discrete counterparts. The obtained discrete problems are on the one hand interesting on their own, and on the other hand give a natural explanation of the structure of the extremal functions for the continuous problems.

Cross-modal hashing (CMH) maps heterogeneous multiple modality data into compact binary code to achieve fast and flexible retrieval across different modalities, especially in large-scale retrieval. As the data don't need a lot of manual annotation, unsupervised cross-modal hashing has a wider application prospect than supervised method. However, the existing unsupervised methods are difficult to achieve satisfactory performance due to the lack of credible supervisory information. To solve this problem, inspired by knowledge distillation, we propose a novel unsupervised Knowledge Distillation Cross-Modal Hashing method (KDCMH), which can use similarity information distilled from unsupervised method to guide supervised method. Specifically, firstly, the teacher model adopted an unsupervised distribution-based similarity hashing method, which can construct a modal fusion similarity matrix.Secondly, under the supervision of teacher model distillation information, student model can generate more discriminative hash codes. In two public datasets NUS-WIDE and MIRFLICKR-25K, extensive experiments have proved the significant improvement of KDCMH on several representative unsupervised cross-modal hashing methods.

Cross-modal hashing maps heterogeneous multimedia data into a common Hamming space to realize fast and flexible cross-modal retrieval. Supervised cross-modal hashing methods have achieved considerable progress by incorporating semantic side information. However, they heavily rely on large-scale labeled cross-modal training data which are hard to obtain, since multiple modalities are involved. They also ignore the rich information contained in the large amount of unlabeled data across different modalities, which can help to model the correlations between different modalities. To address these problems, in this paper, we propose a novel semi-supervised cross-modal hashing approach by generative adversarial network (SCH-GAN). The main contributions can be summarized as follows: 1) we propose a novel generative adversarial network for cross-modal hashing, in which the generative model tries to select margin examples of one modality from unlabeled data when given a query of another modality (e.g., giving a text query to retrieve images and vice versa). The discriminative model tries to distinguish the selected examples and true positive examples of the query. These two models play a minimax game so that the generative model can promote the hashing performance of the discriminative model and 2) we propose a reinforcement learning-based algorithm to drive the training of proposed SCH-GAN. The generative model takes the correlation score predicted by discriminative model as a reward, and tries to select the examples close to the margin to promote a discriminative model. Extensive experiments verify the effectiveness of our proposed approach, compared with nine state-of-the-art methods on three widely used datasets.

Label consistent locally linear embedding based cross-modal hashing

With the rapid development of information science and statistics, significant improvement in the ability to handle huge-sized data has been seen, including linear regression. However, traditional statistical methods remain as a problem when the number of samples is less than the rapidly increasing data dimensions and constructing a mathematical model in high-dimensional scenario may work it out. Hopefully linear regression becomes kind of solvable problem as far as singular matrix is transformed into nonsingular matrix through introduction of L2 norm as penalty term. Nevertheless, this method has to be ungraded by a new method titled ‘Lasso’ when options of variables is inaccessible to it. Coordinate descent method, alternating direction method of multipliers and proximal gradient descent method are gateways to Lasso, among others. The coordinate descent method gets the minimum value of each component on basis of L1 penalty term. Alternating direction method of multipliers the minimum value by processing decomposed objective functions separately. The proximal gradient descent method is a method of Taylor expansion at a point where initial value is selected. This paper has showed the results of simulation experiments on the three algorithms in terms of accuracy and convergence speed. It reveals that alternating direction method of multipliers, superior to the rest two both by speed and accuracy, is followed by The proximal gradient descent method, while The coordinate descent method is not equal.

Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation

The rapid development of Internet and mobile communication, smart phone, tablet computer and other mobile devices become widespread, they have become an indispensable part of life, changing the human lifestyle, way of working and learning style, it brings great convenience and fun to us. This paper mainly discusses the status of personalized recommendation system, mobile application and analyse the main problems of recommendation system. This research proposes a rising mobile application domain, which uses web crawling technique to get explicit feedback from a real-world mobile application market. The explicit feedback is the users’ ratings data on Apps and the corresponding category information. To establish a mobile application recommendation model based on user interest and categorization information and propose a novel collective matrix factorization algorithm. Through the crawled data, the improved algorithm, and the traditional collaborative. The traditional mobile application recommendation systems are mostly based on keyword search, popularity, download usage and categories, thus they do not make personalized recommendation to users, and invalid to find applications that users are interested in. Through the user’s historical behaviour, a personalized recommendation system can be established to recommend the applications that fit user’s interests effectively. This paper is based on the collective matrix factorization using user interest such as user’s ratings and category information, designs a personalized recommendation system for mobile applications by using the relationship between them.

The amount of multi-modal data available on the Internet is enormous. Cross-modal hash retrieval maps heterogeneous cross-modal data into a single Hamming space to offer fast and flexible retrieval services. However, existing cross-modal methods mainly rely on the feature-level similarity between multi-modal data and ignore the relationship between relative rankings and label-level fine-grained similarity of neighboring instances. To overcome these issues, we propose a novel <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</u> eep <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</u> ross-modal <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</u> ashing based on <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> emantic <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</u> onsistent <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> anking (DCH-SCR) that comprehensively investigates the intra-modal semantic similarity relationship. Firstly, to the best of our knowledge, it is an early attempt to preserve semantic similarity for cross-modal hashing retrieval by combining label-level and feature-level information. Secondly, the inherent gap between modalities is narrowed by developing a ranking alignment loss function. Thirdly, the compact and efficient hash codes are optimized based on the common semantic space. Finally, we use the gradient to specify the optimization direction and introduce the Normalized Discounted Cumulative Gain (NDCG) to achieve varying optimization strengths for data pairs with different similarities. Extensive experiments on three real-world image-text retrieval datasets demonstrate the superiority of DCH-SCR over several state-of-the-art cross-modal retrieval methods.

Cross-modal hashing retrieval approaches maps heterogeneous multi-modal data into a common hamming space to achieve efficient and flexible retrieval performance. However, existing cross-modal methods mainly exploit feature-level similarity between multi-modal data, the label-level similarity and relative ranking relationship between adjacent instances have been ignored. To address these problems, we propose a novel Deep Rank Cross-modal Hashing(DRCH) method that fully explores the intra-modal semantic similarity relationship. Firstly, DRCH preserves semantic similarity by combining both label-level and feature-level information. Secondly, the inherent gap between modalities are narrowed by proposing a ranking alignment loss function. Finally, the compact and efficient hash codes are optimized from the common semantic space. Extensive experiments on two real-world image-text retrieval datasets demonstrate the superiority of DRCH compared with several state-of-the-art(SOTA) methods.

For two types of non-parametric hypotheses optimum tests are derived against certain classes of alternatives. The two kinds of hypotheses are related and may be illustrated by the following example: (1) The joint distribution of the variables Xi, • • •, Xm, Yi, • • •, Yn is invariant under all permutations of the variables; (2) the variables are independently and identically distributed. It is shown that the theory of optimum tests for hypotheses of the first kind is the same as that of optimum similar tests for hypotheses of the second kind. Most powerful tests are obtained against arbitrary simple alternatives, and in a number of important cases most stringent tests are derived against certain composite alternatives. For the example (1), if the distributions are restricted to probability densities, Pitman’s test based on ȳ — x is most powerful against the alternatives that the X’s and F’s are independently normally distributed with common variance, and that E(Xi) = ξ, E(Yi) =η where η > ξ If η — ξ may be positive or negative the test based on | ȳ — x| is most stringent. The definitions are sufficiently general that the theory applies to both continuous and discrete problems, and that tied observations present no difficulties. It is shown that continuous and discrete problems may be combined. Pitman’s test for example, when applied to certain discrete problems, coincides with Fisher’s exact test, and when m = n the test based on | ȳ — x | is most stringent for hypothesis (1) against a broad class of alternatives which includes both discrete and absolutely continuous distributions.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

As the scale and dimensionality of data continue to grow in many applications of data analytics (e.g., bioinformatics, finance, computer vision, medical informatics), it becomes critical to develop efficient and effective algorithms to solve numerous machine learning and data mining problems. This tutorial will focus on simple yet practically effective techniques and algorithms for big data analytics. In the first part, we plan to present the state-of-the-art large-scale optimization algorithms, including various stochastic gradient descent methods, stochastic coordinate descent methods and distributed optimization algorithms, for solving various machine learning problems. In the second part, we will focus on randomized approximation algorithms for learning from large-scale data. We will discuss i) randomized algorithms for low-rank matrix approximation; ii) approximation techniques for solving kernel learning problems; iii) randomized reduction methods for addressing the high-dimensional challenge. Along with the description of algorithms, we will also present some empirical results to facilitate understanding of different algorithms and comparison between them.