Multi-view learning accomplishes the task objectives of classification by leverag-ing the relationships between different views of the same object. Most existing methods usually focus on consistency and complementarity between multiple views. But not all of this information is useful for classification tasks. Instead, it is the specific discriminating information that plays an important role. Zhong Zhang et al. explore the discriminative and non-discriminative information exist-ing in common and view-specific parts among different views via joint non-negative matrix factorization. In this paper, we improve this algorithm on this ba-sis by using the cross entropy loss function to constrain the objective function better. At last, we implement better classification effect than original on the same data sets and show its superiority over many state-of-the-art algorithms.
Information Technologies Institute, CERTH（希腊国家研究和技术基金会信息技术研究所）
In this paper, using a novel matrix factorization and simultaneous reduction to diagonal form approach (or in short simultaneous reduction approach), Accelerated Kernel Discriminant Analysis (AKDA) and Accelerated Kernel Subclass Discriminant Analysis (AKSDA) are proposed. Specifically, instead of performing the simultaneous reduction of the between- and within-class or subclass scatter matrices, the nonzero eigenpairs (NZEP) of the so-called core matrix, which is of relatively small dimensionality, and the Cholesky factorization of the kernel matrix are computed, achieving more than one order…
Fox Chase Cancer Center, Temple University Health System（天普大学卫生系统福克斯·蔡斯癌症中心）
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. The proposed approach generalizes some existing methods for different noise structures and contrasts with the recently proposed quasi-likelihood approach, thus providing a useful alternative for non-negative matrix factorizations. A measure to evaluate the goodness-of-fit of the …
Northeastern University（东北大学）；Stevens Institute of Technology（斯蒂文斯理工学院）
Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representation. For example, in a human-face data set, if an image contains a hat on the head, the hat should be removed or the importance of its corresponding attributes should be decreased during matrix factorizing. This paper proposes a new type of NMF called entropy weighted NMF (EWNMF), which uses an optimizable weight for each attribute of each data point to emphasize thei…
Northwestern Polytechnical University（西北工业大学）；Center for Optical Imagery Analysis and Learning (OPTIMAL)（光学影像分析与学习中心）
Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal centroids by minimizing the sum of the approximation errors. However, the outliers deviating from the normal data distribution may have large residues, and then dominate the objective value seriously. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually…
A Unified MDL-based Binning and Tensor Factorization Framework for PDF Estimation
Communications Research Laboratory（通信研究中心）；Ilmenau University of Technology（伊门瑙技术大学）；School of Electrical Engineering（电气工程学院）；Tel Aviv University（特拉维夫大学）
Northeastern University（东北大学）；Stevens Institute of Technology（史蒂文斯理工学院）
Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the robustness of NMF, this paper proposes an adaptive weighted NMF, which introduces weights to emphasize the different importance of each data point, thus the algorithmic sensitivity to noisy data is decreased. It is very different from the existing robust NMFs that use a slow growth similarity measure. Specifically, two strategies are proposed to achieve this: fuzzier…
When recommending personalized top-$k$ items to users, how can we recommend the items diversely to them while satisfying their needs? Aggregately diversified recommender systems aim to recommend a variety of items across whole users without sacrificing the recommendation accuracy. They increase the exposure opportunities of various items, which in turn increase potential revenue of sellers as well as user satisfaction. However, it is challenging to tackle aggregate-level diversity with a matrix factorization (MF), one of the most common recommendation model, since skewed real world data lead t…
Northeastern University（东北大学）；Stevens Institute of Technology（史蒂文斯理工学院）
Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical applications, and redundant features can be invalid or even harmful. For example, if a camera has some sensors destroyed, then the corresponding pixels in the photos from this camera are not helpful to identify the content, which means only the subspace consisting of remaining pixels is worthy of attention. This paper proposes a new NMF method by introducing ada…
Duke University（杜克大学）；PA Consulting Group（PA咨询集团）；University College London（伦敦大学学院）
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely relate…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Shirshov Institute of Oceanology, Russian Academy of Sciences（俄罗斯科学院希尔绍夫海洋研究所）；Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences（俄罗斯科学院马尔丘克数值数学研究所）
We propose a new approach to the optimal placement of sensors for the problem of reconstructing geophysical fields from sparse measurements. Our method consists of two stages. In the first stage, we estimate the variability of the physical field as a function of spatial coordinates by approximating its information entropy through the Conditional PixelCNN network. To calculate the entropy, a new ordering of a two-dimensional data array (spiral ordering) is proposed, which makes it possible to obtain the entropy of a physical field simultaneously for several spatial scales. In the second stage, …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Research（谷歌研究院）
We introduce the Mutual Information Machine (MIM), a novel formulation of representation learning, using a joint distribution over the observations and latent state in an encoder/decoder framework. Our key principles are symmetry and mutual information, where symmetry encourages the encoder and decoder to learn different factorizations of the same underlying distribution, and mutual information, to encourage the learning of useful representations for downstream tasks. Our starting point is the symmetric Jensen-Shannon divergence between the encoding and decoding joint distributions, plus a mut…
ShanghaiTech University（上海科技大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
Knowledge distillation is a critical technique to transfer knowledge between models, typically from a large model (the teacher) to a more fine-grained one (the student). The objective function of knowledge distillation is typically the cross-entropy between the teacher and the student's output distributions. However, for structured prediction problems, the output space is exponential in size; therefore, the cross-entropy objective becomes intractable to compute and optimize directly. In this paper, we derive a factorized form of the knowledge distillation objective for structured prediction, w…
A common practice in most of deep convolutional neural architectures is to employ fully-connected layers followed by Softmax activation to minimize cross-entropy loss for the sake of classification. Recent studies show that substitution or addition of the Softmax objective to the cost functions of support vector machines or linear discriminant analysis is highly beneficial to improve the classification performance in hybrid neural networks. We propose a novel paradigm to link the optimization of several hybrid objectives through unified backpropagation. This highly alleviates the burden of ext…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Research（谷歌研究院）
We introduce the Mutual Information Machine (MIM), a probabilistic auto-encoder for learning joint distributions over observations and latent variables. MIM reflects three design principles: 1) low divergence, to encourage the encoder and decoder to learn consistent factorizations of the same underlying distribution; 2) high mutual information, to encourage an informative relation between data and latent variables; and 3) low marginal entropy, or compression, which tends to encourage clustered latent representations. We show that a combination of the Jensen-Shannon divergence and the joint ent…
