Common Low-dimensional Subspace Research Articles

Dynamics-Evolution Correspondence in Protein Structures.

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

Autoweighted multi-view smooth representation preserve projection for dimensionality reduction

Over the past few decades, we have witnessed a large family of algorithms that has been designed to provide different solutions to the problem of dimensionality reduction (DR). DR is an essential tool to excavate important information from the high-dimensional data by mapping the data to a low-dimensional subspace. Even though most DR algorithms can achieve satisfactory performance for many practical applications, they fail to fully consider the information from multiple views. Therefore, how to learn the subspace for high-dimensional features by utilizing the consistency and complementary properties of multi-view features is important and challenging in the present. To tackle this problem, we propose an effective multi-view DR algorithm named multi-view smooth representation preserve projection (MvSMRP2). MvSMRP2 seeks to find a set of linear transformations to project each view features into one common low-dimensional subspace where the multi-view smooth reconstructive weights are preserved as much as possible. A pair-wise-consistent scheme is designed by fully exploiting the Hilbert–Schmidt independence criterion to maximize the dependence among different views, which can obtain one common subspace and force multiple views to learn from each other jointly. Moreover, MvSMRP2 can allocate ideal weight for each view automatically according to view importance without explicit weight definition. Finally, an iterative alternating strategy is proposed to obtain the optimal solution of MvSMRP2. Plenty of experiments on various datasets show the excellent performances of the proposed method.

Cross-view kernel collaborative representation classification for person re-identification

Currently, person re-identification (re-ID) has been applied in many public security applications. Yet owing to the big visual appearance changes of the same identity under different views, re-ID still faces many challenges. To reduce the intra-person discrepancy, extracting more power feature representations from pedestrian images is a reasonable solution. We propose a cross-view kernel collaborative representation based classification (CV-KCRC) method for person re-ID in our work. Our method aims to find more robust and discriminative feature representations that embody cross-view information to enhance the identification capability of features. We map the image features into a high dimensional feature space first and then use view-specific projection matrices to project the high dimensional features into a common low dimensional subspace. We expect that in the shared subspace the codings of same person from different views have the highest similarity and better performance can be achieved. Experiments on seven commonly used datasets reveal that our algorithm outperforms many state-of-the-art algorithms.

Dynamic community discovery via common subspace projection

Detecting communities of highly internal and low external interactions in dynamically evolving networks has become increasingly important owing to its wide applications in divers fields. Conventional solutions based on static community detection approaches treat each snapshot of dynamic networks independently, which may fragment communities in time (Aynaud T and Guillaume J L 2010 8th Int. Symp. on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (IEEE) pp 513–9), resulting in the problem of instability. In this work, we develop a novel dynamic community detection algorithm by leveraging the encoding–decoding scheme present in a succinct network representation method to reconstruct each snapshot via a common low-dimensional subspace, which can remove non-significant links and highlight the community structures, resulting in the mitigation of community instability to a large degree. We conduct experiments on simulated data and real social networking data with ground truths (GT) and compare the proposed method with several baselines. Our method is shown to be more stable without missing communities and more effective than the baselines with competitive performance. The distribution of community size in our method is more in line with the real distribution than those of the baselines at the same time.

Multiplex Cellular Communities in Multi-Gigapixel Colorectal Cancer Histology Images for Tissue Phenotyping.

In computational pathology, automated tissue phenotyping in cancer histology images is a fundamental tool for profiling tumor microenvironments. Current tissue phenotyping methods use features derived from image patches which may not carry biological significance. In this work, we propose a novel multiplex cellular community-based algorithm for tissue phenotyping integrating cell-level features within a graph-based hierarchical framework. We demonstrate that such integration offers better performance compared to prior deep learning and texture-based methods as well as to cellular community based methods using uniplex networks. To this end, we construct celllevel graphs using texture, alpha diversity and multi-resolution deep features. Using these graphs, we compute cellular connectivity features which are then employed for the construction of a patch-level multiplex network. Over this network, we compute multiplex cellular communities using a novel objective function. The proposed objective function computes a low-dimensional subspace from each cellular network and subsequently seeks a common low-dimensional subspace using the Grassmann manifold. We evaluate our proposed algorithm on three publicly available datasets for tissue phenotyping, demonstrating a significant improvement over existing state-of-the-art methods.

Supervised dictionary-based transfer subspace learning and applications for fault diagnosis of sucker rod pumping systems

Sucker rod pumping wells are systems that their operation states varies slowly. For a relatively new well, it is hard to collect all kinds of fault samples for training. Moreover, samples from different wells are not always have similar distributions, so directly using samples from other wells as the training data may hardly get good results. In this paper, a novel framework is proposed to solve the aforementioned problems. For the source data from one well and the target data from another well, a transform matrix is calculated to transfer these data into a common low dimensional subspace. In this subspace, the source data that contain all kinds of fault samples and the target data that lack some kinds of fault samples can be represented by a shared dictionary matrix. By introducing two idea regularization terms, the structure information of source data and target data are included into the dictionary learning process. So the obtained dictionary has discriminative ability. Extensive experiments are conducted to evaluate the effectiveness of the proposed method.

Flexible Multi-View Dimensionality Co-Reduction.

Dimensionality reduction aims to map the high-dimensional inputs onto a low-dimensional subspace, in which the similar points are close to each other and vice versa. In this paper, we focus on unsupervised dimensionality reduction for the data with multiple views, and propose a novel method, called Multi-view Dimensionality co-Reduction. Our method flexibly exploits the complementarity of multiple views during the dimensionality reduction and respects the similarity relationships between data points across these different views. The kernel matching constraint based on Hilbert-Schmidt Independence Criterion enhances the correlations and penalizes the disagreement of different views. Specifically, our method explores the correlations within each view independently, and maximizes the dependence among different views with kernel matching jointly. Thus, the locality within each view and the consistence between different views are guaranteed in the subspaces corresponding to different views. More importantly, benefiting from the kernel matching, our method need not depend on a common low-dimensional subspace, which is critical to reduce the influence of the unbalanced dimensionalities of multiple views. Specifically, our method explicitly produces individual low-dimensional projections for individual views, which could be applied for new coming data in the out-of-sample manner. Experiments on both clustering and recognition tasks demonstrate the advantages of the proposed method over the state-of-the-art approaches.

Super-Resolution of Complex Exponentials From Modulations With Unknown Waveforms

Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex exponentials from their modulations with unknown waveforms, allowing for non-stationary blind super-resolution. This problem, however, is ill-posed since both the parameters associated with the complex exponentials and the modulating waveforms are unknown. To alleviate this, we assume that the unknown waveforms live in a common low-dimensional subspace. Using a lifting trick, we recast the blind super-resolution problem as a structured low-rank matrix recovery problem. Atomic norm minimization is then used to enforce the structured low-rankness, and is reformulated as a semidefinite program that is solvable in polynomial time. We show that, up to scaling ambiguities, exact recovery of both of the complex exponential parameters and the unknown waveforms is possible when the waveform subspace is random and the number of measurements is proportional to the number of degrees of freedom in the problem. Numerical simulations support our theoretical findings, showing that non-stationary blind super-resolution using atomic norm minimization is possible.

Multi-view Sparsity Preserving Projection for dimension reduction

In the past decade, we have witnessed a surge of interests of learning a low-dimensional subspace for dimension reduction (DR). However, facing with features from multiple views, most DR methods fail to integrate compatible and complementary information from multi-view features to construct low-dimensional subspace. Meanwhile, multi-view features always locate in different dimensional spaces which challenges multi-view subspace learning. Therefore, how to learn one common subspace which can exploit information from multi-view features is of vital importance but challenging. To address this issue, we propose a multi-view sparse subspace learning method called Multi-view Sparsity Preserving Projection (MvSPP) in this paper. MvSPP seeks to find a set of linear transforms to project multi-view features into one common low-dimensional subspace where multi-view sparse reconstructive weights are preserved as much as possible. Therefore, MvSPP can avoid incorrect sparse correlations which are caused by the global property of sparse representation from one single view. A co-regularization scheme is designed to integrate multi-view features to seek one common subspace which is consistent across multiple views. An iterative alternating strategy is presented to obtain the optimal solution of MvSPP. Various experiments on multi-view datasets show the excellent performance of this novel method.

Factor analysis of auto-associative neural networks with application in speaker verification.

Auto-associative neural network (AANN) is a fully connected feed-forward neural network, trained to reconstruct its input at its output through a hidden compression layer, which has fewer numbers of nodes than the dimensionality of input. AANNs are used to model speakers in speaker verification, where a speaker-specific AANN model is obtained by adapting (or retraining) the universal background model (UBM) AANN, an AANN trained on multiple held out speakers, using corresponding speaker data. When the amount of speaker data is limited, this adaptation procedure may lead to overfitting as all the parameters of UBM-AANN are adapted. In this paper, we introduce and develop the factor analysis theory of AANNs to alleviate this problem. We hypothesize that only the weight matrix connecting the last nonlinear hidden layer and the output layer is speaker-specific, and further restrict it to a common low-dimensional subspace during adaptation. The subspace is learned using large amounts of development data, and is held fixed during adaptation. Thus, only the coordinates in a subspace, also known as i-vector, need to be estimated using speaker-specific data. The update equations are derived for learning both the common low-dimensional subspace and the i-vectors corresponding to speakers in the subspace. The resultant i-vector representation is used as a feature for the probabilistic linear discriminant analysis model. The proposed system shows promising results on the NIST-08 speaker recognition evaluation (SRE), and yields a 23% relative improvement in equal error rate over the previously proposed weighted least squares-based subspace AANNs system. The experiments on NIST-10 SRE confirm that these improvements are consistent and generalize across datasets.

Joint covariate selection and joint subspace selection for multiple classification problems

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ? 2 norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.