arXiv subjects

Zhang Yi

Publications and source records attributed to Zhang Yi.

36 records · Page 2Linked to original sources

arXiv2018

Evolving Unsupervised Deep Neural Networks for Learning Meaningful Representations

Deep Learning (DL) aims at learning the \emph{meaningful representations}. A meaningful representation refers to the one that gives rise to significant performance improvement of associated Machine Learning (ML) tasks by replacing the raw data as the input. However, optimal architecture design and model parameter estimation in DL algorithms are widely considered to be intractable. Evolutionary algorithms are much preferable for complex and non-convex problems due to its inherent characteristics of gradient-free and insensitivity to local optimum. In this paper, we propose a computationally economical algorithm for evolving \emph{unsupervised deep neural networks} to efficiently learn \emph{meaningful representations}, which is very suitable in the current Big Data era where sufficient labeled data for training is often expensive to acquire. In the proposed algorithm, finding an appropriate architecture and the initialized parameter values for a ML task at hand is modeled by one computational efficient gene encoding approach, which is employed to effectively model the task with a large number of parameters. In addition, a local search strategy is incorporated to facilitate the exploitation search for further improving the performance. Furthermore, a small proportion labeled data is utilized during evolution search to guarantee the learnt representations to be meaningful. The performance of the proposed algorithm has been thoroughly investigated over classification tasks. Specifically, error classification rate on MNIST with $1.15\%$ is reached by the proposed algorithm consistently, which is a very promising result against state-of-the-art unsupervised DL algorithms.

cs.NE↗

arXiv2017

Deep Sparse Subspace Clustering

In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data affinity matrix by simultaneously satisfying the sparsity principle of SSC and the nonlinearity given by neural networks. One of the appealing advantages brought by DSSC is: when original real-world data do not meet the class-specific linear subspace distribution assumption, DSSC can employ neural networks to make the assumption valid with its hierarchical nonlinear transformations. To the best of our knowledge, this is among the first deep learning based subspace clustering methods. Extensive experiments are conducted on four real-world datasets to show the proposed DSSC is significantly superior to 12 existing methods for subspace clustering.

cs.CV↗

arXiv2017

Locally linear representation for image clustering

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme and linear representation based scheme. Most existing works have only involved one of the above schemes and suffered from some limitations. Specifically, pairwise distance based methods are sensitive to the noises and outliers compared with linear representation based methods. On the other hand, there is the possibility that linear representation based algorithms wrongly select inter-subspaces points to represent a point, which will degrade the performance. In this paper, we propose an algorithm, called Locally Linear Representation (LLR), which integrates pairwise distance with linear representation together to address the problems. The proposed algorithm can automatically encode each data point over a set of points that not only could denote the objective point with less residual error, but also are close to the point in Euclidean space. The experimental results show that our approach is promising in subspace learning and subspace clustering.

cs.LG↗

arXiv2017

Subspace clustering using a symmetric low-rank representation

In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can simultaneously recover the dimension and members of each subspace. LRRSC extends the original low-rank representation algorithm by integrating a symmetric constraint into the low-rankness property of high-dimensional data representation. The symmetric low-rank representation, which preserves the subspace structures of high-dimensional data, guarantees weight consistency for each pair of data points so that highly correlated data points of subspaces are represented together. Moreover, it can be efficiently calculated by solving a convex optimization problem. We provide a rigorous proof for minimizing the nuclear-norm regularized least square problem with a symmetric constraint. The affinity matrix for spectral clustering can be obtained by further exploiting the angular information of the principal directions of the symmetric low-rank representation. This is a critical step towards evaluating the memberships between data points. Experimental results on benchmark databases demonstrate the effectiveness and robustness of LRRSC compared with several state-of-the-art subspace clustering algorithms.

cs.CV↗

arXiv2016

Automatic Subspace Learning via Principal Coefficients Embedding

In this paper, we address two challenging problems in unsupervised subspace learning: 1) how to automatically identify the feature dimension of the learned subspace (i.e., automatic subspace learning), and 2) how to learn the underlying subspace in the presence of Gaussian noise (i.e., robust subspace learning). We show that these two problems can be simultaneously solved by proposing a new method (called principal coefficients embedding, PCE). For a given data set $\mathbf{D}\in \mathds{R}^{m\times n}$, PCE recovers a clean data set $\mathbf{D}_{0}\in \mathds{R}^{m\times n}$ from $\mathbf{D}$ and simultaneously learns a global reconstruction relation $\mathbf{C}\in \mathbf{R}^{n\times n}$ of $\mathbf{D}_{0}$. By preserving $\mathbf{C}$ into an $m^{\prime}$-dimensional space, the proposed method obtains a projection matrix that can capture the latent manifold structure of $\mathbf{D}_{0}$, where $m^{\prime}\ll m$ is automatically determined by the rank of $\mathbf{C}$ with theoretical guarantees. PCE has three advantages: 1) it can automatically determine the feature dimension even though data are sampled from a union of multiple linear subspaces in presence of the Gaussian noise, 2) Although the objective function of PCE only considers the Gaussian noise, experimental results show that it is robust to the non-Gaussian noise (\textit{e.g.}, random pixel corruption) and real disguises, 3) Our method has a closed-form solution and can be calculated very fast. Extensive experimental results show the superiority of PCE on a range of databases with respect to the classification accuracy, robustness and efficiency.

cs.CV↗

arXiv2016

Connections Between Nuclear Norm and Frobenius Norm Based Representations

A lot of works have shown that frobenius-norm based representation (FNR) is competitive to sparse representation and nuclear-norm based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this paper, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption, 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.

cs.CV↗

arXiv2015

Discriminating cosmic muon and x-ray based on rising time using GEM detector

Gas electron multiplier(GEM) detector is used in Cosmic Muon Scattering Tomography and neutron imaging in the last decade. In this work, a triple GEM device with an effective readout area of 10 cm X 10 cm is developed, and an experiment of discriminating between cosmic muon and x-ray based on rising time is tested. The energy resolution of GEM detector is tested by 55Fe ray source to prove the GEM detector has a good performance. The analysis of the complete signal-cycles allows to get the rising time and pulse heights. The experiment result indicates that cosmic muon and x-ray can be discriminated with an appropriate rising time threshold.

physics.ins-det↗

arXiv2015

A Unified Framework for Representation-based Subspace Clustering of Out-of-sample and Large-scale Data

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and $\ell_2$-norm-based representation, and have achieved state-of-the-art performance. However, these methods have suffered from the following two limitations. First, the time complexities of these methods are at least proportional to the cube of the data size, which make those methods inefficient for solving large-scale problems. Second, they cannot cope with out-of-sample data that are not used to construct the similarity graph. To cluster each out-of-sample datum, the methods have to recalculate the similarity graph and the cluster membership of the whole data set. In this paper, we propose a unified framework which makes representation-based subspace clustering algorithms feasible to cluster both out-of-sample and large-scale data. Under our framework, the large-scale problem is tackled by converting it as out-of-sample problem in the manner of "sampling, clustering, coding, and classifying". Furthermore, we give an estimation for the error bounds by treating each subspace as a point in a hyperspace. Extensive experimental results on various benchmark data sets show that our methods outperform several recently-proposed scalable methods in clustering large-scale data set.

cs.LG↗

arXiv2015

Fast Low-rank Representation based Spatial Pyramid Matching for Image Classification

Spatial Pyramid Matching (SPM) and its variants have achieved a lot of success in image classification. The main difference among them is their encoding schemes. For example, ScSPM incorporates Sparse Code (SC) instead of Vector Quantization (VQ) into the framework of SPM. Although the methods achieve a higher recognition rate than the traditional SPM, they consume more time to encode the local descriptors extracted from the image. In this paper, we propose using Low Rank Representation (LRR) to encode the descriptors under the framework of SPM. Different from SC, LRR considers the group effect among data points instead of sparsity. Benefiting from this property, the proposed method (i.e., LrrSPM) can offer a better performance. To further improve the generalizability and robustness, we reformulate the rank-minimization problem as a truncated projection problem. Extensive experimental studies show that LrrSPM is more efficient than its counterparts (e.g., ScSPM) while achieving competitive recognition rates on nine image data sets.

cs.CV↗

arXiv2015

Symmetric low-rank representation for subspace clustering

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative singular value decomposition in some existing low-rank representation based algorithms, the symmetric low-rank representation in the SLRR method can be calculated as a closed form solution by solving the symmetric low-rank optimization problem. By making use of the angular information of the principal directions of the symmetric low-rank representation, an affinity graph matrix is constructed for spectral clustering. Extensive experimental results show that it outperforms state-of-the-art subspace clustering algorithms.

cs.CV↗

arXiv2015

Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering

Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intra-subspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that $\ell_1$-, $\ell_2$-, $\ell_{\infty}$-, and nuclear-norm based linear projection spaces share the property of Intra-subspace Projection Dominance (IPD), i.e., the coefficients over intra-subspace data points are larger than those over inter-subspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-Graph. The subspace clustering and subspace learning algorithms are developed upon L2-Graph. Experiments show that L2-Graph algorithms outperform the state-of-the-art methods for feature extraction, image clustering, and motion segmentation in terms of accuracy, robustness, and time efficiency.

cs.CV↗

arXiv2014

A linear calibration method on DNL error for energy spectrum

A calibration method aimed for the differential nonlinearity (DNL) error of the Low Energy X-ray Instrument (LE) onboard the Hard X-ray Modulation Telescope (HXMT) is presented, which is independent with electronic systems used as testing platform and is only determined by the analog-to-digital converter (ADC) itself. Exploring this method, ADCs that are used within the flight model phase of HXMT-LE can be calibrated individually and independently by a non-destructive and low-cost way, greatly alleviating the complexity of the problem. As a result, the performance of the energy spectrum can be significantly improved, further more, noise reduced and resolution enhanced.

astro-ph.IM↗

arXiv2013

Calibration of pulse transit time through a cable for EAS experiments

In ground-based extensive air shower experiments, the direction and energy are reconstructed by measuring the relative arrival time of secondary particles, and the energy they deposit. The measurement precision of the arrival time is crucial for determination of the angular resolution. For this purpose, we need to obtain a precise relative time offset for each detector, and to apply the calibration process. The time offset is associated with the photomultiplier tube, cable, relevant electronic circuits, etc. In view of the transit time through long cables being heavily dependent on the ambient temperature, a real-time calibration method for the cable transit time is investigated in this paper. Even with a poor-resolution time-to-digital converter, this method can achieve high precision. This has been successfully demonstrated with the Front-End-Electronic board used in the Daya Bay neutrino experiment.

astro-ph.IM↗

arXiv2013

Infinite Horizon Optimal Impulsive Control Theory with Application to Internet Congestion Control

We develop Bellman equation based approach for infinite time horizon optimal impulsive control problems. Both discounted and time average criteria are considered. We establish very general and at the same time natural conditions under which a canonical control triplet produces an optimal feedback policy. Then, we apply our general results for Internet congestion control providing a convenient setting for the design of active queue management algorithms. In particular, our general theoretical results suggest a simple threshold-based active queue management scheme which takes into account the main parameters of the transmission control protocol.

cs.NI↗

arXiv2013

Measurements of Charge Transfer Efficiency in a Proton-irradiated Swept Charge Device

Charge Coupled Devices (CCDs) have been successfully used in several low energy X-ray astronomical satellite over the past two decades. Their high energy resolution and high spatial resolution make them an perfect tool for low energy astronomy, such as formation of galaxy clusters and environment of black holes. The Low Energy X-ray Telescope (LE) group is developing Swept Charge Device (SCD) for the Hard X-ray Modulation Telescope (HXMT) satellite. SCD is a special low energy X-ray CCD, which could be read out a thousand times faster than traditional CCDs, simultaneously keeping excellent energy resolution. A test method for measuring the charge transfer efficiency (CTE) of a prototype SCD has been set up. Studies of the charge transfer inefficiency (CTI) have been performed at a temperature range of operation, with a proton-irradiated SCD.

astro-ph.IM↗

arXiv2013

Learning Locality-Constrained Collaborative Representation for Face Recognition

The model of low-dimensional manifold and sparse representation are two well-known concise models that suggest each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by preserving some expected local geometric structures from the original space to a low-dimensional one. The structures are generally determined by using pairwise distance, e.g., Euclidean distance. Alternatively, sparse representation denotes a data point as a linear combination of the points from the same subspace. In practical applications, however, the nearby points in terms of pairwise distance may not belong to the same subspace, and vice versa. Consequently, it is interesting and important to explore how to get a better representation by integrating these two models together. To this end, this paper proposes a novel coding algorithm, called Locality-Constrained Collaborative Representation (LCCR), which improves the robustness and discrimination of data representation by introducing a kind of local consistency. The locality term derives from a biologic observation that the similar inputs have similar code. The objective function of LCCR has an analytical solution, and it does not involve local minima. The empirical studies based on four public facial databases, ORL, AR, Extended Yale B, and Multiple PIE, show that LCCR is promising in recognizing human faces from frontal views with varying expression and illumination, as well as various corruptions and occlusions.

cs.CV↗

arXiv2013

Inductive Sparse Subspace Clustering

Sparse Subspace Clustering (SSC) has achieved state-of-the-art clustering quality by performing spectral clustering over a $\ell^{1}$-norm based similarity graph. However, SSC is a transductive method which does not handle with the data not used to construct the graph (out-of-sample data). For each new datum, SSC requires solving $n$ optimization problems in O(n) variables for performing the algorithm over the whole data set, where $n$ is the number of data points. Therefore, it is inefficient to apply SSC in fast online clustering and scalable graphing. In this letter, we propose an inductive spectral clustering algorithm, called inductive Sparse Subspace Clustering (iSSC), which makes SSC feasible to cluster out-of-sample data. iSSC adopts the assumption that high-dimensional data actually lie on the low-dimensional manifold such that out-of-sample data could be grouped in the embedding space learned from in-sample data. Experimental results show that iSSC is promising in clustering out-of-sample data.

cs.LG↗

arXiv2012

Markov Processes with Restart

We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such processes comes from modeling human and animal mobility patterns, restart processes in communication protocols, and from application of restarting random walks in information retrieval. We provide a connection between the transition probability functions of the original Markov process and the modified process with restarts. We give closed-form expressions for the invariant probability measure of the modified process. When the process evolves on the Euclidean space there is also a closed-form expression for the moments of the modified process. We show that the modified process is always positive Harris recurrent and exponentially ergodic with the index equal to (or bigger than) the rate of restarts. Finally, we illustrate the general results by the standard and geometric Brownian motions.

math.PR↗