Junbin Gao

A review on applications of wavelet transform techniques in chemical analysis: 1989–1997

Abstract Starting from 1989, a new mathematical technique known as wavelet transform (WT) has been applied successfully for signal processing in chemistry. The number of publications related to the application of WT to manipulate chemical data has increased rapidly in the last 2 years from one paper being published in 1989 to 18 papers in 1996 and 41 papers in 1997. More than 70 papers were published within the period from 1989 to 1997. In these published works, WT was mainly employed for noise removal and data compression in different fields of analytical chemistry that include flow injection analysis, high performance liquid chromatography, infrared spectrometry, mass spectrometry, nuclear magnetic resonance spectrometry, ultraviolet–visible spectrometry and voltammetry. It has been employed to solve certain problems in quantum chemistry and chemical physics. In this paper, applications of the wavelet transform and its derivative wavelet packet transform (WPT) are reviewed. Research works on WT by Chinese researchers in China are also included.

Some Remarks on Kalman Filters for the Multisensor Fusion

Abstract Multisensor data fusion has found widespread application in industry and commerce. The purpose of data fusion is to produce an improved model or estimate of a system from a set of independent data sources. There are various multisensor data fusion approaches, of which Kalman filtering is one of the most significant. Methods for Kalman filter based data fusion includes measurement fusion and state fusion. This paper gives first a simple a review of both measurement fusion and state fusion, and secondly proposes two new methods of state fusion based on fusion procedures at the prediction and update level, respectively, of the Kalman filter. The theoretical derivation for these algorithms are derived. To illustrate their application, a simple example is performed to evaluate the proposed methods and compare their performance with the conventional state fusion method and measurement fusion methods.

A Probabilistic Framework for SVM Regression and Error Bar Estimation

In this paper, we elaborate on the well-known relationship between Gaussian Processes (GP) and Support Vector Machines (SVM) under some convex assumptions for the loss functions. This paper concentrates on the derivation of the evidence and error bar approximation for regression problems. An error bar formula is derived based on the ∈-insensitive loss function.

Simulated maximum likelihood method for estimating kinetic rates in gene expression

MOTIVATION Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. RESULTS In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Laplacian Regularized Low-Rank Representation and Its Applications

Low-rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest-rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low-dimensional manifolds embedded in a high-dimensional ambient space. However, the LRR method does not take into account the non-linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR). By taking advantage of the graph regularizer, our proposed method not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information in data. The extensive experimental results on image clustering, semi-supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.

Robust l1 principal component analysis and its bayesian variational inference

We introduce a robust probabilistic L1-PCA model in which the conventional gaussian distribution for the noise in the observed data was replaced by the Laplacian distribution (or L1 distribution). Due to the heavy tail characteristics of the L1 distribution, the proposed model is supposed to be more robust against data outliers. In this letter, we demonstrate how a variational approximation scheme enables effective inference of key parameters in the probabilistic L1-PCA model. As the L1 density can be expanded as a superposition of infinite number of gaussian densities, we express the L1-PCA model as a marginalized model over the superpositions. By doing so, a tractable Bayesian inference can be achieved based on the variational expectation-maximization-type algorithm.

Sensitivity analysis applied to the construction of radial basis function networks

Conventionally, a radial basis function (RBF) network is constructed by obtaining cluster centers of basis function by maximum likelihood learning. This paper proposes a novel learning algorithm for the construction of radial basis function using sensitivity analysis. In training, the number of hidden neurons and the centers of their radial basis functions are determined by the maximization of the outputs sensitivity to the training data. In classification, the minimal number of such hidden neurons with the maximal sensitivity will be the most generalizable to unknown data. Our experimental results show that our proposed sensitivity-based RBF classifier outperforms the conventional RBFs and is as accurate as support vector machine (SVM). Hence, sensitivity analysis is expected to be a new alternative way to the construction of RBF networks.

Application of the Fast Wavelet Transform Method to Compress Ultraviolet-Visible Spectra

Data compression methods based on the fast wavelet transform and the multiresolution signal decomposition algorithms were devised and applied to ultraviolet-visible absorption spectra. Wavelet functions of the Daubechies type were employed for the purpose. In addition, two data pretreatment procedures were proposed and used to cope with the side-lobe problem. The performance of these methods was evaluated by using both synthetic and experimental data. It was found that the storage space of the spectral information under study can be reduced significantly by using the suggested methods with good-quality spectra generated from the compressed data.

Subspace Clustering for Sequential Data

We propose Ordered Subspace Clustering (OSC) to segment data drawn from a sequentially ordered union of subspaces. Current subspace clustering techniques learn the relationships within a set of data and then use a separate clustering algorithm such as NCut for final segmentation. In contrast our technique, under certain conditions, is capable of segmenting clusters intrinsically without providing the number of clusters as a parameter. Similar to Sparse Subspace Clustering (SSC) we formulate the problem as one of finding a sparse representation but include a new penalty term to take care of sequential data. We test our method on data drawn from infrared hyper spectral data, video sequences and face images. Our experiments show that our method, OSC, outperforms the state of the art methods: Spatial Subspace Clustering (SpatSC), Low-Rank Representation (LRR) and SSC.

Wavelet Transform: A Method for Derivative Calculation in Analytical Chemistry

A novel method based on wavelet transform is proposed in this work for approximate derivative calculation. An approximate first derivative of an analytical signal can be expressed as the difference between the two scale coefficients C1, which were generated from any two Daubechies wavelet functions. The optimal results for both synthetic and experimental data were obtained with the use of the Daubechies wavelet functions D8 and D18. Our work demonstrated that the new method can enhance the signal-to-noise ratio at higher order derivative calculation and retain all major properties of the conventional methods.