Rui Xu

Survey of clustering algorithms

Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.

Electron tomography at 2.4-angstrom resolution

Transmission electron microscopy is a powerful imaging tool that has found broad application in materials science, nanoscience and biology. With the introduction of aberration-corrected electron lenses, both the spatial resolution and the image quality in transmission electron microscopy have been significantly improved and resolution below 0.5u2009ångströms has been demonstrated. To reveal the three-dimensional (3D) structure of thin samples, electron tomography is the method of choice, with cubic-nanometre resolution currently achievable. Discrete tomography has recently been used to generate a 3D atomic reconstruction of a silver nanoparticle two to three nanometres in diameter, but this statistical method assumes prior knowledge of the particle’s lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic-scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of an approximately ten-nanometre gold nanoparticle at 2.4-ångström resolution. Although we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified in three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic-scale resolution, but also to improve the spatial resolution and image quality in other tomography fields.

Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Microscopy has greatly advanced our understanding of biology. Although significant progress has recently been made in optical microscopy to break the diffraction-limit barrier, reliance of such techniques on fluorescent labeling technologies prohibits quantitative 3D imaging of the entire contents of cells. Cryoelectron microscopy can image pleomorphic structures at a resolution of 3–5 nm, but is only applicable to thin or sectioned specimens. Here, we report quantitative 3D imaging of a whole, unstained cell at a resolution of 50–60 nm by X-ray diffraction microscopy. We identified the 3D morphology and structure of cellular organelles including cell wall, vacuole, endoplasmic reticulum, mitochondria, granules, nucleus, and nucleolus inside a yeast spore cell. Furthermore, we observed a 3D structure protruding from the reconstructed yeast spore, suggesting the spore germination process. Using cryogenic technologies, a 3D resolution of 5–10 nm should be achievable by X-ray diffraction microscopy. This work hence paves a way for quantitative 3D imaging of a wide range of biological specimens at nanometer-scale resolutions that are too thick for electron microscopy.

Clustering Algorithms in Biomedical Research: A Review

Applications of clustering algorithms in biomedical research are ubiquitous, with typical examples including gene expression data analysis, genomic sequence analysis, biomedical document mining, and MRI image analysis. However, due to the diversity of cluster analysis, the differing terminologies, goals, and assumptions underlying different clustering algorithms can be daunting. Thus, determining the right match between clustering algorithms and biomedical applications has become particularly important. This paper is presented to provide biomedical researchers with an overview of the status quo of clustering algorithms, to illustrate examples of biomedical applications based on cluster analysis, and to help biomedical researchers select the most suitable clustering algorithms for their own applications.

Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization

In the last decade, recurrent neural networks (RNNs) have attracted more efforts in inferring genetic regulatory networks (GRNs), using time series gene expression data from microarray experiments. This is critically important for revealing fundamental cellular processes, investigating gene functions, and understanding their relations. However, RNNs are well known for training difficulty. Traditional gradient descent-based methods are easily stuck in local minima and the computation of the derivatives is also not always possible. Here, the performance of three evolutionary-swarm computation technology-based methods, known as differential evolution (DE), particle swarm optimization (PSO), and the hybrid of DE and PSO (DEPSO), in training RNNs is investigated. Furthermore, the gene networks are reconstructed via the identification of the gene interactions, which are explained through corresponding connection weight matrices. The experimental results on two data sets studied in this paper demonstrate that the DEPSO algorithm performs better in RNN training. Also, the RNN-based model can provide meaningful insight in capturing the nonlinear dynamics of genetic networks and revealing genetic regulatory interactions.

Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities

Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free-electron lasers, high harmonic generation, soft X-ray lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stages of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. The MATLAB (The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.

Multiclass Cancer Classification Using Semisupervised Ellipsoid ARTMAP and Particle Swarm Optimization with Gene Expression Data

It is crucial for cancer diagnosis and treatment to accurately identify the site of origin of a tumor. With the emergence and rapid advancement of DNA microarray technologies, constructing gene expression profiles for different cancer types has already become a promising means for cancer classification. In addition to research on binary classification such as normal versus tumor samples, which attracts numerous efforts from a variety of disciplines, the discrimination of multiple tumor types is also important. Meanwhile, the selection of genes which are relevant to a certain cancer type not only improves the performance of the classifiers, but also provides molecular insights for treatment and drug development. Here, we use Semisupervised Ellipsoid ARTMAP (ssEAM) for multiclass cancer discrimination and particle swarm optimization for informative gene selection. ssEAM is a neural network architecture rooted in Adaptive Resonance Theory and suitable for classification tasks. ssEAM features fast, stable, and finite learning and creates hyperellipsoidal clusters, inducing complex nonlinear decision boundaries. PSO is an evolutionary algorithm-based technique for global optimization. A discrete binary version of PSO is employed to indicate whether genes are chosen or not. The effectiveness of ssEAM/PSO for multiclass cancer diagnosis is demonstrated by testing it on three publicly available multiple-class cancer data sets. ssEAM/PSO achieves competitive performance on all these data sets, with results comparable to or better than those obtained by other classifiers.

A Comparison Study of Validity Indices on Swarm-Intelligence-Based Clustering

Swarm intelligence has emerged as a worthwhile class of clustering methods due to its convenient implementation, parallel capability, ability to avoid local minima, and other advantages. In such applications, clustering validity indices usually operate as fitness functions to evaluate the qualities of the obtained clusters. However, as the validity indices are usually data dependent and are designed to address certain types of data, the selection of different indices as the fitness functions may critically affect cluster quality. Here, we compare the performances of eight well-known and widely used clustering validity indices, namely, the Caliński-Harabasz index, the CS index, the Davies-Bouldin index, the Dunn index with two of its generalized versions, the I index, and the silhouette statistic index, on both synthetic and real data sets in the framework of differential-evolution-particle-swarm-optimization (DEPSO)-based clustering. DEPSO is a hybrid evolutionary algorithm of the stochastic optimization approach (differential evolution) and the swarm intelligence method (particle swarm optimization) that further increases the search capability and achieves higher flexibility in exploring the problem space. According to the experimental results, we find that the silhouette statistic index stands out in most of the data sets that we examined. Meanwhile, we suggest that users reach their conclusions not just based on only one index, but after considering the results of several indices to achieve reliable clustering structures.

Single-shot three-dimensional structure determination of nanocrystals with femtosecond X-ray free-electron laser pulses

Conventional three-dimensional (3D) structure determination methods require either multiple measurements at different sample orientations or a collection of serial sections through a sample. Here we report the experimental demonstration of single-shot 3D structure determination of an object; in this case, individual gold nanocrystals at ~5.5 nm resolution using ~10 fs X-ray free-electron laser pulses. Coherent diffraction patterns are collected from high-index-faceted nanocrystals, each struck by an X-ray free-electron laser pulse. Taking advantage of the symmetry of the nanocrystal and the curvature of the Ewald sphere, we reconstruct the 3D structure of each nanocrystal from a single-shot diffraction pattern. By averaging a sufficient number of identical nanocrystals, this method may be used to determine the 3D structure of nanocrystals at atomic resolution. As symmetry exists in many virus particles, this method may also be applied to 3D structure studies of such particles at nanometer resolution on femtosecond time scales.

Three-dimensional coordinates of individual atoms in materials revealed by electron tomography

Crystallography, the primary method for determining the 3D atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal. Here, we report, for the first time, the determination of the 3D coordinates of thousands of individual atoms and a point defect in a material by electron tomography with a precision of ∼19u2009pm, where the crystallinity of the material is not assumed. From the coordinates of these individual atoms, we measure the atomic displacement field and the full strain tensor with a 3D resolution of ∼1u2009nm(3) and a precision of ∼10(-3), which are further verified by density functional theory calculations and molecular dynamics simulations. The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics, chemistry and biology.