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Huafeng Xu

Publications and source records attributed to Huafeng Xu.

6 recordsLinked to original sources
PubMed2003

Exploring the nonlinear geometry of protein homology.

The explosion of biological data resulting from genomic and proteomic research has created a pressing need for data analysis techniques that work effectively on a large scale. An area of particular interest is the organization and visualization of large families of protein sequences. An increasingly popular approach is to embed the sequences into a low-dimensional Euclidean space in a way that preserves some predefined measure of sequence similarity. This method has been shown to produce maps that exhibit global order and continuity and reveal important evolutionary, structural, and functional relationships between the embedded proteins. However, protein sequences are related by evolutionary pathways that exhibit highly nonlinear geometry, which is invisible to classical embedding procedures such as multidimensional scaling (MDS) and nonlinear mapping (NLM). Here, we describe the use of stochastic proximity embedding (SPE) for producing Euclidean maps that preserve the intrinsic dimensionality and metric structure of the data. SPE extends previous approaches in two important ways: (1) It preserves only local relationships between closely related sequences, thus allowing the map to unfold and reveal its intrinsic dimension, and (2) it scales linearly with the number of sequences and therefore can be applied to very large protein families. The merits of the algorithm are illustrated using examples from the protein kinase and nuclear hormone receptor superfamilies.

Algorithms↗
PubMed2002

A self-organizing principle for learning nonlinear manifolds.

Modern science confronts us with massive amounts of data: expression profiles of thousands of human genes, multimedia documents, subjective judgments on consumer products or political candidates, trade indices, global climate patterns, etc. These data are often highly structured, but that structure is hidden in a complex set of relationships or high-dimensional abstractions. Here we present a self-organizing algorithm for embedding a set of related observations into a low-dimensional space that preserves the intrinsic dimensionality and metric structure of the data. The embedding is carried out by using an iterative pairwise refinement strategy that attempts to preserve local geometry while maintaining a minimum separation between distant objects. In effect, the method views the proximities between remote objects as lower bounds of their true geodesic distances and uses them as a means to impose global structure. Unlike previous approaches, our method can reveal the underlying geometry of the manifold without intensive nearest-neighbor or shortest-path computations and can reproduce the true geodesic distances of the data points in the low-dimensional embedding without requiring that these distances be estimated from the data sample. More importantly, the method is found to scale linearly with the number of points and can be applied to very large data sets that are intractable by conventional embedding procedures.

Journal Article↗
PubMedDate not supplied

A geodesic framework for analyzing molecular similarities.

A fast self-organizing algorithm for extracting the minimum number of independent variables that can fully describe a set of observations was recently described (Agrafiotis, D. K.; Xu, H. Proc. Natl. Acad. Sci.U.S.A. 2002, 99, 15869-15872). The method, called stochastic proximity embedding (SPE), attempts to generate low-dimensional Euclidean maps that best preserve the similarities between a set of related objects. Unlike conventional multidimensional scaling (MDS) and nonlinear mapping (NLM), SPE preserves only local relationships and, by doing so, reveals the intrinsic dimensionality and metric structure of the data. Its success depends critically on the choice of the neighborhood radius, which should be consistent with the local curvature of the underlying manifold. Here, we describe a procedure for determining that radius by examining the tradeoff between the stress function and the number of connected components in the neighborhood graph and show that it can be used to produce meaningful maps in any embedding dimension. The power of the algorithm is illustrated in two major areas of computational drug design: conformational analysis and diversity profiling of large chemical libraries.

Journal Article↗
PubMedDate not supplied

Conformational sampling by self-organization.

A new stochastic algorithm for conformational sampling is described. The algorithm generates molecular conformations that are consistent with a set of geometric constraints, which include interatomic distance bounds and chiral volumes derived from the molecular connectivity table. The algorithm repeatedly selects individual geometric constraints at random and updates the respective atomic coordinates toward satisfying the chosen constraint. When compared to a conventional distance geometry algorithm based on the same set of geometric constraints, our method is faster and generates conformations that are more diverse and more energetically favorable.

Algorithms↗
PubMedDate not supplied

Nearest neighbor search in general metric spaces using a tree data structure with a simple heuristic.

We present a new algorithm for nearest neighbor search in general metric spaces. The algorithm organizes the database into recursively partitioned Voronoi regions and represents these partitions in a tree. The separations between the Voronoi regions as well as the radius of each region are used with triangular inequality to derive the minimum possible distance between any point in a region and the query and to discard the region from further search if a smaller distance has already been found. The algorithm also orders the search sequence of the tree branches using the estimate of the minimum possible distance. This simple heuristic proves to considerably enhance the pruning of the search tree. The efficiency of the algorithm is demonstrated on several artificial data sets and real problems in computational chemistry.

Journal Article↗