Biomedical subjects

Dimitris K Agrafiotis

Publications and source records attributed to Dimitris K Agrafiotis.

11 recordsLinked to original sources

PubMed2003

Stochastic proximity embedding.

We introduce stochastic proximity embedding (SPE), a novel self-organizing algorithm for producing meaningful underlying dimensions from proximity data. SPE attempts to generate low-dimensional Euclidean embeddings that best preserve the similarities between a set of related observations. The method starts with an initial configuration, and iteratively refines it by repeatedly selecting pairs of objects at random, and adjusting their coordinates so that their distances on the map match more closely their respective proximities. The magnitude of these adjustments is controlled by a learning rate parameter, which decreases during the course of the simulation to avoid oscillatory behavior. Unlike classical multidimensional scaling (MDS) and nonlinear mapping (NLM), SPE scales linearly with respect to sample size, and can be applied to very large data sets that are intractable by conventional embedding procedures. The method is programmatically simple, robust, and convergent, and can be applied to a wide range of scientific problems involving exploratory data analysis and visualization.

Journal Article↗

PubMed2003

A modified update rule for stochastic proximity embedding.

Recently, we described a fast self-organizing algorithm for embedding a set of objects into a low-dimensional Euclidean space in a way that preserves the intrinsic dimensionality and metric structure of the data [Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 15869-15872]. The method, called stochastic proximity embedding (SPE), attempts to preserve the geodesic distances between the embedded objects, and scales linearly with the size of the data set. SPE starts with an initial configuration, and iteratively refines it by repeatedly selecting pairs of objects at random, and adjusting their coordinates so that their distances on the map match more closely their respective proximities. Here, we describe an alternative update rule that drastically reduces the number of calls to the random number generator and thus improves the efficiency of the algorithm.

Algorithms↗

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↗

PubMed2002

Feature selection for structure-activity correlation using binary particle swarms.

We present a new feature selection algorithm for structure-activity and structure-property correlation based on particle swarms. Particle swarms explore the search space through a population of individuals that adapt by returning stochastically toward previously successful regions, influenced by the success of their neighbors. This method, which was originally intended for searching multidimensional continuous spaces, is adapted to the problem of feature selection by viewing the location vectors of the particles as probabilities and employing roulette wheel selection to construct candidate subsets. The algorithm is applied in the construction of parsimonious quantitative structure-activity relationship (QSAR) models based on feed-forward neural networks and is tested on three classical data sets from the QSAR literature. It is shown that the method compares favorably with simulated annealing and is able to identify a better and more diverse set of solutions given the same amount of simulation time.

Algorithms↗

PubMed2002

Combinatorial informatics in the post-genomics ERA.

The multitude of potential drug targets emerging from genome sequencing demands new approaches to drug discovery. A chemogenomics strategy, which involves the generation of small-molecule compounds that can be used both as tools to probe biological mechanisms and as leads for drug-property optimization, provides a highly parallel, industrialized solution. Key to the success of this strategy is an integrated suite of chemi-informatics applications that can allow the rapid and directed optimization of chemical compounds with drug-like properties using 'just-in-time' combinatorial chemical synthesis. An effective embodiment of this process requires new computational and data-mining tools that cover all aspects of library generation, compound selection and experimental design, and work effectively on a massive scale.

Combinatorial Chemistry Techniques↗

PubMed2002

Scalable methods for the construction and analysis of virtual combinatorial libraries.

One can distinguish between two kinds of virtual combinatorial libraries: viable and accessible . Viable libraries are relatively small in size, are assembled from readily available reagents that have been filtered by the medicinal chemist, and often have a physical counterpart. Conversely, accessible libraries can encompass millions or billions of structures, typically include all possible reagents that are in principle compatible with a particular reaction scheme, and they can never be physically synthesized in their entirety. Although the analysis of viable virtual libraries is relatively straightforward, the handling of large accessible libraries requires methods that scale well with respect to library size. In this work, we present novel, efficient and scalable techniques for the construction, analysis, and in silico screening of massive virtual combinatorial libraries.

Combinatorial Chemistry Techniques↗

PubMedDate not supplied

A fractal approach for selecting an appropriate bin size for cell-based diversity estimation.

A novel approach for selecting an appropriate bin size for cell-based diversity assessment is presented. The method measures the sensitivity of the diversity index as a function of grid resolution, using a box-counting algorithm that is reminiscent of those used in fractal analysis. It is shown that the relative variance of the diversity score (sum of squared cell occupancies) of several commonly used molecular descriptor sets exhibits a bell-shaped distribution, whose exact characteristics depend on the distribution of the data set, the number of points considered, and the dimensionality of the feature space. The peak of this distribution represents the optimal bin size for a given data set and sample size. Although box counting can be performed in an algorithmically efficient manner, the ability of cell-based methods to distinguish between subsets of different spread falls sharply with dimensionality, and the method becomes useless beyond a few dimensions.

Journal Article↗

PubMedDate not supplied

On the use of neural network ensembles in QSAR and QSPR.

Despite their growing popularity among neural network practitioners, ensemble methods have not been widely adopted in structure-activity and structure-property correlation. Neural networks are inherently unstable, in that small changes in the training set and/or training parameters can lead to large changes in their generalization performance. Recent research has shown that by capitalizing on the diversity of the individual models, ensemble techniques can minimize uncertainty and produce more stable and accurate predictors. In this work, we present a critical assessment of the most common ensemble technique known as bootstrap aggregation, or bagging, as applied to QSAR and QSPR. Although aggregation does offer definitive advantages, we demonstrate that bagging may not be the best possible choice and that simpler techniques such as retraining with the full sample can often produce superior results. These findings are rationalized using Krogh and Vedelsby's decomposition of the generalization error into a term that measures the average generalization performance of the individual networks and a term that measures the diversity among them. For networks that are designed to resist over-fitting, the benefits of aggregation are clear but not overwhelming.

Computer Simulation↗

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↗