Brijnesh J. Jain

Central Clustering of Attributed Graphs

Partitioning a data set of attributed graphs into clusters arises in different application areas of structural pattern recognition and computer vision. Despite its importance, graph clustering is currently an underdeveloped research area in machine learning due to the lack of theoretical analysis and the high computational cost of measuring structural proximities. To address the first issue, we introduce the concept of metric graph spaces that enables central (or center-based) clustering algorithms to be applied to the domain of attributed graphs. The key idea is to embed attributed graphs into Euclidean space without loss of structural information. In addressing the second issue of computational complexity, we propose a neural network solution of the K-means algorithm for structures (KMS). As a distinguishing feature to improve the computational time, the proposed algorithm classifies the data graphs according to the principle of elimination of competition where the input graph is assigned to the winning model of the competition. In experiments we investigate the behavior and performance of the neural KMS algorithm.

Users and noise: the magic barrier of recommender systems

Recommender systems are crucial components of most commercial web sites to keep users satisfied and to increase revenue. Thus, a lot of effort is made to improve recommendation accuracy. But when is the best possible performance of the recommender reached? The magic barrier, refers to some unknown level of prediction accuracy a recommender system can attain. The magic barrier reveals whether there is still room for improving prediction accuracy, or indicates that any further improvement is meaningless. In this work, we present a mathematical characterization of the magic barrier based on the assumption that user ratings are afflicted with inconsistencies - noise. In a case study with a commercial movie recommender, we investigate the inconsistencies of the user ratings and estimate the magic barrier in order to assess the actual quality of the recommender system.

A maximum common subgraph kernel method for predicting the chromosome aberration test.

The chromosome aberration test is frequently used for the assessment of the potential of chemicals and drugs to elicit genetic damage in mammalian cells in vitro. Due to the limitations of experimental genotoxicity testing in early drug discovery phases, a model to predict the chromosome aberration test yielding high accuracy and providing guidance for structure optimization is urgently needed. In this paper, we describe a machine learning approach for predicting the outcome of this assay based on the structure of the investigated compound. The novelty of the proposed method consists in combining a maximum common subgraph kernel for measuring the similarity of two chemical graphs with the potential support vector machine for classification. In contrast to standard support vector machine classifiers, the proposed approach does not provide a black box model but rather allows to visualize structural elements with high positive or negative contribution to the class decision. In order to compare the performance of different methods for predicting the outcome of the chromosome aberration test, we compiled a large data set exhibiting high quality, reliability, and consistency from public sources and configured a fixed cross-validation protocol, which we make publicly available. In a comparison to standard methods currently used in pharmaceutical industry as well as to other graph kernel approaches, the proposed method achieved significantly better performance.

On the sample mean of graphs

We present an analytic and geometric view of the sample mean of graphs. The theoretical framework yields efficient subgradient methods for approximating a structural mean and a simple plug-in mechanism to extend existing central clustering algorithms to graphs. Experiments in clustering protein structures show the benefits of the proposed theory.

Joining softassign and dynamic programming for the contact map overlap problem

Comparison of 3-dimensional protein folds is a core problem in molecular biology. The Contact Map Overlap (CMO) scheme provides one of the most common measures for protein structure similarity. Maximizing CMO is, however, NP-hard. To approximately solve CMO, we combine softassign and dynamic programming. Softassign approximately solves the maximum common subgraph (MCS) problem. Dynamic programming converts the MCS solution to a solution of the CMO problem. We present and discuss experiments using proteins with up to 1500 residues. The results indicate that the proposed method is extremely fast compared to other methods, scales well with increasing problem size, and is useful for comparing similar protein structures.

Molecule Kernels: A Descriptor- and Alignment-Free Quantitative Structure–Activity Relationship Approach

Quantitative structure activity relationship (QSAR) analysis is traditionally based on extracting a set of molecular descriptors and using them to build a predictive model. In this work, we propose a QSAR approach based directly on the similarity between the 3D structures of a set of molecules measured by a so-called molecule kernel, which is independent of the spatial prealignment of the compounds. Predictors can be build using the molecule kernel in conjunction with the potential support vector machine (P-SVM), a recently proposed machine learning method for dyadic data. The resulting models make direct use of the structural similarities between the compounds in the test set and a subset of the training set and do not require an explicit descriptor construction. We evaluated the predictive performance of the proposed method on one classification and four regression QSAR datasets and compared its results to the results reported in the literature for several state-of-the-art descriptor-based and 3D QSAR approaches. In this comparison, the proposed molecule kernel method performed better than the other QSAR methods.

SVM learning with the Schur-Hadamard inner product for graphs

We apply support vector learning to attributed graphs where the kernel matrices are based on approximations of the Schur-Hadamard inner product. The evaluation of the Schur-Hadamard inner product for a pair of graphs requires the determination of an optimal match between their nodes and edges. It is therefore efficiently approximated by means of recurrent neural networks. The optimal mapping involved allows a direct understanding of the similarity or dissimilarity of the two graphs considered. We present and discuss experimental results of different classifiers constructed by a SVM operating on positive semi-definite (psd) and non-psd kernel matrices.

Algorithms for the Sample Mean of Graphs

Measures of central tendency for graphs are important for protoype construction, frequent substructure mining, and multiple alignment of protein structures. This contribution proposes subgradient-based methods for determining a sample mean of graphs. We assess the performance of the proposed algorithms in a comparative empirical study.

Graph quantization

Vector quantization (VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution aims at extending VQ to the quantization of graphs in a theoretically principled way in order to overcome practical limitations known in the context of prototype-based clustering of graphs. For this, we present the following results: (i) A proof of the necessary Lloyd-Max conditions for optimality of a graph quantizer, (ii) consistency statements for optimal graph quantizer design, and (iii) an accelerated version of competitive learning graph quantization. In order to achieve the proposed results, we present graphs as points in some orbifold. The orbifold framework will introduce sufficient mathematical structure to allow an extension of VQ to graph quantization in a theoretically sound way without discarding the relational information of the graphs. In doing so the proposed approach provides a template of how to link structural pattern recognition methods other than graph quantization to statistical pattern recognition.

Learning graph quantization

This contribution extends learning vector quantization to the domain of graphs. For this, we first identify graphs with points in some orbifold, then derive a generalized differentiable intrinsic metric, and finally extend the update rule of LVQ for generalized differentiable distance metrics. First experiments indicate that the proposed approach can perform comparable to state-of-the-art methods in structural pattern recognition.