Kernel learning for ligand-based virtual screening: discovery of a new PPARgamma agonist

Poster presentation at 5th German Conference on Cheminformatics: 23. CIC-Workshop Goslar, Germany. 8-10 November 2009 We demonstrate the theoretical and practical application of modern kernel-based machine learning methods to ligand-based virtual screening by successful prospective screening for novel agonists of the peroxisome proliferator-activated receptor gamma (PPARgamma) [1]. PPARgamma is a nuclear receptor involved in lipid and glucose metabolism, and related to type-2 diabetes and dyslipidemia. Applied methods included a graph kernel designed for molecular similarity analysis [2], kernel principle component analysis [3], multiple kernel learning [4], and, Gaussian process regression [5]. In the machine learning approach to ligand-based virtual screening, one uses the similarity principle [6] to identify potentially active compounds based on their similarity to known reference ligands. Kernel-based machine learning [7] uses the "kernel trick", a systematic approach to the derivation of non-linear versions of linear algorithms like separating hyperplanes and regression. Prerequisites for kernel learning are similarity measures with the mathematical property of positive semidefiniteness (kernels). The iterative similarity optimal assignment graph kernel (ISOAK) [2] is defined directly on the annotated structure graph, and was designed specifically for the comparison of small molecules. In our virtual screening study, its use improved results, e.g., in principle component analysis-based visualization and Gaussian process regression. Following a thorough retrospective validation using a data set of 176 published PPARgamma agonists [8], we screened a vendor library for novel agonists. Subsequent testing of 15 compounds in a cell-based transactivation assay [9] yielded four active compounds. The most interesting hit, a natural product derivative with cyclobutane scaffold, is a full selective PPARgamma agonist (EC50 = 10 ± 0.2 microM, inactive on PPARalpha and PPARbeta/delta at 10 microM). We demonstrate how the interplay of several modern kernel-based machine learning approaches can successfully improve ligand-based virtual screening results

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral-regularized algorithms, including ridge regression, principal component analysis, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases

Kernel Feature Extraction for Hyperspectral Image Classification Using Chunklet Constraints

A novel semi-supervised kernel feature extraction algorithm to combine an efficient metric learning method, i.e. relevant component analysis (RCA), and kernel trick is presented for hyperspectral imagery land-cover classification. This method obtains projection of the input data by learning an optimal nonlinear transformation via a chunklet constraints-based FDA criterion, and called chunklet-based kernel relevant component analysis (CKRCA). The proposed method is appealing as it constructs the kernel very intuitively for the RCA method and does not require any labeled information. The effectiveness of the proposed CKRCA is successfully illustrated in hyperspectral remote sensing image classification. Experimental results demonstrate that the proposed method can greatly improve the classification accuracy compared with traditional linear and conventional kernel-based methods

Random walks with drift : a sequential approach

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its associated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there is a unit root (random walk component). To obtain meaningful asymptotic results we consider local nonparametric alternatives for the drift component. It turns out that the rate of convergence at which the drift vanishes determines whether the asymptotic properties of the monitoring procedure are determined by a deterministic or random function. Further, we provide a theoretical result about the optimal kernel for a given alternative. --Control chart,nonparametric smoothing,sequential analysis,unit roots,weighted partial sum process

Efficient Clustering via Kernel Principal Component Analysis and Optimal One-dimensional Thresholding

Several techniques are used for clustering of high-dimensional data. Traditionally, clustering approaches are based on performing dimensionality reduction of high-dimensional data followed by classical clustering such as k-means in lower dimensions. However, this approach based on k-means does not guarantee optimality. Moreover, the result of k-means is highly dependent on initialization of cluster centers and hence not repeatable, while not being optimal. To overcome this drawback, an optimal clustering approach in one dimension based on dimensionality reduction is proposed. The one-dimensional representation of high dimensional data is obtained using Kernel Principal Component Analysis. The one-dimensional representation of the data is then clustered optimally using a dynamic programming algorithm in polynomial time. Clusters in the one-dimensional data are obtained by minimizing the sum of within-class variance while maximizing the sum of between-class variance. The advantage of the proposed approach is demonstrated on synthetic and real-life datasets over standard k-means in terms of optimality and repeatability