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193
Data Clustering: 50 Years Beyond KMeans
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 274 (6 self)
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Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is exploratory in nature to find structure in data. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, Kmeans, was first published in 1955. In spite of the fact that Kmeans was proposed over 50 years ago and thousands of clustering algorithms have been published since then, Kmeans is still widely used. This speaks to the difficulty of designing a general purpose clustering algorithm and the illposed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semisupervised clustering, ensemble clustering, simultaneous feature selection, and data clustering and large scale data clustering.
On graph kernels: Hardness results and efficient alternatives
 IN: CONFERENCE ON LEARNING THEORY
, 2003
"... As most ‘realworld’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances tha ..."
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Cited by 185 (5 self)
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As most ‘realworld’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. This paper investigates kernels on labeled directed graphs with general structure. It is shown that computing a strictly positive definite graph kernel is at least as hard as solving the graph isomorphism problem. It is also shown that computing an inner product in a feature space indexed by all possible graphs, where each feature counts the number of subgraphs isomorphic to that graph, is NPhard. On the other hand, inner products in an alternative feature space, based on walks in the graph, can be computed in polynomial time. Such kernels are defined in this paper.
Probability product kernels
 Journal of Machine Learning Research
, 2004
"... The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product i ..."
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Cited by 179 (9 self)
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The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product is then evaluated as the integral of the product of pairs of distributions. The kernel is straightforward to evaluate for all exponential family models such as multinomials and Gaussians and yields interesting nonlinear kernels. Furthermore, the kernel is computable in closed form for latent distributions such as mixture models, hidden Markov models and linear dynamical systems. For intractable models, such as switching linear dynamical systems, structured meanfield approximations can be brought to bear on the kernel evaluation. For general distributions, even if an analytic expression for the kernel is not feasible, we show a straightforward sampling method to evaluate it. Thus, the kernel permits discriminative learning methods, including support vector machines, to exploit the properties, metrics and invariances of the generative models we infer from each datum. Experiments are shown using multinomial models for text, hidden Markov models for biological data sets and linear dynamical systems for time series data.
A Survey of Kernels for Structured Data
, 2003
"... Kernel methods in general and support vector machines in particular have been successful in various learning tasks on data represented in a single table. Much ‘realworld’ data, however, is structured – it has no natural representation in a single table. Usually, to apply kernel methods to ‘realwor ..."
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Cited by 146 (2 self)
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Kernel methods in general and support vector machines in particular have been successful in various learning tasks on data represented in a single table. Much ‘realworld’ data, however, is structured – it has no natural representation in a single table. Usually, to apply kernel methods to ‘realworld’ data, extensive preprocessing is performed to embed the data into a real vector space and thus in a single table. This survey describes several approaches of defining positive definite kernels on structured instances directly.
Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis
 Journal of Machine Learning Research
, 2007
"... Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in highdimensional data analysis. Fisher discriminant analysis (FDA) is a traditional technique for supervised dimensionality reduction, but it tends to give undesired results if samples in a ..."
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Cited by 123 (11 self)
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Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in highdimensional data analysis. Fisher discriminant analysis (FDA) is a traditional technique for supervised dimensionality reduction, but it tends to give undesired results if samples in a class are multimodal. An unsupervised dimensionality reduction method called localitypreserving projection (LPP) can work well with multimodal data due to its locality preserving property. However, since LPP does not take the label information into account, it is not necessarily useful in supervised learning scenarios. In this paper, we propose a new linear supervised dimensionality reduction method called local Fisher discriminant analysis (LFDA), which effectively combines the ideas of FDA and LPP. LFDA has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem. We demonstrate the practical usefulness and high scalability of the LFDA method in data visualization and classification tasks through extensive simulation studies. We also show that LFDA can be extended to nonlinear dimensionality reduction scenarios by applying the kernel trick.
A Review of Kernel Methods in Machine Learning
, 2006
"... We review recent methods for learning with positive definite kernels. All these methods formulate learning and estimation problems as linear tasks in a reproducing kernel Hilbert space (RKHS) associated with a kernel. We cover a wide range of methods, ranging from simple classifiers to sophisticate ..."
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Cited by 95 (4 self)
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We review recent methods for learning with positive definite kernels. All these methods formulate learning and estimation problems as linear tasks in a reproducing kernel Hilbert space (RKHS) associated with a kernel. We cover a wide range of methods, ranging from simple classifiers to sophisticated methods for estimation with structured data.
ShortestPath Kernels on Graphs
 In Proceedings of the 2005 International Conference on Data Mining
, 2005
"... Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have bee ..."
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Cited by 61 (5 self)
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Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NPhard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortestpath kernels show significantly higher classification accuracy than walkbased kernels. 1
Graph Kernels for Chemical Informatics
, 2005
"... Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their cova ..."
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Cited by 58 (7 self)
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Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their covalent bonds, machine learning methods in this domain must be capable of processing graphical structures with variable size. Here we first briefly review the literature on graph kernels and then introduce three new kernels (Tanimoto, MinMax, Hybrid) based on the idea of molecular fingerprints and counting labeled paths of depth up to d using depthfirst search from each possible vertex. The kernels are applied to three classification problems to predict mutagenicity, toxicity, and anticancer activity on three publicly available data sets. The kernels achieve performances at least comparable, and most often superior, to those previously reported in the literature reaching accuracies of 91.5 % on the Mutag dataset, 6567 % on the PTC (Predictive Toxicology Challenge) dataset, and 72 % on the NCI (National Cancer Institute) dataset. Properties and tradeoffs of these kernels, as well as other proposed kernels that leverage 1D or 3D representations of molecules, are briefly discussed.
Extensions of marginalized graph kernels
 In Proc. of ICML
, 2004
"... Positive denite kernels between labeled graphs have recently been proposed. They enable the application of kernel methods, such as support vector machines, to the analysis and classication of graphs, for example, chemical compounds. These graph kernels are obtained by marginalizing a kernel betwee ..."
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Cited by 46 (2 self)
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Positive denite kernels between labeled graphs have recently been proposed. They enable the application of kernel methods, such as support vector machines, to the analysis and classication of graphs, for example, chemical compounds. These graph kernels are obtained by marginalizing a kernel between paths with respect to a random walk model on the graph vertices along the edges. We propose two extensions of these graph kernels, with the double goal to reduce their computation time and increase their relevance as measure of similarity between graphs. First, we propose to modify the label of each vertex by automatically adding information about its environment with the use of the Morgan algorithm. Second, we suggest a modication of the random walk model to prevent the walk from coming back to a vertex that was just visited. These extensions are then tested on benchmark experiments of chemical compounds classication, with promising results. 1.
Graph Kernels and Gaussian Processes for Relational Reinforcement Learning
 Machine Learning
, 2003
"... Relational reinforcement learning is a Qlearning technique for relational stateaction spaces. It aims to enable agents to learn how to act in an environment that has no natural representation as a tuple of constants. In this case, the learning algorithm used to approximate the mapping between stat ..."
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Cited by 46 (9 self)
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Relational reinforcement learning is a Qlearning technique for relational stateaction spaces. It aims to enable agents to learn how to act in an environment that has no natural representation as a tuple of constants. In this case, the learning algorithm used to approximate the mapping between stateaction pairs and their so called Q(uality)value has to be not only very reliable, but it also has to be able to handle the relational representation of stateaction pairs. In this paper we investigate...