An Object-Oriented Language-Database Integration Model: The Composition-Filters Approach

This paper introduces a new model, based on so-called object-composition filters, that uniformly integrates database-like features into an object-oriented language. The focus is on providing persistent dynamic data structures, data sharing, transactions, multiple views and associative access, integrated with the object-oriented paradigm. The main contribution is that the database-like features are part of this new object-oriented model, and therefore, are uniformly integrated with object-oriented features such as data abstraction, encapsulation, message passing and inheritance. This approach eliminates the problems associated with existing systems such as lack of reusability and extensibility for database operations, the violation of encapsulation, the need to define specific types such as sets, and the incapability to support multiple views. The model is illustrated through the object-oriented language Sina

Domain Adaptation on Graphs by Learning Graph Topologies: Theoretical Analysis and an Algorithm

Traditional machine learning algorithms assume that the training and test data have the same distribution, while this assumption does not necessarily hold in real applications. Domain adaptation methods take into account the deviations in the data distribution. In this work, we study the problem of domain adaptation on graphs. We consider a source graph and a target graph constructed with samples drawn from data manifolds. We study the problem of estimating the unknown class labels on the target graph using the label information on the source graph and the similarity between the two graphs. We particularly focus on a setting where the target label function is learnt such that its spectrum is similar to that of the source label function. We first propose a theoretical analysis of domain adaptation on graphs and present performance bounds that characterize the target classification error in terms of the properties of the graphs and the data manifolds. We show that the classification performance improves as the topologies of the graphs get more balanced, i.e., as the numbers of neighbors of different graph nodes become more proportionate, and weak edges with small weights are avoided. Our results also suggest that graph edges between too distant data samples should be avoided for good generalization performance. We then propose a graph domain adaptation algorithm inspired by our theoretical findings, which estimates the label functions while learning the source and target graph topologies at the same time. The joint graph learning and label estimation problem is formulated through an objective function relying on our performance bounds, which is minimized with an alternating optimization scheme. Experiments on synthetic and real data sets suggest that the proposed method outperforms baseline approaches

Feature Selection via Binary Simultaneous Perturbation Stochastic Approximation

Feature selection (FS) has become an indispensable task in dealing with today's highly complex pattern recognition problems with massive number of features. In this study, we propose a new wrapper approach for FS based on binary simultaneous perturbation stochastic approximation (BSPSA). This pseudo-gradient descent stochastic algorithm starts with an initial feature vector and moves toward the optimal feature vector via successive iterations. In each iteration, the current feature vector's individual components are perturbed simultaneously by random offsets from a qualified probability distribution. We present computational experiments on datasets with numbers of features ranging from a few dozens to thousands using three widely-used classifiers as wrappers: nearest neighbor, decision tree, and linear support vector machine. We compare our methodology against the full set of features as well as a binary genetic algorithm and sequential FS methods using cross-validated classification error rate and AUC as the performance criteria. Our results indicate that features selected by BSPSA compare favorably to alternative methods in general and BSPSA can yield superior feature sets for datasets with tens of thousands of features by examining an extremely small fraction of the solution space. We are not aware of any other wrapper FS methods that are computationally feasible with good convergence properties for such large datasets.Comment: This is the Istanbul Sehir University Technical Report #SHR-ISE-2016.01. A short version of this report has been accepted for publication at Pattern Recognition Letter

Out-of-sample generalizations for supervised manifold learning for classification

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets

Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing methods primarily focus on the embedding of the training data, and the generalization of the embedding to initially unseen test data is rather ignored. In this work, we build on recent theoretical results on the generalization performance of supervised manifold learning algorithms. Motivated by these performance bounds, we propose a supervised manifold learning method that computes a nonlinear embedding while constructing a smooth and regular interpolation function that extends the embedding to the whole data space in order to achieve satisfactory generalization. The embedding and the interpolator are jointly learnt such that the Lipschitz regularity of the interpolator is imposed while ensuring the separation between different classes. Experimental results on several image data sets show that the proposed method outperforms traditional classifiers and the supervised dimensionality reduction algorithms in comparison in terms of classification accuracy in most settings