Maximum Margin Multiclass Nearest Neighbors

We develop a general framework for margin-based multicategory classification in metric spaces. The basic work-horse is a margin-regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of the art in sample size $n$ and significantly improve the dependence on the number of classes $k$. Our point of departure is a nearly Bayes-optimal finite-sample risk bound independent of $k$. Although $k$-free, this bound is unregularized and non-adaptive, which motivates our main result: Rademacher and scale-sensitive margin bounds with a logarithmic dependence on $k$. As the best previous risk estimates in this setting were of order $\sqrt k$, our bound is exponentially sharper. From the algorithmic standpoint, in doubling metric spaces our classifier may be trained on $n$ examples in $O(n^2\log n)$ time and evaluated on new points in $O(\log n)$ time

An adaptive nearest neighbor rule for classification

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k$ for predicting the labels of points in noisy regions.) We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, $k$-NN with an optimal choice of $k$. In particular, we derive bounds on the convergence rates of our classifier that depend on a local quantity we call the `advantage' which is significantly weaker than the Lipschitz conditions used in previous convergence rate proofs. These generalization bounds hinge on a variant of the seminal Uniform Convergence Theorem due to Vapnik and Chervonenkis; this variant concerns conditional probabilities and may be of independent interest

Kernel-based distance metric learning for microarray data classification

BACKGROUND: The most fundamental task using gene expression data in clinical oncology is to classify tissue samples according to their gene expression levels. Compared with traditional pattern classifications, gene expression-based data classification is typically characterized by high dimensionality and small sample size, which make the task quite challenging. RESULTS: In this paper, we present a modified K-nearest-neighbor (KNN) scheme, which is based on learning an adaptive distance metric in the data space, for cancer classification using microarray data. The distance metric, derived from the procedure of a data-dependent kernel optimization, can substantially increase the class separability of the data and, consequently, lead to a significant improvement in the performance of the KNN classifier. Intensive experiments show that the performance of the proposed kernel-based KNN scheme is competitive to those of some sophisticated classifiers such as support vector machines (SVMs) and the uncorrelated linear discriminant analysis (ULDA) in classifying the gene expression data. CONCLUSION: A novel distance metric is developed and incorporated into the KNN scheme for cancer classification. This metric can substantially increase the class separability of the data in the feature space and, hence, lead to a significant improvement in the performance of the KNN classifier

Local feature weighting in nearest prototype classification

The distance metric is the corner stone of nearest neighbor (NN)-based methods, and therefore, of nearest prototype (NP) algorithms. That is because they classify depending on the similarity of the data. When the data is characterized by a set of features which may contribute to the classification task in different levels, feature weighting or selection is required, sometimes in a local sense. However, local weighting is typically restricted to NN approaches. In this paper, we introduce local feature weighting (LFW) in NP classification. LFW provides each prototype its own weight vector, opposite to typical global weighting methods found in the NP literature, where all the prototypes share the same one. Providing each prototype its own weight vector has a novel effect in the borders of the Voronoi regions generated: They become nonlinear. We have integrated LFW with a previously developed evolutionary nearest prototype classifier (ENPC). The experiments performed both in artificial and real data sets demonstrate that the resulting algorithm that we call LFW in nearest prototype classification (LFW-NPC) avoids overfitting on training data in domains where the features may have different contribution to the classification task in different areas of the feature space. This generalization capability is also reflected in automatically obtaining an accurate and reduced set of prototypes.Publicad

Adaptive Nonparametric Image Parsing

In this paper, we present an adaptive nonparametric solution to the image parsing task, namely annotating each image pixel with its corresponding category label. For a given test image, first, a locality-aware retrieval set is extracted from the training data based on super-pixel matching similarities, which are augmented with feature extraction for better differentiation of local super-pixels. Then, the category of each super-pixel is initialized by the majority vote of the $k$-nearest-neighbor super-pixels in the retrieval set. Instead of fixing $k$ as in traditional non-parametric approaches, here we propose a novel adaptive nonparametric approach which determines the sample-specific k for each test image. In particular, $k$ is adaptively set to be the number of the fewest nearest super-pixels which the images in the retrieval set can use to get the best category prediction. Finally, the initial super-pixel labels are further refined by contextual smoothing. Extensive experiments on challenging datasets demonstrate the superiority of the new solution over other state-of-the-art nonparametric solutions.Comment: 11 page