Modified Large Margin Nearest Neighbor Metric Learning for Regression

The main objective of this letter is to formulate a new approach of learning a Mahalanobis distance metric for nearest neighbor regression from a training sample set. We propose a modified version of the large margin nearest neighbor metric learning method to deal with regression problems. As an application, the prediction of post-operative trunk 3-D shapes in scoliosis surgery using nearest neighbor regression is described. Accuracy of the proposed method is quantitatively evaluated through experiments on real medical data.IRSC / CIH

Study and Observation of the Variation of Accuracies of KNN, SVM, LMNN, ENN Algorithms on Eleven Different Datasets from UCI Machine Learning Repository

Machine learning qualifies computers to assimilate with data, without being solely programmed [1, 2]. Machine learning can be classified as supervised and unsupervised learning. In supervised learning, computers learn an objective that portrays an input to an output hinged on training input-output pairs [3]. Most efficient and widely used supervised learning algorithms are K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Large Margin Nearest Neighbor (LMNN), and Extended Nearest Neighbor (ENN). The main contribution of this paper is to implement these elegant learning algorithms on eleven different datasets from the UCI machine learning repository to observe the variation of accuracies for each of the algorithms on all datasets. Analyzing the accuracy of the algorithms will give us a brief idea about the relationship of the machine learning algorithms and the data dimensionality. All the algorithms are developed in Matlab. Upon such accuracy observation, the comparison can be built among KNN, SVM, LMNN, and ENN regarding their performances on each dataset.Comment: To be published in the 4th IEEE International Conference on Electrical Engineering and Information & Communication Technology (iCEEiCT 2018

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

Tile2Vec: Unsupervised representation learning for spatially distributed data

Geospatial analysis lacks methods like the word vector representations and pre-trained networks that significantly boost performance across a wide range of natural language and computer vision tasks. To fill this gap, we introduce Tile2Vec, an unsupervised representation learning algorithm that extends the distributional hypothesis from natural language -- words appearing in similar contexts tend to have similar meanings -- to spatially distributed data. We demonstrate empirically that Tile2Vec learns semantically meaningful representations on three datasets. Our learned representations significantly improve performance in downstream classification tasks and, similar to word vectors, visual analogies can be obtained via simple arithmetic in the latent space.Comment: 8 pages, 4 figures in main text; 9 pages, 11 figures in appendi

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