Unsupervised nearest neighbors is the foundation of many other learning methods, notably manifold learning and spectral clustering. Supervised neighbors-based learning comes in two flavors: classification for data with discrete labels, and regression for data with continuous labels. The principle behind nearest neighbor methods is to find a predefined number of training samples closest in distance to the new point, and predict the label from these. The number of samples can be a user-defined constant (k-nearest neighbor learning), or vary based on the local density of points (radius-based neighbor learning). The distance can, in general, be any metric measure: standard Euclidean distance is the most common choice. Neighbors-based methods are known as non-generalizing machine learning methods, since they simply "remember" all of its training data (possibly transformed into a fast indexing structure such as a Ball Tree or KD Tree.).
We introduce a new nearest neighbor search al-gorithm. The algorithm builds a nearest neighborgraph in an offline phase and when queried witha new point, performs hill-climbing starting froma randomly sampled node of the graph. We pro-vide theoretical guarantees for the accuracy and thecomputational complexity and empirically showthe effectiveness of this algorithm.
Can we leverage learning techniques to build a fast nearest-neighbor (NN) retrieval data structure? We present a general learning framework for the NN problem in which sample queries are used to learn the parameters of a data structure that minimize the retrieval time and/or the miss rate. We explore the potential of this novel framework through two popular NN data structures: KD-trees and the rectilinear structures employed by locality sensitive hashing. We derive a generalization theory for these data structure classes and present simple learning algorithms for both. Experimental results reveal that learning often improves on the already strong performance of these data structures.
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 . 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.
A significantly faster algorithm is presented for the original kNN mode seeking procedure. It has the advantages over the well-known mean shift algorithm that it is feasible in high-dimensional vector spaces and results in uniquely, well defined modes. Moreover, without any additional computational effort it may yield a multi-scale hierarchy of clusterings. The time complexity is just O(n^1.5). resulting computing times range from seconds for 10^4 objects to minutes for 10^5 objects and to less than an hour for 10^6 objects. The space complexity is just O(n). The procedure is well suited for finding large sets of small clusters and is thereby a candidate to analyze thousands of clusters in millions of objects. The kNN mode seeking procedure can be used for active learning by assigning the clusters to the class of the modal objects of the clusters. Its feasibility is shown by some examples with up to 1.5 million handwritten digits. The obtained classification results based on the clusterings are compared with those obtained by the nearest neighbor rule and the support vector classifier based on the same labeled objects for training. It can be concluded that using the clustering structure for classification can be significantly better than using the trained classifiers. A drawback of using the clustering for classification, however, is that no classifier is obtained that may be used for out-of-sample objects.