K-nearest neighbors (KNN) method is used in many supervised learning classification problems. Potential Energy (PE) method is also developed for classification problems based on its physical metaphor. The energy potential used in the experiments are Yukawa potential and Gaussian Potential. In this paper, I use both applet and MATLAB program with real life benchmark data to analyze the performances of KNN and PE method in classification problems. The results show that in general, KNN and PE methods have similar performance. In particular, PE with Yukawa potential has worse performance than KNN when the density of the data is higher in the distribution of the database. When the Gaussian potential is applied, the results from PE and KNN have similar behavior. The indicators used are correlation coefficients and information gain.

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the remaining vertices can be classified with error converging to Bayes optimal using the $k$-nearest-neighbors classification rule. We evaluate the proposed methods on simulated data and a graph derived from Wikipedia.

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

The importance of algorithm portfolio techniques for SAT has long been noted, and a number of very successful systems have been devised, including the most successful one --- SATzilla. However, all these systems are quite complex (to understand, reimplement, or modify). In this paper we propose a new algorithm portfolio for SAT that is extremely simple, but in the same time so efficient that it outperforms SATzilla. For a new SAT instance to be solved, our portfolio finds its k-nearest neighbors from the training set and invokes a solver that performs the best at those instances. The main distinguishing feature of our algorithm portfolio is the locality of the selection procedure --- the selection of a SAT solver is based only on few instances similar to the input one.

In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on fitting K-nearest neighbor regression to the unsupervised regression framework for learning of low-dimensional manifolds. Similar to related approaches that are mostly based on kernel methods, unsupervised K-nearest neighbor (UNN) regression optimizes latent variables w.r.t. the data space reconstruction error employing the K-nearest neighbor heuristic. The problem of optimizing latent neighborhoods is difficult to solve, but the UNN formulation allows the design of efficient strategies that iteratively embed latent points to fixed neighborhood topologies. UNN is well appropriate for sorting of high-dimensional data. The iterative variants are analyzed experimentally.

Data streams containing objects that are (or can be) associated with more than one label at the same time are ubiquitous. In spite of its important applications, classification of streaming multi-label data is largely unexplored. Existing approaches try to tackle the problem by transferring traditional single-label stream classification practices to the multi-label domain. Nevertheless, they fail to consider some of the unique properties of the problem such as within and between class imbalance and multiple concept drift. To deal with these challenges, this paper proposes a novel multi-label stream classification approach that employs two windows for each label, one for positive and one for negative examples. Instance-sharing is exploited for space efficiency, while a time-efficient instantiation based on the k-Nearest Neighbor algorithm is also proposed. Finally, a batch-incremental thresholding technique is proposed to further deal with the class imbalance problem. Results of an empirical comparison against two other methods on three real world datasets are in favor of the proposed approach.

There are a number of papers that use hill-climbing or k-We introduce a new nearest neighbor search algorithm. NN graphs for nearest neighbor search, but to the best of our The algorithm builds a nearest neighbor knowledge, using hill-climbing on k-NN graphs is a new idea.

Many existing approaches employ one-vs-rest method to decompose a multi-label classification problem into a set of 2- class classification problems, one for each class. This method is valid in traditional single-label classification, it, however, incurs training inconsistency in multi-label classification, because in the latter a data point could belong to more than one class. In order to deal with this problem, in this work, we further develop classicalK-Nearest Neighbor classifier and propose a novel Class Balanced K-Nearest Neighbor approach for multi-label classification by emphasizing balanced usage of data from all the classes. In addition, we also propose a Class Balanced Linear Discriminant Analysis approach to address high-dimensional multi-label input data. Promising experimental results on three broadly used multi-label data sets demonstrate the effectiveness of our approach.

We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph should one choose, mutual k-nearest neighbor or symmetric k-nearest neighbor? What is the optimal parameter k? In our setting, clusters are defined as connected components of the t-level set of the underlying probability distribution. Clusters are said to be identified in the neighborhood graph if connected components in the graph correspond to the true underlying clusters. Using techniques from random geometric graph theory, we prove bounds on the probability that clusters are identified successfully, both in a noise-free and in a noisy setting. Those bounds lead to several conclusions. First, k has to be chosen surprisingly high (rather of the order n than of the order log n) to maximize the probability of cluster identification. Secondly, the major difference between the mutual and the symmetric k-nearest neighbor graph occurs when one attempts to detect the most significant cluster only.

In this paper, we present an application of neural networks in the renewable energy domain. We have developed a methodology for the daily prediction of global solar radiation on a horizontal surface. We use an ad-hoc time series preprocessing and a Multi-Layer Perceptron (MLP) in order to predict solar radiation at daily horizon. First results are promising with nRMSE < 21% and RMSE < 998 Wh/m2. Our optimized MLP presents prediction similar to or even better than conventional methods such as ARIMA techniques, Bayesian inference, Markov chains and k-Nearest-Neighbors approximators. Moreover we found that our data preprocessing approach can reduce significantly forecasting errors.