A method to speed up the Bayes classifier

Machine learning (ML) applications have been thriving recently, largely attributed to the increasing availability of data. However, inconsistency and incomplete information are ubiquitous in real-world datasets, and their impact on ML applications remains elusive. In this paper, we present a formal study of this impact by extending the notion of Certain Answers for Codd tables, which has been explored by the database research community for decades, into the field of machine learning. Specifically, we focus on classification problems and propose the notion of "Certain Predictions" (CP) --- a test data example can be certainly predicted (CP'ed) if all possible classifiers trained on top of all possible worlds induced by the incompleteness of data would yield the same prediction. We study two fundamental CP queries: (Q1) checking query that determines whether a data example can be CP'ed; and (Q2) counting query that computes the number of classifiers that support a particular prediction (i.e., label). Given that general solutions to CP queries are, not surprisingly, hard without assumption over the type of classifier, we further present a case study in the context of nearest neighbor (NN) classifiers, where efficient solutions to CP queries can be developed --- we show that it is possible to answer both queries in linear or polynomial time over exponentially many possible worlds. We demonstrate one example use case of CP in the important application of "data cleaning for machine learning (DC for ML)." We show that our proposed CPClean approach built based on CP can often significantly outperform existing techniques, particularly on datasets with systematic missing values. For example, on 5 datasets with systematic missingness, CPClean (with early termination) closes 100% gap on average by cleaning 36% of dirty data on average, while the best automatic cleaning approach BoostClean can only close 14% gap on average.

The nearest neighbor classifier (NNC) is a non-parametric classification technique that classifies a test pattern to the class of its nearest neighbor in the training data. In this research, we applied the NNC to a standard letter recognition data and obtained a superior classification rate in comparison to extant approaches. A prime drawback to the NNC technique has been the relative inefficiency of the model. A modified NNC was implemented and applied to the same recognition problem. It is found that if we choose a suitable threshold minimum difference for classification, we can reduce the CPU time by half without lowering the performance of the classifier.

Probability theory is the framework for making decision under uncertainty. In classification, Bayes' rule is used to calculate the probabilities of the classes and it is a big issue how to classify raw data rationally to minimize expected risk. Bayesian theory can roughly be boiled down to one principle: to see the future, one must look at the past. Naive Bayes classifier is one of the mostly used practical Bayesian learning methods. K-nearest neighbor is a supervised learning algorithm where the result of new instance query is classified based on majority of k-nearest neighbor category. The classifiers do not use any model to fit and only based on memory/training data. In this paper, after reviewing Bayesian theory, the naive Bayes classifier and k-nearest neighbor classifier is implemented and applied to a dataset "credit card approval" application. Eventually the performance of these two classifiers is observed on this application in terms of the correct classification and misclassification and how the performance of k-nearest neighbor classifier can be improved by varying the value of k.

Recent experimental studies have shown that the support vector machine and the random forest are "stand out" models that outperform most other supervised learning methods in benchmarked evaluations on real-world data sets. Studies have also established that both these models are closely related to nearest neighbor classifiers. Due to this connection, one would expect a similar performance from a nearest neighbor classifier; however, the latter lags greatly behind the support vector machine and the random forest in most evaluations. On the contrary, the nearest neighbor classifier has great theoretical potential because of its ability to model complex decision boundaries with low bias. Furthermore, it theoretically guarantees an error of no more than twice the Bayes error rate on an infinite data set. In this paper, we examine this obvious disconnect between the great theoretical promise and empirical reality of the nearest neighbor classifier. An additional point is that the random forest and support vector machine can be considered eager forms of the (lazy) nearest neighbor classifier. Inspired by the connections between nearest neighbor classifiers, support vector machines and random forest models, we propose a nearest neighbor classifier that is competitive to these models.

This paper is about a variant of k nearest neighbor classification on large many-class high dimensional datasets.K nearest neighbor remains a popular classification technique, especially in areas such as computer vision, drug activity prediction and astrophysics. Furthermore, many more modern classifiers, such as kernel-based Bayes classifiers or the prediction phase of SVMs, require computational regimes similar to k-NN. We believe that tractable k-NN algorithms therefore continue to be important.This paper relies on the insight that even with many classes, the task of finding the majority class among the k nearest neighbors of a query need not require us to explicitly find those k nearest neighbors. This insight was previously used in (Liu et al., 2003) in two algorithms called KNS2 and KNS3 which dealt with fast classification in the case of two classes. In this paper we show how a different approach, IOC (standing for the International Olympic Committee) can apply to the case of n classes where n > 2.IOC assumes a slightly different processing of the datapoints in the neighborhood of the query. This allows it to search a set of metric trees, one for each class. During the searches it is possible to quickly prune away classes that cannot possibly be the majority.We give experimental results on datasets of up to 5.8 x 105 records and 1.5 x 103 attributes, frequently showing an order of magnitude acceleration compared with each of (i) conventional linear scan, (ii) a well-known independent SR-tree implementation of conventional k-NN and (iii) a highly optimized conventional k-NN metric tree search.

This paper proposes an approach based on fuzzy rough set theory to improve nearest neighbor based classification. Six measures are introduced to evaluate the quality of the nearest neighbors. This quality is combined with the frequency at which classes occur among the nearest neighbors and the similarity w.r.t. the nearest neighbor, to decide which class to pick among the neighbor's classes. The importance of each aspect is weighted using optimized weights. An experimental study shows that our method, Quality, Frequency and Similarity based Fuzzy Nearest Neighbor (QFSNN), outperforms state-of-the-art nearest neighbor classifiers.

The Nearest Neighbor (NN) classifier is one of the most used and well-known techniques for classification. However, NN suffers from several drawbacks such as high storage requirements, low efficiency in classification response, and noise sensitivity in the neighborhood. Prototype weighting as one the effective learning methods, assigns a weight to each prototype in order to determine its importance and simultaneously removes both redundant and noisy ones as a side effect. NN has an instance-based structure, and this is why; it is one of the rare methods for which the results of cross validation can be achieved for all possible combinations called as Complete-Cross-Validation (CCV) without need to construct and train exponential number of models. Using CCV as the objective function in learning the weights of prototypes can increase generalization capability of the classifier and also decrease the randomness of the learning method. Nevertheless, it cannot be computed such efficiently to be used as a fitness function during most of learning algorithms. In this paper, an iterative learning method has been proposed, in which the objective is incrementally improved without computing CCV even once. The proposed approach was assessed through a series of experiments with UCI in comparison with basic NN and related prototype weighting scheme and could outperform them.

Learning from high-dimensional data is usually quite challenging, as captured by the well-known phrase curse of dimensionality. Data analysis often involves measuring the similarity between different examples. This sometimes becomes a problem, as many widely used metrics tend to concentrate in high-dimensional feature spaces. The reduced contrast makes it more difficult to distinguish between close and distant points, which renders many traditional distance-based learning methods ineffective. Secondary distances based on shared neighbor similarities have recently been proposed as one possible solution to this problem. However, these initial metrics failed to take hubness into account. Hubness is a recently described aspect of the dimensionality curse, and it affects all sorts of $$k$$ -nearest neighbor learning methods in severely negative ways. This paper is the first to discuss the impact of hubs on forming the shared neighbor similarity scores. We propose a novel, hubness-aware secondary similarity measure $$simhub_s$$ and an extensive experimental evaluation shows it to be much more appropriate for high-dimensional data classification than the standard $$simcos_s$$ measure. The proposed similarity changes the underlying $$k$$ NN graph in such a way that it reduces the overall frequency of label mismatches in $$k$$ -neighbor sets and increases the purity of occurrence profiles, which improves classifier performance. It is a hybrid measure, which takes into account both the supervised and the unsupervised hubness information. The analysis shows that both components are useful in their own ways and that the measure is therefore properly defined. This new similarity does not increase the overall computational cost, and the improvement is essentially ‘free’.

Currently, Nearest-Neighbor approaches (NN) have been widely applied to real world image data mining. These approaches have the following three disadvantages: (i) the performance is inferior on small datasets; (ii) the performance of approximated nearest neighbor search will degrade for data with high dimensions; (iii) they are heavily dependent on the chosen feature and distance measure. To overcome these intrinsic weaknesses, we propose a novel Nearest-Neighbor method, which improves the original NN approaches from three aspects. Firstly, we propose a novel neighborhood similarity measure, where the similarity between test images and labeled images in the database is calculated jointly by the original image-to-image similarity and the average similarity of their neighboring unlabeled data. Secondly, we adopt the kernelized locality sensitive hashing to effectively conduct the nearest neighbor search for high dimensional data. Finally, to enhance the robustness of the method on different genres of images, we propose to fuse the discrimination power of different features by considering all the retrieved nearest neighbors via hashing systems using different features/kernels. Experimental result shows the advantage over traditional Nearest-Neighbor methods using the labeled data only. Even when the ratio of labeled data is very small, our method could also achieve remarkable results, thanks to the help of unlabeled data and multiple features.

Forensic human identification with targeted microbiome markers using nearest neighbor classification

Learning vector quantization (LVQ), developed by T. Kohonen (1989), is a neural network based method to find a good set of reference vectors to be stored as a nearest neighbor classifier's reference set. An efficient method of finding reference vectors along class boundaries instead of finding vectors representing class distribution, as LQV does, is described. A quantitative comparison with LVQ is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bioinspired design is the adaptation of methods, strategies, or principles found in nature to solve engineering problems. One formalized approach to bioinspired solution seeking is the abstraction of the engineering problem into a functional need and then seeking solutions to this function using a keyword type search method on text based biological knowledge. These function keyword search approaches have shown potential for success, but as with many text based search methods, they produce a large number of results, many of little relevance to the problem in question. In this paper, we develop a method to train a computer to identify text passages more likely to suggest a solution to a human designer. The work presented examines the possibility of filtering biological keyword search results by using text mining algorithms to automatically identify which results are likely to be useful to a designer. The text mining algorithms are trained on a pair of surveys administered to human subjects to empirically identify a large number of sentences that are, or are not, helpful for idea generation. We develop and evaluate three text classification algorithms, namely, a Naïve Bayes (NB) classifier, a k nearest neighbors (kNN) classifier, and a support vector machine (SVM) classifier. Of these methods, the NB classifier generally had the best performance. Based on the analysis of 60 word stems, a NB classifier's precision is 0.87, recall is 0.52, and F score is 0.65. We find that word stem features that describe a physical action or process are correlated with helpful sentences. Similarly, we find biological jargon feature words are correlated with unhelpful sentences.

Machine Learning algorithms have been known for their simplicity and easier implementation, and they have been used predominantly for disease prediction, diagnosis, and decision-making systems to improve healthcare services. These mechanisms are easier to implement than Deep Learning techniques, require fewer resources, and can be easily integrated with other healthcare applications; hence, they have gained popularity recently. In this paper, a comparative analysis is performed with the most widely used Machine Learning classifiers: Naïve Bayes, Nearest Neighbor, and Logistic Regression for the prediction of diabetes. This experiment is performed with 2 diabetes datasets (National Institute of Diabetes and Digestive and Kidney Diseases and Diabetes prediction dataset) from Kaggle and 1 diabetes dataset from Mendeley data using the MATLAB Online Tool. This paper explores the challenges such as the variables being relatively independent stating the class label in Naïve Bayes classifiers and 10 models' performance evaluation with these 3 different datasets for choosing the best model. Developing adaptive methods for selecting optimal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> and distance metrics based on the dataset characteristics to improve KNN's accuracy and performance. The no. of the population suffering from metabolic disorders is growing day by day and relevant diseases are increased at an early age indicating the urgency of early diagnosis and timely treatment to prevent further damage. Diabetes is one of the leading diseases in India including in many developed countries, hence this disease diagnosis is pertinent to the prognosis of patients across the globe. Timely diagnosis can benefit the patients from developing other disorders such as heart diseases, obesity, and renal diseases.

Combining multiple classifiers is an effective technique for improving accuracy. There are many general combining algorithms, such as Bagging, Boosting, or Error Correcting Output Coding, that significantly improve classifiers like decision trees, rule learners, or neural networks. Unfortunately, t hese combining methods do not improve the nearest neighbor classifier. In this paper, we present MFS, a combining algorithm designed to improve the accuracy of the nearest neighbor (NN) classifier. MFS combines multiple NN classifiers each using only a random subset of features. The experimental results are encouraging: On 25 datasets from the UCI repository, MFS significantly outperformed several standard NN variants and was competitive with boosted decision trees. In additional experiments, we show that MFS is robust to irrelevant features, and is able to reduce both bias and variance components of error.

Nearest neighbor classifiers are a popular method for multiclass recognition in a wide range of computer vision and pattern recognition domains. At the same time, the accuracy of nearest neighbor classi?ers is sensitive to the choice of distance measure. This paper introduces an algorithm that uses boosting to learn a distance measure for multiclass k-nearest neighbor classification. Given a family of distance measures as input, AdaBoost is used to learn a weighted distance measure, that is a linear combination of the input measures. The proposed method can be seen both as a novel way to learn a distance measure from data, and as a novel way to apply boosting to multiclass recognition problems that does not require output codes. In our approach, multiclass recognition of objects is reduced to a single binary recognition task, defined on triples of objects. Preliminary experiments with eight UCI datasets yield no clear winner among our method, boosting using output codes, and k-nn classification using an unoptimized distance measure. Our algorithm did achieve lower error rates in some of the datasets, which indicates that it is a method worth considering for nearest neighbor recognition in various pattern recognition domains.