Discriminatory Analysis - Nonparametric Discrimination: Consistency Properties

By E. Fix, J. Hodges. 1989

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “A classic example of nearest neighbor-based techniques is k-nearest neighbors (kNN) [98, 68].”
Learning to Continually Learn (2020, methodology): “Totest this prediction, we use the K-Nearest-Neighbor (KNN) al-gorithm [10] to predict the class label of images from the meta-test test set, using the Euclidean distance in the space of NM activations (labels come from the meta-test training set).”
Machine Learning in Agriculture: A Review (2018, methodology): “The most common learning algorithms in this category are the k-nearest neighbor [39], locally weighted learning [40], and learning vector quantization [41].”
Improved binary PSO for feature selection using gene expression data (2008, methodology): “The K -nearest neighbor ( K -NN) method was ﬁrst introduced by Fix and Hodges in 1951, and is one of the most popular nonparametric methods (Cover and Hart, 1967; Fix and Hodges, 1951).”
A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions (2013, background): “K-NN was first introduced by Fix and Hodges [25] in 1951.”
Data mining in the Life Sciences with Random Forest: a walk in the park or lost in the jungle? (2012, methodology): “The prediction performance of RF compares well to other classification algorithms [7] such as support vector machines (SVMs, [9, 10]), artificial neural networks [11–13], Bayesian classifiers [14, 15], logistic regression [16], k-nearest-neighbours [17], discriminant analysis such as Fisher’s linear”
A review of unsupervised feature selection methods (2019, methodology): “Evaluation using the classification accuracy or error rate of supervised classifiers such as kNN (Fix and Hodges 1951), SVM (Cortes and Vapnik 1995), and Naive Bayes (NB) (Maron 1961; John and Langley 1995), among others.”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, methodology): “Modern non-parametric density estimation began with the introduction of a kernel density estimator in the pioneering work of Fix and Hodges (1951), which was later republished as Fix and Hodges (1989).”
Modeling object appearance using Context-Conditioned Component Analysis (2015, methodology): “A simple example of this is K-Nearest Neighbors regression [12].”
On Bias, Variance, 0/1—Loss, and the Curse-of-Dimensionality (2004, methodology): “Some simple highly biased procedures such as “naive” Bayes (Good, 1965) and nearest neighbor methods (Fix and Hodges, 1951) remain competitive with and sometimes outperform more sophisticated ones, even with moderate to large training samples (Holte, 1993).”
Divergence Estimation for Multidimensional Densities Via $k$-Nearest-Neighbor Distances (2009, methodology): “Since its inception in 1951 [13], the nearest neighbor method has been shown to be a powerful nonparametric technique for classification [3], [9], density estimation [28], and regression estimation [8], [22].”
A weighted k-nearest neighbor density estimate for geometric inference (2011, methodology): “When ν is the Dirac measure at 1, we obtain k n (cid:5) j =1 p nj j = k n and, consequently, This is the original Loftsgaarden and Quesenberry k -nearest neighbor density estimate.”
Convergence of functional k-nearest neighbor regression estimate with functional responses (2011, methodology): “The k-nearest neighbor (k-NN) method addresses this problem by using adaptive neighborhood size based on the distance of a point from its neighbors [5, 4, 13].”
Selection of Variables for Cluster Analysis and Classification Rules (2006, methodology): “rules, such as Fisher’s linear discrimination (Fisher, 1936), nearest neighbor rules ( Fix and Hodges, 1951 ), regression trees-CART (Breiman et al., 1984), or reduced kernel discriminant analysis (Hern´andez and Velilla, 2005).”
Effects of Distance Measure Choice on K-Nearest Neighbor Classifier Performance: A Review (2017, unknown): “a, data science and machine learning. The K-nearest neighbor (KNN) is one of the oldest, simplest and accurate algorithms for patterns classication and regression models. KNN was proposed in 1951 by [20], and then modied by [15]. KNN has been identied as one of the top ten methods in data mining [82”