Multiclass classification

Summary

In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). While many classification algorithms (notably multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance. General strategies The existing multi-class classification techniques can be categorised into

transformation to binary
extension from binary
hierarchical classification.

Transformation to binary This section discusses strategies for reducing the problem of multiclass classification to multiple binary cla

Official source

https://en.wikipedia.org/wiki/Multiclass_classification

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Advances In Morphological Neural Networks: Training, Pruning And Enforcing Shape Constraints

Nikolaos Dimitriadis

In this paper, we study an emerging class of neural networks, the Morphological Neural networks, from some modern perspectives. Our approach utilizes ideas from tropical geometry and mathematical morphology. First, we state the training of a binary morphological classifier as a Difference-of-Convex optimization problem and extend this method to multiclass tasks. We then focus on general morphological networks trained with gradient descent variants and show, quantitatively via pruning schemes as well as qualitatively, the sparsity of the resulted representations compared to FeedForward networks with ReLU activations as well as the effect the training optimizer has on such compression techniques. Finally, we show how morphological networks can be employed to guarantee monotonicity and present a softened version of a known architecture, based on Maslov Dequantization, which alleviates issues of gradient propagation associated with its "hard" counterparts and moderately improves performance.

IEEE2021

In this work, we investigate the possible use of k-nearest neighbour (kNN) classifiers to perform frame-based acoustic phonetic classification, hence replacing Gaussian Mixture Models (GMM) or MultiLayer Perceptrons (MLP) used in standard Hidden Markov Models (HMMs). The driving motivation behind this idea is the fact that kNN is known to be an "optimal" classifier if a very large amount of training data is available (replacing the training of functional parameters by plain memorization of the training examples) and the correct distance metric is found. Nowadays, amount of training data is no longer an issue. In the current work, we thus specifically focused on the "correct" distance metric, mainly using an MLP to compute the probability that two input feature vectors are part of the same phonetic class or not. This MLP output can thus be used as a distance metric for kNN. While providing a "universal" distance metric, this work also enabled us to consider the speech recognition problem under a different angle, simply formulated in terms of hypothesis tests: "Given two feature vectors, what is the probability that these belong to the same (phonetic) class or not?". Actually, one of the main goals of the present thesis finally boils down to one interesting question: “Is it easier to classify feature vectors into C phonetic classes or to tell whether or not two feature vectors belong to the same class?”. This work was done with standard acoustic features as inputs (PLP) and with posterior features (resulting of another pre-training MLP). Both feature sets indeed exhibit different properties and metric spaces. For example, while the use of posteriors as input is motivated by the fact that they are speaker and environment independent (so they capture much of the phonetic information contained in the signal), they are also no longer Gaussian distributed. When showing mathematically that using the MLP as a similarity measure makes sense, we discovered that this measure was equivalent to a very simple metric that can be analytically computed without needing the use of an MLP. This new type of measure is in fact the scalar product between two posterior feature vectors. Experiments have been conducted on hypothesis tests and on kNN classification. Results of the hypothesis tests show that posterior feature vectors achieve better performance than acoustic feature vectors. Moreover, the use of the scalar product leads to better performance than the use of all other metrics (including the MLP-based distance metric), whatever the input features.

Idiap2009

A multi-class framework for a pedestrian cell transmission model accounting for population heterogeneity

Guy Alexander Cooper

This work is an extension of PedCTM, an aggregate and transient cell transmission model for multidirectional pedestrian flows in which pedestrian characteristics are assumed to be homogeneous across the population considered. Critically, one fundamental diagram relating pedestrian speed and flow to local pedestrian density is employed across the entire population. This work extends the model to population heterogeneity with a multi-class approach wherein each sub-population is assigned its own characteristic fundamental diagram. The model presented requires the implementation of an update cycle to minimize numerical dis- persion of pedestrians across all classes. In addition, multi-class dynamics introduces an element of competition in determining the flow constraints of the various classes. A priority scheme is implemented that allows for static, dynamic and stochastic determination of flow priorities throughout the network over the course of simulation. An attempt was made to base the class-specific fundamental diagrams off of inference from a dataset related to the PedFlux collaboration. Ultimately, however, the implementation made use of the Kladek formula for the speed-density relation. Preliminary simulations and results are presented to serve as a proof of concept.

2014

Idiap2009