This article proposes a comprehensive investigation of the automatic classification of functional gait disorders based solely on ground reaction force (GRF) measurements. The aim of the study is twofold: (1) to investigate the suitability of stateof-the-art GRF parameterization techniques (representations) for the discrimination of functional gait disorders; and (2) to provide a first performance baseline for the automated classification of functional gait disorders for a large-scale dataset. The utilized database comprises GRF measurements from 279 patients with gait disorders (GDs) and data from 161 healthy controls (N). Patients were manually classified into four classes with different functional impairments associated with the "hip", "knee", "ankle", and "calcaneus". Different parameterizations are investigated: GRF parameters, global principal component analysis (PCA)-based representations and a combined representation applying PCA on GRF parameters. The discriminative power of each parameterization for different classes is investigated by linear discriminant analysis (LDA). Based on this analysis, two classification experiments are pursued: (1) distinction between healthy and impaired gait (N vs. GD) and (2) multi-class classification between healthy gait and all four GD classes. Experiments show promising results and reveal among others that several factors, such as imbalanced class cardinalities and varying numbers of measurement sessions per patient have a strong impact on the classification accuracy and therefore need to be taken into account. The results represent a promising first step towards the automated classification of gait disorders and a first performance baseline for future developments in this direction.
The difficulty of multi-class classification generally increases with the number of classes. Using data from a subset of the classes, can we predict how well a classifier will scale with an increased number of classes? Under the assumptions that the classes are sampled identically and independently from a population, and that the classifier is based on independently learned scoring functions, we show that the expected accuracy when the classifier is trained on k classes is the (k-1)st moment of a certain distribution that can be estimated from data. We present an unbiased estimation method based on the theory, and demonstrate its application on a facial recognition example.
In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for empirical multi-class risk minimization algorithms using an arbitrary norm as regularizer. Key to our analysis are new structural results for multi-class Gaussian complexities and empirical $\ell_\infty$-norm covering numbers, which exploit the Lipschitz continuity of the loss function with respect to the $\ell_2$- and $\ell_\infty$-norm, respectively. We establish data-dependent error bounds in terms of complexities of a linear function class defined on a finite set induced by training examples, for which we show tight lower and upper bounds. We apply the results to several prominent multi-class learning machines, exhibiting a tighter dependency on the number of classes than the state of the art. For instance, for the multi-class SVM by Crammer and Singer (2002), we obtain a data-dependent bound with a logarithmic dependency which significantly improves the previous square-root dependency. Experimental results are reported to verify the effectiveness of our theoretical findings.
Considered in this short note is the design of output layer nodes of feedforward neural networks for solving multi-class classification problems with r (bigger than or equal to 3) classes of samples. The common and conventional setting of output layer, called "one-to-one approach" in this paper, is as follows: The output layer contains r output nodes corresponding to the r classes. And for an input sample of the i-th class, the ideal output is 1 for the i-th output node, and 0 for all the other output nodes. We propose in this paper a new "binary approach": Suppose r is (2^(q minus 1), 2^q] with q bigger than or equal to 2, then we let the output layer contain q output nodes, and let the ideal outputs for the r classes be designed in a binary manner. Numerical experiments carried out in this paper show that our binary approach does equally good job as, but uses less output nodes than, the traditional one-to-one approach.
A common method of generalizing binary to multi-class classification is the error correcting code (ECC). ECCs may be optimized in a number of ways, for instance by making them orthogonal. Here we test two types of orthogonal ECCs on seven different datasets using three types of binary classifier and compare them with three other multi-class methods: 1 vs. 1, one-versus-the-rest and random ECCs. The first type of orthogonal ECC, in which the codes contain no zeros, admits a fast and simple method of solving for the probabilities. Orthogonal ECCs are always more accurate than random ECCs as predicted by recent literature. Improvments in uncertainty coefficient (U.C.) range between 0.4--17.5% (0.004--0.139, absolute), while improvements in Brier score between 0.7--10.7%. Unfortunately, orthogonal ECCs are rarely more accurate than 1 vs. 1. Disparities are worst when the methods are paired with logistic regression, with orthogonal ECCs never beating 1 vs. 1. When the methods are paired with SVM, the losses are less significant, peaking at 1.5%, relative, 0.011 absolute in uncertainty coefficient and 6.5% in Brier scores. Orthogonal ECCs are always the fastest of the five multi-class methods when paired with linear classifiers. When paired with a piecewise linear classifier, whose classification speed does not depend on the number of training samples, classifications using orthogonal ECCs were always more accurate than the other methods and also faster than 1 vs. 1. Losses against 1 vs. 1 here were higher, peaking at 1.9% (0.017, absolute), in U.C. and 39% in Brier score. Gains in speed ranged between 1.1% and over 100%. Whether the speed increase is worth the penalty in accuracy will depend on the application.
Relational data sources are still one of the most popular ways to store enterprise or Web data, however, the issue with relational schema is the lack of a well-defined semantic description. A common ontology provides a way to represent the meaning of a relational schema and can facilitate the integration of heterogeneous data sources within a domain. Semantic labeling is achieved by mapping attributes from the data sources to the classes and properties in the ontology. We formulate this problem as a multi-class classification problem where previously labeled data sources are used to learn rules for labeling new data sources. The majority of existing approaches for semantic labeling have focused on data integration challenges such as naming conflicts and semantic heterogeneity. In addition, machine learning approaches typically have issues around class imbalance, lack of labeled instances and relative importance of attributes. To address these issues, we develop a new machine learning model with engineered features as well as two deep learning models which do not require extensive feature engineering. We evaluate our new approaches with the state-of-the-art.
Both neural networks and decision trees are popular machine learning methods and are widely used to solve problems from diverse domains. These two classifiers are commonly used base classifiers in an ensemble framework. In this paper, we first present a new variant of oblique decision tree based on a linear classifier, then construct an ensemble classifier based on the fusion of a fast neural network, random vector functional link network and oblique decision trees. Random Vector Functional Link Network has an elegant closed form solution with extremely short training time. The neural network partitions each training bag (obtained using bagging) at the root level into C subsets where C is the number of classes in the dataset and subsequently, C oblique decision trees are trained on such partitions. The proposed method provides a rich insight into the data by grouping the confusing or hard to classify samples for each class and thus, provides an opportunity to employ fine-grained classification rule over the data. The performance of the ensemble classifier is evaluated on several multi-class datasets where it demonstrates a superior performance compared to other state-of- the-art classifiers.
Hierarchical classification is supervised multi-class classification problem over the set of class labels organized according to a hierarchy. In this report, we study the work by Ramaswamy et. al. on hierarchical classification over symmetric tree distance loss. We extend the consistency of hierarchical classification algorithm over asymmetric tree distance loss. We design a $\mathcal{O}(nk\log{}n)$ algorithm to find Bayes optimal classification for a k-ary tree as a hierarchy. We show that under reasonable assumptions over asymmetric loss function, the Bayes optimal classification over this asymmetric loss can be found in $\mathcal{O}(k\log{}n)$. We exploit this insight and attempt to extend the Ova-Cascade algorithm \citet{ramaswamy2015convex} for hierarchical classification over the asymmetric loss.
It is a usual practice to ignore any structural information underlying classes in multi-class classification. In this paper, we propose a graph convolutional network (GCN) augmented neural network classifier to exploit a known, underlying graph structure of labels. The proposed approach resembles an (approximate) inference procedure in, for instance, a conditional random field (CRF). We evaluate the proposed approach on document classification and object recognition and report both accuracies and graph-theoretic metrics that correspond to the consistency of the model's prediction. The experiment results reveal that the proposed model outperforms a baseline method which ignores the graph structures of a label space in terms of graph-theoretic metrics.
Direction of arrival (DoA) estimation of targets improves with the number of elements employed by a phased array radar antenna. Since larger arrays have high associated cost, area and computational load, there is recent interest in thinning the antenna arrays without loss of far-field DoA accuracy. In this context, a cognitive radar may deploy a full array and then select an optimal subarray to transmit and receive the signals in response to changes in the target environment. Prior works have used optimization and greedy search methods to pick the best subarrays cognitively. In this paper, we leverage deep learning to address the antenna selection problem. Specifically, we construct a convolutional neural network (CNN) as a multi-class classification framework where each class designates a different subarray. The proposed network determines a new array every time data is received by the radar, thereby making antenna selection a cognitive operation. Our numerical experiments show that {the proposed CNN structure provides 22% better classification performance than a Support Vector Machine and the resulting subarrays yield 72% more accurate DoA estimates than random array selections.
Classification is a fundamental task in machine learning and data mining. Existing classification methods are designed to classify unknown instances within a set of previously known training classes. Such a classification takes the form of a prediction within a closed-set of classes. However, a more realistic scenario that fits real-world applications is to consider the possibility of encountering instances that do not belong to any of the training classes, $i.e.$, an open-set classification. In such situation, existing closed-set classifiers will assign a training label to these instances resulting in a misclassification. In this paper, we introduce Galaxy-X, a novel multi-class classification approach for open-set recognition problems. For each class of the training set, Galaxy-X creates a minimum bounding hyper-sphere that encompasses the distribution of the class by enclosing all of its instances. In such manner, our method is able to distinguish instances resembling previously seen classes from those that are of unknown ones. To adequately evaluate open-set classification, we introduce a novel evaluation procedure. Experimental results on benchmark datasets show the efficiency of our approach in classifying novel instances from known as well as unknown classes.
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class classification and inversion of partial differential equations. One popular formulation of such problems is as Bayesian inverse problems, where a prior distribution is used to regularize inference on a high-dimensional latent state, typically a function or a field. It is common that such priors are non-Gaussian, for example piecewise-constant or heavy-tailed, and/or hierarchical, in the sense of involving a further set of low-dimensional parameters, which, for example, control the scale or smoothness of the latent state. In this formulation prediction and uncertainty quantification relies on efficient exploration of the posterior distribution of latent states and parameters. This article introduces a framework for efficient MCMC sampling in Bayesian inverse problems that capitalizes upon two fundamental ideas in MCMC, non-centred parameterisations of hierarchical models and dimension-robust samplers for latent Gaussian processes. Using a range of diverse applications we showcase that the proposed framework is dimension-robust, that is, the efficiency of the MCMC sampling does not deteriorate as the dimension of the latent state gets higher. We showcase the full potential of the machinery we develop in the article in semi-supervised multi-class classification, where our sampling algorithm is used within an active learning framework to guide the selection of input data to manually label in order to achieve high predictive accuracy with a minimal number of labelled data.
The behavior of users in certain services could be a clue that can be used to infer their preferences and may be used to make recommendations for other services they have never used. However, the cross-domain relationships between items and user consumption patterns are not simple, especially when there are few or no common users and items across domains. To address this problem, we propose a content-based cross-domain recommendation method for cold-start users that does not require user- and item- overlap. We formulate recommendation as extreme multi-class classification where labels (items) corresponding to the users are predicted. With this formulation, the problem is reduced to a domain adaptation setting, in which a classifier trained in the source domain is adapted to the target domain. For this, we construct a neural network that combines an architecture for domain adaptation, Domain Separation Network, with a denoising autoencoder for item representation. We assess the performance of our approach in experiments on a pair of data sets collected from movie and news services of Yahoo! JAPAN and show that our approach outperforms several baseline methods including a cross-domain collaborative filtering method.
We design differentially private learning algorithms that are agnostic to the learning model. Our algorithms are interactive in nature, i.e., instead of outputting a model based on the training data, they provide predictions for a set of $m$ feature vectors that arrive online. We show that, for the feature vectors on which an ensemble of models (trained on random disjoint subsets of a dataset) makes consistent predictions, there is almost no-cost of privacy in generating accurate predictions for those feature vectors. To that end, we provide a novel coupling of the distance to instability framework with the sparse vector technique. We provide algorithms with formal privacy and utility guarantees for both binary/multi-class classification, and soft-label classification. For binary classification in the standard (agnostic) PAC model, we show how to bootstrap from our privately generated predictions to construct a computationally efficient private learner that outputs a final accurate hypothesis. Our construction - to the best of our knowledge - is the first computationally efficient construction for a label-private learner. We prove sample complexity upper bounds for this setting. As in non-private sample complexity bounds, the only relevant property of the given concept class is its VC dimension. For soft-label classification, our techniques are based on exploiting the stability properties of traditional learning algorithms, like stochastic gradient descent (SGD). We provide a new technique to boost the average-case stability properties of learning algorithms to strong (worst-case) stability properties, and then exploit them to obtain private classification algorithms. In the process, we also show that a large class of SGD methods satisfy average-case stability properties, in contrast to a smaller class of SGD methods that are uniformly stable as shown in prior work.
We introduce SentEval, a toolkit for evaluating the quality of universal sentence representations. SentEval encompasses a variety of tasks, including binary and multi-class classification, natural language inference and sentence similarity. The set of tasks was selected based on what appears to be the community consensus regarding the appropriate evaluations for universal sentence representations. The toolkit comes with scripts to download and preprocess datasets, and an easy interface to evaluate sentence encoders. The aim is to provide a fairer, less cumbersome and more centralized way for evaluating sentence representations.
Optimization of patient throughput and wait time in emergency departments (ED) is an important task for hospital systems. For that reason, Emergency Severity Index (ESI) system for patient triage was introduced to help guide manual estimation of acuity levels, which is used by nurses to rank the patients and organize hospital resources. However, despite improvements that it brought to managing medical resources, such triage system greatly depends on nurse's subjective judgment and is thus prone to human errors. Here, we propose a novel deep model based on the word attention mechanism designed for predicting a number of resources an ED patient would need. Our approach incorporates routinely available continuous and nominal (structured) data with medical text (unstructured) data, including patient's chief complaint, past medical history, medication list, and nurse assessment collected for 338,500 ED visits over three years in a large urban hospital. Using both structured and unstructured data, the proposed approach achieves the AUC of $\sim 88\%$ for the task of identifying resource intensive patients (binary classification), and the accuracy of $\sim 44\%$ for predicting exact category of number of resources (multi-class classification task), giving an estimated lift over nurses' performance by 16\% in accuracy. Furthermore, the attention mechanism of the proposed model provides interpretability by assigning attention scores for nurses' notes which is crucial for decision making and implementation of such approaches in the real systems working on human health.
We investigate the classification performance of K-nearest neighbors (K-NN) and deep neural networks (DNNs) in the presence of label noise. We first show empirically that a DNN's prediction for a given test example depends on the labels of the training examples in its local neighborhood. This motivates us to derive a realizable analytic expression that approximates the multi-class K-NN classification error in the presence of label noise, which is of independent importance. We then suggest that the expression for K-NN may serve as a first-order approximation for the DNN error. Finally, we demonstrate empirically the proximity of the developed expression to the observed performance of K-NN and DNN classifiers. Our result may explain the already observed surprising resistance of DNN to some types of label noise. It also characterizes an important factor of it showing that the more concentrated the noise the greater is the degradation in performance.
For many biological image segmentation tasks, including topological knowledge, such as the nesting of classes, can greatly improve results. However, most `out-of-the-box' CNN models are still blind to such prior information. In this paper, we propose a novel approach to encode this information, through a multi-level activation layer and three compatible losses. We benchmark all of them on nuclei segmentation in bright-field microscopy cell images from the 2018 Data Science Bowl challenge, offering an exemplary segmentation task with cells and nested subcellular structures. Our scheme greatly speeds up learning, and outperforms standard multi-class classification with soft-max activation and a previously proposed method stemming from it, improving the Dice score significantly (p-values<0.007). Our approach is conceptually simple, easy to implement and can be integrated in any CNN architecture. It can be generalized to a higher number of classes, with or without further relations of containment.
Various types of atherosclerotic plaque and varying grades of stenosis could lead to different management of patients with coronary artery disease. Therefore, it is crucial to detect and classify the type of coronary artery plaque, as well as to detect and determine the degree of coronary artery stenosis. This study includes retrospectively collected clinically obtained coronary CT angiography (CCTA) scans of 163 patients. To perform automatic analysis for coronary artery plaque and stenosis classification, a multi-task recurrent convolutional neural network is applied on multi-planar reformatted (MPR) images of the coronary arteries. First, a 3D convolutional neural network is utilized to extract features along the coronary artery. Subsequently, the extracted features are aggregated by a recurrent neural network that performs two simultaneous multi-class classification tasks. In the first task, the network detects and characterizes the type of the coronary artery plaque (no plaque, non-calcified, mixed, calcified). In the second task, the network detects and determines the anatomical significance of the coronary artery stenosis (no stenosis, non-significant i.e. <50% luminal narrowing, significant i.e. >50% luminal narrowing). For detection and classification of coronary plaque, the method achieved an accuracy of 0.77. For detection and classification of stenosis, the method achieved an accuracy of 0.80. The results demonstrate that automatic detection and classification of coronary artery plaque and stenosis are feasible. This may enable automated triage of patients to those without coronary plaque and those with coronary plaque and stenosis in need for further cardiovascular workup.
We introduce a novel approach for discriminative classification using evolutionary algorithms. We first propose an algorithm to optimize the total loss value using a modified 0-1 loss function in a one-dimensional space for classification. We then extend this algorithm for multi-dimensional classification using an evolutionary algorithm. The proposed evolutionary algorithm aims to find a hyperplane which best classifies instances while minimizes the classification risk. We test particle swarm optimization, evolutionary strategy, and covariance matrix adaptation evolutionary strategy for optimization purpose. Finally, we compare our results with well-established and state-of-the-art classification algorithms, for both binary and multi-class classification, on 19 benchmark classification problems, with and without noise and outliers. Results show that the performance of the proposed algorithm is significantly (t-test) better than all other methods in almost all problems tested. We also show that the proposed algorithm is significantly more robust against noise and outliers comparing to other methods. The running time of the algorithm is within a reasonable range for the solution of real-world classification problems.