A comparison of two dissimilarity functions for mixed-type predictor variables in the $$\delta $$-machine

The $$\delta $$ δ -machine is a statistical learning tool for classification based on dissimilarities or distances between profiles of the observations to profiles of a representation set, which was proposed by Yuan et al. (J Claasif 36(3): 442–470, 2019). So far, the $$\delta $$ δ -machine was restricted to continuous predictor variables only. In this article, we extend the $$\delta $$ δ -machine to handle continuous, ordinal, nominal, and binary predictor variables. We utilized a tailored dissimilarity function for mixed type variables which was defined by Gower. This measure has properties of a Manhattan distance. We develop, in a similar vein, a Euclidean dissimilarity function for mixed type variables. In simulation studies we compare the performance of the two dissimilarity functions and we compare the predictive performance of the $$\delta $$ δ -machine to logistic regression models. We generated data according to two population distributions where the type of predictor variables, the distribution of categorical variables, and the number of predictor variables was varied. The performance of the $$\delta $$ δ -machine using the two dissimilarity functions and different types of representation set was investigated. The simulation studies showed that the adjusted Euclidean dissimilarity function performed better than the adjusted Gower dissimilarity function; that the $$\delta $$ δ -machine outperformed logistic regression; and that for constructing the representation set, K-medoids clustering achieved fewer active exemplars than the one using K-means clustering while maintaining the accuracy. We also applied the $$\delta $$ δ -machine to an empirical example, discussed its interpretation in detail, and compared the classification performance with five other classification methods. The results showed that the $$\delta $$ δ -machine has a good balance between accuracy and interpretability.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

ToFU: Topology functional units for deep learning

<p style='text-indent:20px;'>We propose ToFU, a new trainable neural network unit with a persistence diagram dissimilarity function as its activation. Since persistence diagrams are topological summaries of structures, this new activation measures and learns the topology of data to leverage it in machine learning tasks. We showcase the utility of ToFU in two experiments: one involving the classification of discrete-time autoregressive signals, and another involving a variational autoencoder. In the former, ToFU yields competitive results with networks that use spectral features while outperforming CNN architectures. In the latter, ToFU produces topologically-interpretable latent space representations of inputs without sacrificing reconstruction fidelity.</p>

Inhibition of Occluded Facial Regions for Distance-Based Face Recognition

This work focuses on the design and validation of a CBR system for efficient face recognition under partial occlusion conditions. The proposed CBR system is based on a classical distance-based classification method, modified to increase its robustness to partial occlusion. This is achieved by using a novel dissimilarity function which discards features coming from occluded facial regions. In addition, we explore the integration of an efficient dimensionality reduction method into the proposed framework to reduce computational cost. We present experimental results showing that the proposed CBR system outperforms classical methods of similar computational requirements in the task of face recognition under partial occlusion.