Unsupervised learning by minimal entropy encoding

GenURL: A General Framework for Unsupervised Representation Learning

Unsupervised representation learning (URL) that learns compact embeddings of high-dimensional data without supervision has achieved remarkable progress recently. However, the development of URLs for different requirements is independent, which limits the generalization of the algorithms, especially prohibitive as the number of tasks grows. For example, dimension reduction (DR) methods, t-SNE and UMAP, optimize pairwise data relationships by preserving the global geometric structure, while self-supervised learning, SimCLR and BYOL, focuses on mining the local statistics of instances under specific augmentations. To address this dilemma, we summarize and propose a unified similarity-based URL framework, GenURL, which can adapt to various URL tasks smoothly. In this article, we regard URL tasks as different implicit constraints on the data geometric structure that help to seek optimal low-dimensional representations that boil down to data structural modeling (DSM) and low-dimensional transformation (LDT). Specifically, DSM provides a structure-based submodule to describe the global structures, and LDT learns compact low-dimensional embeddings with given pretext tasks. Moreover, an objective function, general Kullback-Leibler (GKL) divergence, is proposed to connect DSM and LDT naturally. Comprehensive experiments demonstrate that GenURL achieves consistent state-of-the-art performance in self-supervised visual learning, unsupervised knowledge distillation (KD), graph embeddings (GEs), and DR.

Self-Supervised Self-Organizing Clustering Network: A Novel Unsupervised Representation Learning Method

Deep learning-based clustering methods usually regard feature extraction and feature clustering as two independent steps. In this way, the features of all images need to be extracted before feature clustering, which consumes a lot of calculation. Inspired by the self-organizing map network, a self-supervised self-organizing clustering network ( [Formula: see text]OCNet) is proposed to jointly learn feature extraction and feature clustering, thus realizing a single-stage clustering method. In order to achieve joint learning, we propose a self-organizing clustering header (SOCH), which takes the weight of the self-organizing layer as the cluster centers, and the output of the self-organizing layer as the similarities between the feature and the cluster centers. In order to optimize our network, we first convert the similarities into probabilities which represents a soft cluster assignment, and then we obtain a target for self-supervised learning by transforming the soft cluster assignment into a hard cluster assignment, and finally we jointly optimize backbone and SOCH. By setting different feature dimensions, a Multilayer SOCHs strategy is further proposed by cascading SOCHs. This strategy achieves clustering features in multiple clustering spaces. [Formula: see text]OCNet is evaluated on widely used image classification benchmarks such as Canadian Institute For Advanced Research (CIFAR)-10, CIFAR-100, Self-Taught Learning (STL)-10, and Tiny ImageNet. Experimental results show that our method significant improvement over other related methods. The visualization of features and images shows that our method can achieve good clustering results.

A Weighting Method for Feature Dimension by Semisupervised Learning With Entropy

In this article, a semisupervised weighting method for feature dimension based on entropy is proposed for classification, dimension reduction, and correlation analysis. For real-world data, different feature dimensions usually show different importance. Generally, data in the same class are supposed to be similar, so their entropy should be small; and those in different classes are supposed to be dissimilar, so their entropy should be large. According to this, we propose a way to construct the weights of feature dimensions with the whole entropy and the innerclass entropies. The weights indicate the contribution of their corresponding feature dimensions in classification. They can be used to improve the performance of classification by giving a weighted distance metric and can be applied to dimension reduction and correlation analysis as well. Some numerical experiments are given to test the proposed method by comparing it with some other representative methods. They demonstrate that the proposed method is feasible and efficient in classification, dimension reduction, and correlation analysis.

Cognitive Action Laws: The Case of Visual Features

This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Artificial neural networks are regarded as systems whose connections are Lagrangian variables, namely, functions depending on time. They are used to minimize the cognitive action, an appropriate functional index that measures the agent interactions with the environment. The cognitive action contains a potential and a kinetic term that nicely resemble the classic formulation of regularization in machine learning. A special choice of the functional index, which leads to the fourth-order differential equations-Cognitive Action Laws (CAL)-exhibits a structure that mirrors classic formulation of machine learning. In particular, unlike the action of mechanics, the stationarity condition corresponds with the global minimum. Moreover, it is proven that typical asymptotic learning conditions on the weights can coexist with the initialization provided that the system dynamics is driven under a policy referred to as information overloading control. Finally, the theory is experimented for the problem of feature extraction in computer vision.

Insights Into the Robustness of Minimum Error Entropy Estimation

The minimum error entropy (MEE) is an important and highly effective optimization criterion in information theoretic learning (ITL). For regression problems, MEE aims at minimizing the entropy of the prediction error such that the estimated model preserves the information of the data generating system as much as possible. In many real world applications, the MEE estimator can outperform significantly the well-known minimum mean square error (MMSE) estimator and show strong robustness to noises especially when data are contaminated by non-Gaussian (multimodal, heavy tailed, discrete valued, and so on) noises. In this brief, we present some theoretical results on the robustness of MEE. For a one-parameter linear errors-in-variables (EIV) model and under some conditions, we derive a region that contains the MEE solution, which suggests that the MEE estimate can be very close to the true value of the unknown parameter even in presence of arbitrarily large outliers in both input and output variables. Theoretical prediction is verified by an illustrative example.

Power Quality Analysis Using a Hybrid Model of the Fuzzy Min-Max Neural Network and Clustering Tree

A hybrid intelligent model comprising a modified fuzzy min-max (FMM) clustering neural network and a modified clustering tree (CT) is developed. A review of clustering models with rule extraction capabilities is presented. The hybrid FMM-CT model is explained. We first use several benchmark problems to illustrate the cluster evolution patterns from the proposed modifications in FMM. Then, we employ a case study with real data related to power quality monitoring to assess the usefulness of FMM-CT. The results are compared with those from other clustering models. More importantly, we extract explanatory rules from FMM-CT to justify its predictions. The empirical findings indicate the usefulness of the proposed model in tackling data clustering and power quality monitoring problems under different environments.

Learning With Jensen-Tsallis Kernels

Jensen-type [Jensen-Shannon (JS) and Jensen-Tsallis] kernels were first proposed by Martins et al. (2009). These kernels are based on JS divergences that originated in the information theory. In this paper, we extend the Jensen-type kernels on probability measures to define positive-definite kernels on Euclidean space. We show that the special cases of these kernels include dot-product kernels. Since Jensen-type divergences are multidistribution divergences, we propose their multipoint variants, and study spectral clustering and kernel methods based on these. We also provide experimental studies on benchmark image database and gene expression database that show the benefits of the proposed kernels compared with the existing kernels. The experiments on clustering also demonstrate the use of constructing multipoint similarities.

Online Bayesian learning with natural sequential prior distribution

Online Bayesian learning has been successfully applied to online learning for multilayer perceptrons and radial basis functions. In online Bayesian learning, typically, the conventional transition model has been used. Although the conventional transition model is based on the squared norm of the difference between the current parameter vector and the previous parameter vector, the transition model does not adequately consider the difference between the current observation model and the previous observation model. To adequately consider this difference between the observation models, we propose a natural sequential prior. The proposed transition model uses a Fisher information matrix to consider the difference between the observation models more naturally. For validation, the proposed transition model is applied to an online learning problem for a three-layer perceptron.