There are two famous function decomposition methods in math: 1) Taylor Series and 2) Fourier Series. The Fourier series developed into the Fourier spectrum, which was applied to signal analysis. However, Because a function without a functional expression cannot be solved for its Taylor series, Taylor Series has rarely been used in engineering. Here we have solved this problem, learned from Fourier, developed Taylor series, constructed a relation spectrum, and applied it to system analysis. Specific engineering application: the knowledge of the intuitive link between muscle activity and the finger movement is vital for the design of commercial prosthetic hands that do not need user pre-training. However, this link has yet to be understood due to the complexity of human hand. In this study, the relation spectrum was developed for the first time and applied to analyze the muscle-finger system. We established controllable and human-readable polynomial neural network (CR-PNN) models for six degrees of freedom ( DOFs) in 8 subjects. Multiple fingers may be controlled by a single muscle, or multiple muscles may control a single finger. Thus, the research is based on two aspects: muscle synergy and muscle coupling for hand. The research gave the relation spectrum of the muscle-finger system and the knowledge of muscle coupling. The article is very short but significant. The contributions of this paper can be divided into two parts: (1) The findings of hand can contribute to design prosthetic hands. (2) The relation spectrum using CR-PNN can provide a reference for analyzing complex systems in multiple areas. (We're strong believers in Open Source, and provide CR-PNN code for others. GitHub: https://github.com/liugang1234567/CR-PNN#cr-pnn. )

Subsampling of received wireless signals is important for relaxing hardware requirements as well as the computational cost of signal processing algorithms that rely on the output samples. We propose a subsampling technique to facilitate the use of deep learning for automatic modulation classification in wireless communication systems. Unlike traditional approaches that rely on pre-designed strategies that are solely based on expert knowledge, the proposed data-driven subsampling strategy employs deep neural network architectures to simulate the effect of removing candidate combinations of samples from each training input vector, in a manner inspired by how wrapper feature selection models work. The subsampled data is then processed by another deep learning classifier that recognizes each of the considered 10 modulation types. We show that the proposed subsampling strategy not only introduces drastic reduction in the classifier training time, but can also improve the classification accuracy to higher levels than those reached before for the considered dataset. An important feature herein is exploiting the transferability property of deep neural networks to avoid retraining the wrapper models and obtain superior performance through an ensemble of wrappers over that possible through solely relying on any of them. Automatic modulation classification plays an important role in modern wireless communications. It finds applications in various commercial and military areas. For example, Software Defined Radios (SDR) use blind recognition of the modulation type to quickly adapt to various communication systems, without requiring control overhead. In military settings, friendly signals should be securely received, while hostile signals need to be efficiently recognized typically without prior information.

A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to sparse modeling with the vast family of elliptical probability distributions. It can also be directly implemented for $L_0$ norm regularized multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific $L_0$ norm regularized expectation-maximization likelihood maximization procedure is proposed for this sparse Student-t case. Examples with real data from stock prices log-returns and from artificially generated data demonstrate applicability, performances, and potentials of this methodology.

We aim to optimize a black-box function $f:\mathcal{X} \mapsto \mathbb{R}$ under the assumption that $f$ is H\"older smooth and has bounded norm in the RKHS associated with a given kernel $K$. This problem is known to have an agnostic Gaussian Process (GP) bandit interpretation in which an appropriately constructed GP surrogate model with kernel $K$ is used to obtain an upper confidence bound (UCB) algorithm. In this paper, we propose a new algorithm (\texttt{LP-GP-UCB}) where the usual GP surrogate model is augmented with Local Polynomial (LP) estimators of the H\"older smooth function $f$ to construct a multi-scale UCB guiding the search for the optimizer. We analyze this algorithm and derive high probability bounds on its simple and cumulative regret. We then prove that the elements of many common RKHS are H\"older smooth and obtain the corresponding H\"older smoothness parameters, and hence, specialize our regret bounds for several commonly used kernels. When specialized to the Squared Exponential (SE) kernel, \texttt{LP-GP-UCB} matches the optimal performance, while for the case of Mat\'ern kernels $(K_{\nu})_{\nu>0}$, it results in uniformly tighter regret bounds for all values of the smoothness parameter $\nu>0$. Most notably, for certain ranges of $\nu$, the algorithm achieves near-optimal bounds on simple and cumulative regrets, matching the algorithm-independent lower bounds up to polylog factors, and thus closing the large gap between the existing upper and lower bounds for these values of $\nu$. Additionally, our analysis provides the first explicit regret bounds, in terms of the budget $n$, for the Rational-Quadratic (RQ) and Gamma-Exponential (GE). Finally, experiments with synthetic functions as well as a CNN hyperparameter tuning task demonstrate the practical benefits of our multi-scale partitioning approach over some existing algorithms numerically.

Neural networks have seen limited use in prediction for high-dimensional data with small sample sizes, because they tend to overfit and require tuning many more hyperparameters than existing off-the-shelf machine learning methods. With small modifications to the network architecture and training procedure, we show that dense neural networks can be a practical data analysis tool in these settings. The proposed method, Ensemble by Averaging Sparse-Input Hierarchical networks (EASIER-net), appropriately prunes the network structure by tuning only two L1-penalty parameters, one that controls the input sparsity and another that controls the number of hidden layers and nodes. The method selects variables from the true support if the irrelevant covariates are only weakly correlated with the response; otherwise, it exhibits a grouping effect, where strongly correlated covariates are selected at similar rates. On a collection of real-world datasets with different sizes, EASIER-net selected network architectures in a data-adaptive manner and achieved higher prediction accuracy than off-the-shelf methods on average.

Influence maximization is a widely studied topic in network science, where the aim is to reach the maximum possible number of nodes, while only targeting a small initial set of individuals. It has critical applications in many fields, including viral marketing, information propagation, news dissemination, and vaccinations. However, the objective does not usually take into account whether the final set of influenced nodes is fair with respect to sensitive attributes, such as race or gender. Here we address fair influence maximization, aiming to reach minorities more equitably. We introduce Adversarial Graph Embeddings: we co-train an auto-encoder for graph embedding and a discriminator to discern sensitive attributes. This leads to embeddings which are similarly distributed across sensitive attributes. We then find a good initial set by clustering the embeddings. We believe we are the first to use embeddings for the task of fair influence maximization. While there are typically trade-offs between fairness and influence maximization objectives, our experiments on synthetic and real-world datasets show that our approach dramatically reduces disparity while remaining competitive with state-of-the-art influence maximization methods.

This paper focuses on Crime zone Identification. Then, it clarifies how we conducted the Belief Rule Base algorithm to produce interesting frequent patterns for crime hotspots. The paper also shows how we used an expert system to forecast potential types of crime. In order to further analyze the crime datasets, the paper introduces an analysis study by combining our findings of the Chittagong crime dataset with demographic information to capture factors that could affect neighborhood safety. The results of this solution could be used to raise awareness of the dangerous locations and to help agencies predict future crimes at a specific location in a given time.

Intelligent systems designed using machine learning algorithms require a large number of labeled data. Background knowledge provides complementary, real world factual information that can augment the limited labeled data to train a machine learning algorithm. The term Knowledge Graph (KG) is in vogue as for many practical applications, it is convenient and useful to organize this background knowledge in the form of a graph. Recent academic research and implemented industrial intelligent systems have shown promising performance for machine learning algorithms that combine training data with a knowledge graph. In this article, we discuss the use of relevant KGs to enhance input data for two applications that use machine learning -- recommendation and community detection. The KG improves both accuracy and explainability.

Fuzzy rule-based model is a powerful tool for imitating the human way of thinking and solving uncertainty-related problems as it allows for understandable and interpretable rule bases. The objective of this paper is to study the applicability of fuzzy rule-based modelling to quantify soil classification for engineering purposes by qualitatively considering soil index properties. The classification system of the Highway Research Board is considered to illustrate a fuzzy rule-based model. The soil's index properties are fuzzified using triangular functions, and the fuzzy membership values are calculated. Fuzzy arithmetical operators are then applied to the membership values obtained for classification. Fuzzy decision tree classification algorithm is used to derive fuzzy if-then rules to quantify qualitative soil classification. The proposed system is implemented in MATLAB. The results obtained are checked and the implementation of the proposed model is measured against the outcomes of the laboratory tests.

Motivation: Real-world data often contain measurements with both continuous and discrete values. Despite the availability of many libraries, data sets with mixed data types require intensive pre-processing steps, and it remains a challenge to describe the relationships between variables. The data understanding phase is an important step in the data mining process, however, without making any assumptions on the data, the search space is super-exponential in the number of variables. Methods: We propose graphical hypergeometric networks (HNet), a method to test associations across variables for significance using statistical inference. The aim is to determine a network using only the significant associations in order to shed light on the complex relationships across variables. HNet processes raw unstructured data sets and outputs a network that consists of (partially) directed or undirected edges between the nodes (i.e., variables). To evaluate the accuracy of HNet, we used well known data sets and in addition generated data sets with known ground truth. The performance of HNet is compared to Bayesian structure learning. Results: We demonstrate that HNet showed high accuracy and performance in the detection of node links. In the case of the Alarm data set we can demonstrate on average an MCC score of 0.33 + 0.0002 (P<1x10-6), whereas Bayesian structure learning resulted in an average MCC score of 0.52 + 0.006 (P<1x10-11), and randomly assigning edges resulted in a MCC score of 0.004 + 0.0003 (P=0.49). Conclusions: HNet can process raw unstructured data sets, allows analysis of mixed data types, it easily scales up in number of variables, and allows detailed examination of the detected associations. Availability: https://erdogant.github.io/hnet/