Clustering can be used to extract insights from data or to verify some of the assumptions held by the domain experts, namely data segmentation. In the literature, few methods can be applied in clustering qualitative values using the context associated with other variables present in the data, without losing interpretability. Moreover, the metrics for calculating dissimilarity between qualitative values often scale poorly for high dimensional mixed datasets. In this study, we propose a novel method for clustering qualitative values, based on Hierarchical Clustering (HQC), and using Maximum Mean Discrepancy. HQC maintains the original interpretability of the qualitative information present in the dataset. We apply HQC to two datasets. Using a mixed dataset provided by Spotify, we showcase how our method can be used for clustering music artists based on the quantitative features of thousands of songs. In addition, using financial features of companies, we cluster company industries, and discuss the implications in investment portfolios diversification.

Allowing humans to communicate through natural language with robots requires connections between words and percepts. The process of creating these connections is called symbol grounding and has been studied for nearly three decades. Although many studies have been conducted, not many considered grounding of synonyms and the employed algorithms either work only offline or in a supervised manner. In this paper, a cross-situational learning based grounding framework is proposed that allows grounding of words and phrases through corresponding percepts without human supervision and online, i.e. it does not require any explicit training phase, but instead updates the obtained mappings for every new encountered situation. The proposed framework is evaluated through an interaction experiment between a human tutor and a robot, and compared to an existing unsupervised grounding framework. The results show that the proposed framework is able to ground words through their corresponding percepts online and in an unsupervised manner, while outperforming the baseline framework.

Compared to (simple) clustering data into K clusters, hierarchical clustering is much more complex and much less understood. One of the few seminal advances in hierarchical clusterings is the introduction by Dasgupta (2016) of a general yet simple paradigm of hierarchical clustering as loss minimization. This paradigm was expanded by Charikar and Chatziafratis (2016) and Roy and Pokutta (2016). The latter work also introduces a new set of techniques for obtaining hierarchical clusterings by showing that optimizing the loss can be relaxed to a Linear Program (LP). This paper introduces the first method to obtain optimality guarantees in the context of hierarchical clustering. Specifically, it is shown that the Sublevel Set (SS) paradigm invented by Meila (2018) for simple, nonhiearchical clustering, can be extended as well to hierarchical clustering. The main contribution is show that there is a natural distance between hierarchical clusterings whose properties can be exploited in the setting of the SS problem we will present in Section 3. The Sublevel Set method produces stability theorems of the following form.

Though there are many library implementations of the k-means algorithm in Python, I decided to use only Numpy in order to provide an instructive approach. Numpy is a popular library in Python used for numerical computations. We first create a class called Kmeans and pass a single constructor argumentk to it. This argument is a hyperparameter. Hyperparameters are parameters that are set by the user before training the machine learning algorithm.

Improving the fuel efficiency of vehicles is imperative to reduce costs and protect the environment. While the efficient engine and vehicle designs, as well as intelligent route planning, are well-known solutions to enhance the fuel efficiency, research has also demonstrated that the adoption of fuel-efficient driving behaviors could lead to further savings. In this work, we propose a novel framework to promote fuel-efficient driving behaviors through real-time automatic monitoring and driver feedback. In this framework, a random-forest based classification model developed using historical data to identifies fuel-inefficient driving behaviors. The classifier considers driver-dependent parameters such as speed and acceleration/deceleration pattern, as well as environmental parameters such as traffic, road topography, and weather to evaluate the fuel efficiency of one-minute driving events. When an inefficient driving action is detected, a fuzzy logic inference system is used to determine what the driver should do to maintain fuel-efficient driving behavior. The decided action is then conveyed to the driver via a smartphone in a non-intrusive manner. Using a dataset from a long-distance bus, we demonstrate that the proposed classification model yields an accuracy of 85.2% while increasing the fuel efficiency up to 16.4%.

Attributed graph embedding, which learns vector representations from graph topology and node features, is a challenging task for graph analysis. Recently, methods based on graph convolutional networks (GCNs) have made great progress on this task. However,existing GCN-based methods have three major drawbacks. Firstly,our experiments indicate that the entanglement of graph convolutional filters and weight matrices will harm both the performance and robustness. Secondly, we show that graph convolutional filters in these methods reveal to be special cases of generalized Laplacian smoothing filters, but they do not preserve optimal low-pass characteristics. Finally, the training objectives of existing algorithms are usually recovering the adjacency matrix or feature matrix, which are not always consistent with real-world applications. To address these issues, we propose Adaptive Graph Encoder (AGE), a novel attributed graph embedding framework. AGE consists of two modules: (1) To better alleviate the high-frequency noises in the node features, AGE first applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an adaptive encoder that iteratively strengthens the filtered features for better node embeddings. We conduct experiments using four public benchmark datasets to validate AGE on node clustering and link prediction tasks. Experimental results show that AGE consistently outperforms state-of-the-art graph embedding methods considerably on these tasks.

Most of existing clustering algorithms are proposed without considering the selection bias in data. In many real applications, however, one cannot guarantee the data is unbiased. Selection bias might bring the unexpected correlation between features and ignoring those unexpected correlations will hurt the performance of clustering algorithms. Therefore, how to remove those unexpected correlations induced by selection bias is extremely important yet largely unexplored for clustering. In this paper, we propose a novel Decorrelation regularized K-Means algorithm (DCKM) for clustering with data selection bias. Specifically, the decorrelation regularizer aims to learn the global sample weights which are capable of balancing the sample distribution, so as to remove unexpected correlations among features. Meanwhile, the learned weights are combined with k-means, which makes the reweighted k-means cluster on the inherent data distribution without unexpected correlation influence. Moreover, we derive the updating rules to effectively infer the parameters in DCKM. Extensive experiments results on real world datasets well demonstrate that our DCKM algorithm achieves significant performance gains, indicating the necessity of removing unexpected feature correlations induced by selection bias when clustering.

Complex applications such as big data analytics involve different forms of coupling relationships that reflect interactions between factors related to technical, business (domain-specific) and environmental (including socio-cultural and economic) aspects. There are diverse forms of couplings embedded in poor-structured and ill-structured data. Such couplings are ubiquitous, implicit and/or explicit, objective and/or subjective, heterogeneous and/or homogeneous, presenting complexities to existing learning systems in statistics, mathematics and computer sciences, such as typical dependency, association and correlation relationships. Modeling and learning such couplings thus is fundamental but challenging. This paper discusses the concept of coupling learning, focusing on the involvement of coupling relationships in learning systems. Coupling learning has great potential for building a deep understanding of the essence of business problems and handling challenges that have not been addressed well by existing learning theories and tools. This argument is verified by several case studies on coupling learning, including handling coupling in recommender systems, incorporating couplings into coupled clustering, coupling document clustering, coupled recommender algorithms and coupled behavior analysis for groups.

This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes interpolating between the least cost (based on optimal movements) and the commute-cost (based on a random walk on G), depending on a temperature parameter T. To this end, the randomized shortest path formalism (RSP, [2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead of Kullback-Leibler divergence. The main consequence of this change is that the resulting routing policy (local transition probabilities) becomes sparser when T decreases, therefore inducing a sparse random walk on G converging to the least-cost directed acyclic graph when T tends to 0. Experimental comparisons on node clustering and semi-supervised classification tasks show that the derived dissimilarity measures based on expected routing costs provide state-of-the-art results. The sparse RSP is therefore a promising model of movements on a graph, balancing sparse exploitation and exploration in an optimal way.

Despite the popularity of explainable AI, there is limited work on effective methods for unsupervised learning. We study algorithms for $k$-means clustering, focusing on a trade-off between explainability and accuracy. Following prior work, we use a small decision tree to partition a dataset into $k$ clusters. This enables us to explain each cluster assignment by a short sequence of single-feature thresholds. While larger trees produce more accurate clusterings, they also require more complex explanations. To allow flexibility, we develop a new explainable $k$-means clustering algorithm, ExKMC, that takes an additional parameter $k' \geq k$ and outputs a decision tree with $k'$ leaves. We use a new surrogate cost to efficiently expand the tree and to label the leaves with one of $k$ clusters. We prove that as $k'$ increases, the surrogate cost is non-increasing, and hence, we trade explainability for accuracy. Empirically, we validate that ExKMC produces a low cost clustering, outperforming both standard decision tree methods and other algorithms for explainable clustering. Implementation of ExKMC available at https://github.com/navefr/ExKMC.