When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both paradigms have their pros and cons. While minimum cut clusterings are sensitive to noise, density-based clusterings have trouble handling clusters with varying densities. In this paper, we propose \textsc{SpectACl}: a method combining the advantages of both approaches, while solving the two mentioned drawbacks. Our method is easy to implement, such as spectral clustering, and theoretically founded to optimize a proposed density criterion of clusterings. Through experiments on synthetic and real-world data, we demonstrate that our approach provides robust and reliable clusterings.

There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work with both types of data, combining them to obtain better performance for both clustering and classification. Also, these datasets commonly have a high number of dimensions. This article presents a new semi-supervised method based on self-organizing maps (SOMs) for clustering and classification, called Semi-Supervised Self-Organizing Map (SS-SOM). The method can dynamically switch between supervised and unsupervised learning during the training according to the availability of the class labels for each pattern. Our results show that the SS-SOM outperforms other semi-supervised methods in conditions in which there is a low amount of labeled samples, also achieving good results when all samples are labeled.

Mixtures of Gaussian distributions are a popular choice in model-based clustering. Outliers can affect parameters estimation and, as such, must be accounted for. Algorithms such as TCLUST discern the most likely outliers, but only when the proportion of outlying points is known \textit{a priori}. It is proved that, for a finite Gaussian mixture model, the log-likelihoods of the subset models are beta-distributed. An algorithm is then proposed that predicts the proportion of outliers by measuring the adherence of a set of subset log-likelihoods to a beta reference distribution. This algorithm removes the least likely points, which are deemed outliers, until model assumptions are met.

In the recent years, there is a growing interest in semi-supervised learning, since, in many learning tasks, there is a plentiful supply of unlabeled data, but insufficient labeled ones. Hence, Semi-Supervised learning models can benefit from both types of data to improve the obtained performance. Also, it is important to develop methods that are easy to parameterize in a way that is robust to the different characteristics of the data at hand. This article presents a new method based on Self-Organizing Map (SOM) for clustering and classification, called Adaptive Local Thresholds Semi-Supervised Self-Organizing Map (ALTSS-SOM). It can dynamically switch between two forms of learning at training time, according to the availability of labels, as in previous models, and can automatically adjust itself to the local variance observed in each data cluster. The results show that the ALTSS-SOM surpass the performance of other semi-supervised methods in terms of classification, and other pure clustering methods when there are no labels available, being also less sensitive than previous methods to the parameters values.

Mean Shift is a hierarchical clustering algorithm. In contrast to supervised machine learning algorithms, clustering attempts to group data without having first been train on labeled data. Clustering is used in a wide variety of applications such as search engines, academic rankings and medicine. As opposed to K-Means, when using Mean Shift, you don't need to know the number of categories (clusters) beforehand. The downside to Mean Shift is that it is computationally expensive -- O(n²).

A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a nearest neighbour method instead. We formally prove the characteristic of Isolation Similarity with the use of the proposed method. The impact of Isolation Similarity on density-based clustering is studied here. We show for the first time that the clustering performance of the classic density-based clustering algorithm DBSCAN can be significantly uplifted to surpass that of the recent density-peak clustering algorithm DP. This is achieved by simply replacing the distance measure with the proposed nearest-neighbour-induced Isolation Similarity in DBSCAN, leaving the rest of the procedure unchanged. A new type of clusters called mass-connected clusters is formally defined. We show that DBSCAN, which detects density-connected clusters, becomes one which detects mass-connected clusters, when the distance measure is replaced with the proposed similarity. We also provide the condition under which mass-connected clusters can be detected, while density-connected clusters cannot.

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.

Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are only trained to minimize the training/test error, they could suffer from systematic discrimination against individuals based on their sensitive attributes such as gender or race. Recently, there has been a surge in machine learning society to develop algorithms for fair machine learning. In particular, many adversarial learning procedures have been proposed to impose fairness. Unfortunately, these algorithms either can only impose fairness up to first-order dependence between the variables, or they lack computational convergence guarantees. In this paper, we use R\'enyi correlation as a measure of fairness of machine learning models and develop a general training framework to impose fairness. In particular, we propose a min-max formulation which balances the accuracy and fairness when solved to optimality. For the case of discrete sensitive attributes, we suggest an iterative algorithm with theoretical convergence guarantee for solving the proposed min-max problem. Our algorithm and analysis are then specialized to fair classification and the fair clustering problem under disparate impact doctrine. Finally, the performance of the proposed R\'enyi fair inference framework is evaluated on Adult and Bank datasets.

Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this paper, called fission clustering (FC). It focuses on mining the dense families of a dataset and utilizes the information of the distance matrix to fissure clustering dataset into subsets. When we face the dataset which has a few points surround the dense families of clusters, K-nearest neighbors local density indicator is applied to distinguish and remove the points of sparse areas so as to obtain a dense subset that is constituted by the dense families of clusters. A number of frequently-used datasets were used to test the performance of this clustering approach, and to compare the results with those of algorithms. The proposed algorithm is found to outperform other algorithms in speed and accuracy.