Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called "ground truth" communities. This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on those known communities. However, there are no planted communities in real world networks. Instead, it is standard practice to treat some observed discrete-valued node attributes, or metadata, as ground truth. Here, we show that metadata are not the same as ground truth, and that treating them as such induces severe theoretical and practical problems. We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks. However, community detection remains a powerful tool and node metadata still have value so a careful exploration of their relationship with network structure can yield insights of genuine worth. We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models. We demonstrate these techniques using both synthetic and real-world networks, and for multiple types of metadata and community structure.

In this paper, we propose a semi-supervised clustering method, CEC-IB, that models data with a set of Gaussian distributions and that retrieves clusters based on a partial labeling provided by the user (partition-level side information). By combining the ideas from cross-entropy clustering (CEC) with those from the information bottleneck method (IB), our method trades between three conflicting goals: the accuracy with which the data set is modeled, the simplicity of the model, and the consistency of the clustering with side information. Experiments demonstrate that CEC-IB has a performance comparable to Gaussian mixture models (GMM) in a classical semi-supervised scenario, but is faster, more robust to noisy labels, automatically determines the optimal number of clusters, and performs well when not all classes are present in the side information. Moreover, in contrast to other semi-supervised models, it can be successfully applied in discovering natural subgroups if the partition-level side information is derived from the top levels of a hierarchical clustering.

Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well as the robustness of attractor states of networks of neurons performing memory tasks. We find that robustness to output noise requires synaptic connections to be in a balanced regime in which excitation and inhibition are strong and largely cancel each other. We evaluate the conditions required for this regime to exist and determine the properties of networks operating within it. A plausible synaptic plasticity rule for learning that balances weight configurations is presented. Our theory predicts an optimal ratio of the number of excitatory and inhibitory synapses for maximizing the encoding capacity of balanced networks for a given statistics of afferent activations. Previous work has shown that balanced networks amplify spatio-temporal variability and account for observed asynchronous irregular states. Here we present a novel type of balanced network that amplifies small changes in the impinging signals, and emerges automatically from learning to perform neuronal and network functions robustly.

The Microsoft Azure Machine Learning Algorithm Cheat Sheet helps you choose the right algorithm for a predictive analytics model. Azure Machine Learning Studio has a large library of algorithms from the regression, classification, clustering, and anomaly detection families. Each is designed to address a different type of machine learning problem. Download the cheat sheet here: Machine Learning Algorithm Cheat Sheet (11x17 in.) Download and print the Machine Learning Algorithm Cheat Sheet in tabloid size to keep it handy and get help choosing an algorithm.

Today, read any tech article or news and you will be fired with the terms "Artificial Intelligence", "Machine Learning" and "Deep Learning". The biggest corporate giants Google, IBM, Facebook, Microsoft and Amazon are voraciously acquiring Artificial Intelligence startups and companies. In just 3 months of 2017, 34 acquisitions were made. Forrester in the new report, "Prediction 2017: Artificial Intelligence Will Drive the Insights Revolution", predicts a 300% increase in investment in Artificial Intelligence from 2016 to 2017. The report further proceeds to say that "insight-driven businesses will steal $ 1.2 trillion per annum from their less informed peer by 2020."

In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of the functional connection probabilities, to the rate $s$ of membership switching and to the unknown number of clusters. In addition, it is accompanied by non-asymptotic guarantees for the precision of estimation and clustering.

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an algorithm for identifying such linearly separable class utilizing linear programming. We described three application cases including an assumption of linear separability, Gaussian distribution, and the case of linear separability in transformed space of kernel functions. Finally, we demonstrated the work of the proposed algorithm on the USPS dataset and analyzed the relationship of the performance of the algorithm and the size of the initially labeled sample.

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.

Motivated by machine learning applications in networks of sensors, internet-of-things (IoT) devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a network of nodes---each one of which has a stream of data arriving at a constant rate---that solve a stochastic convex optimization problem by collaborating with each other over rate-limited communication links. To this end, we present and analyze two algorithms---termed distributed stochastic approximation mirror descent (D-SAMD) and {\em accelerated} distributed stochastic approximation mirror descent (AD-SAMD)---that are based on two stochastic variants of mirror descent. The main collaborative step in the proposed algorithms is approximate averaging of the local, noisy subgradients using distributed consensus. While distributed consensus is well suited for collaborative learning, its use in our setup results in perturbed subgradient averages due to rate-limited links, which may slow down or prevent convergence. Our main contributions in this regard are: (i) bounds on the convergence rates of D-SAMD and AD-SAMD in terms of the number of nodes, network topology, and ratio of the data streaming and communication rates, and (ii) sufficient conditions for order-optimum convergence of D-SAMD and AD-SAMD. In particular, we show that there exist regimes under which AD-SAMD, when compared to D-SAMD, achieves order-optimum convergence with slower communications rates. This is in contrast to the centralized setting in which use of accelerated mirror descent results in a modest improvement over regular mirror descent for stochastic composite optimization. Finally, we demonstrate the effectiveness of the proposed algorithms using numerical experiments.

We construct $\bf genRBF$ kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in $L_2$. Experiments show that introduced kernel applied to SVM classifier gives better results than other state-of-the-art methods, especially in the case when large number of features is missing. Moreover, it is easy to implement and can be used together with any kernel approaches with no additional modifications.