In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
In this paper we formulate the framework of recovering a hidden orthonormal basis given access to a<lb>certain "Basis Encoding Function". We describe the class of Basis Encoding Functions (BEF), such that<lb>their local maxima on the unit sphere are in one-to-one correspondence with the basis elements. This<lb>description relies on a certain "hidden convexity" property of these functions. A number of theoretical<lb>and practical problems of recent interest can be interpreted as recovering a hidden basis from potentially<lb>noisy observations. Specifically, we show how our simple and general framework applies to Independent<lb>Component Analysis (ICA), tensor decompositions, spectral clustering and Gaussian mixture learning.<lb>We describe a new algorithm, "gradient iteration", for provable recovery of the hidden basis. We<lb>provide a complete theoretical analysis of Gradient Iteration both for the exact case as well as for the<lb>case when the observed function is a perturbation of the "true" underlying BEF. In both cases we show<lb>convergence and complexity bounds polynomial in dimension and other relevant parameters, such as<lb>perturbation size. Our perturbation results can be considered as a very general non-linear version of<lb>the classical Davis-Kahan theorem for eigenvectors of perturbations of symmetric matrices. In addition<lb>we show that in the exact case the algorithm converges superlinearly and give conditions relating the<lb>degree of convergence to properties of the Basis Encoding Function. Our algorithm can be viewed as a<lb>generalization of the classical power iteration method for eigenanalysis of symmetric matrices as well as<lb>a generalization of power iterations for tensors. Moreover, the Gradient Iteration algorithm can be easily<lb>and efficiently implemented in practice.

Ex Output:
Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive

Ex Input:
We propose a framework grounded in Logic Programming for representing and reasoning about business processes from both the procedural and ontological point of views. In particular, our goal is threefold: (1) define a logical language and a formal semantics for process models enriched with ontology-based annotations; (2) provide an effective inference mechanism that supports the combination of reasoning services dealing with the structural definition of a process model, its behavior, and the domain knowledge related to the participating business entities; (3) implement such a theoretical framework into a process modeling and reasoning platform. To this end we define a process ontology coping with a relevant fragment of the popular BPMN modeling notation. The behavioral semantics of a process is defined as a state transition system by following an approach similar to the Fluent Calculus, and allows us to specify state change in terms of preconditions and effects of the enactment of activities. Then we show how the procedural process knowledge can be seamlessly integrated with the domain knowledge specified by using the OWL 2 RL rule-based ontology language. Our framework provides a wide range of reasoning services, including CTL model checking, which can be performed by using standard Logic Programming inference engines through a goal-oriented, efficient, sound and complete evaluation procedure. We also present a software environment implementing the proposed framework, and we report on an experimental evaluation of the system, whose results are encouraging and show the viability of the approach.

Ex Output:
Ontology-based Representation and Reasoning on Process Models: A Logic Programming Approach

Ex Input:
Machine-learning techniques are widely used in security-related applications, like spam and malware detection. However, in such settings, they have been shown to be vulnerable to adversarial attacks, including the deliberate manipulation of data at test time to evade detection. In this work, we focus on the vulnerability of linear classifiers to evasion attacks. This can be considered a relevant problem, as linear classifiers have been increasingly used in embedded systems and mobile devices for their low processing time and memory requirements. We exploit recent findings in robust optimization to investigate the link between regularization and security of linear classifiers, depending on the type of attack. We also analyze the relationship between the sparsity of feature weights, which is desirable for reducing processing cost, and the security of linear classifiers. We further propose a novel octagonal regularizer that allows us to achieve a proper trade-off between them. Finally, we empirically show how this regularizer can improve classifier security and sparsity in real-world application examples including spam and malware detection.

Ex Output:
On Security and Sparsity of Linear Classifiers for Adversarial Settings