Detecting Poisoning Attacks on Hierarchical Malware Classification Systems

Anti-virus software based on unsupervised hierarchical clustering (HC) of malware samples has been shown to be vulnerable to poisoning attacks. In this kind of attack, a malicious player degrades anti-virus performance by submitting to the database samples specifically designed to collapse the classification hierarchy utilized by the anti-virus (and constructed through HC) or otherwise deform it in a way that would render it useless. Though each poisoning attack needs to be tailored to the particular HC scheme deployed, existing research seems to indicate that no particular HC method by itself is immune. We present results on applying a new notion of entropy for combinatorial dendrograms to the problem of controlling the influx of samples into the data base and deflecting poisoning attacks. In a nutshell, effective and tractable measures of change in hierarchy complexity are derived from the above, enabling on-the-fly flagging and rejection of potentially damaging samples. The information-theoretic underpinnings of these measures ensure their indifference to which particular poisoning algorithm is being used by the attacker, rendering them particularly attractive in this setting

Classification in mathematics, discrete metric spaces, and approximation by trees

This is partly an introductory survey paper to clustering and classification problems with particular emphasis on the classification of lists of key words and phrases from a given scientific domain such as mathematics. In addition the paper contains a number of new concepts and results; a number of open questions, and some as yet untried embryo clustering ideas. New are the idea of Urysohn distance (section 3), the idea of using Lipshitz distance (section 4), the universal lower bound in terms of Lipshitz distance for any fixed depth hierarchical classification scheme (section 8), the optimality of single link clustering with respect to Lipshitz distance (section 8); in addition there are new results on what I have started to call the Buneman tree of a metric space (section 9); also new are the ideas of third party support (section 11) and power set metrics (section 10)

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Incremental Non-Greedy Clustering at Scale

Clustering is the task of organizing data into meaningful groups. Modern clustering applications such as entity resolution put several demands on clustering algorithms: (1) scalability to massive numbers of points as well as clusters, (2) incremental additions of data, (3) support for any user-specified similarity functions. Hierarchical clusterings are often desired as they represent multiple alternative flat clusterings (e.g., at different granularity levels). These tree-structured clusterings provide for both fine-grained clusters as well as uncertainty in the presence of newly arriving data. Previous work on hierarchical clustering does not fully address all three of the aforementioned desiderata. Work on incremental hierarchical clustering often makes greedy, irrevocable clustering decisions that are regretted in the presence of future data. Work on scalable hierarchical clustering does not support incremental additions or deletions. These methods often make requirements on the similarity functions used and/or empirically tend to over merge clusters, which can lead to inaccurate clusterings. In this thesis, we present incremental and scalable methods for hierarchical clustering to empirically satisfy the above desiderata. Our work aims to represent uncertainty and meaningful alternative clusterings, to efficiently reconsider past decisions in the incremental case, and to use parallelism to scale to massive datasets. Our method, Grinch, handles incrementally arriving data in a non-greedy fashion, by reconsidering past decisions using tree structure re-arrangements (e.g., rotations and grafts) invoked in accordance with the user’s specified similarity function. To achieve scalability to massive datasets, our method, SCC, builds a hierarchical clusterings in a level-wise bottom-up manner. Certain clustering decisions are made independently in parallel within each level, and a global similarity threshold schedule prevents greedy over-merging. We show how SCC can be combined with the tree-structure re-arrangements in Grinch to form a mini-batch algorithm achieving both scalable and incremental performance. Lastly, we generalize our hierarchical clustering approaches to DAG-structured ones, which can better represent uncertainty in clustering by representing overlapping clusters. We introduce an efficient bottom-up method for DAG-structured clustering, Llama. For each of the proposed methods, we provide both a theoretical and empirical analysis. Empirically, our methods achieve state-of-the-art results on clustering benchmarks in both the batch and the incremental settings, including multiple point improvements in dendrogram purity and scalability to billions of points

Workshop Notes of the Sixth International Workshop "What can FCA do for Artificial Intelligence?"

International audienc

Modeling Faceted Browsing with Category Theory for Reuse and Interoperability

Faceted browsing (also called faceted search or faceted navigation) is an exploratory search model where facets assist in the interactive navigation of search results. Facets are attributes that have been assigned to describe resources being explored; a faceted taxonomy is a collection of facets provided by the interface and is often organized as sets, hierarchies, or graphs. Faceted browsing has become ubiquitous with modern digital libraries and online search engines, yet the process is still difficult to abstractly model in a manner that supports the development of interoperable and reusable interfaces. We propose category theory as a theoretical foundation for faceted browsing and demonstrate how the interactive process can be mathematically abstracted in order to support the development of reusable and interoperable faceted systems. Existing efforts in facet modeling are based upon set theory, formal concept analysis, and light-weight ontologies, but in many regards they are implementations of faceted browsing rather than a specification of the basic, underlying structures and interactions. We will demonstrate that category theory allows us to specify faceted objects and study the relationships and interactions within a faceted browsing system. Resulting implementations can then be constructed through a category-theoretic lens using these models, allowing abstract comparison and communication that naturally support interoperability and reuse. In this context, reuse and interoperability are at two levels: between discrete systems and within a single system. Our model works at both levels by leveraging category theory as a common language for representation and computation. We will establish facets and faceted taxonomies as categories and will demonstrate how the computational elements of category theory, including products, merges, pushouts, and pullbacks, extend the usefulness of our model. More specifically, we demonstrate that categorical constructions such as the pullback and pushout operations can help organize and reorganize facets; these operations in particular can produce faceted views containing relationships not found in the original source taxonomy. We show how our category-theoretic model of facets relates to database schemas and discuss how this relationship assists in implementing the abstractions presented. We give examples of interactive interfaces from the biomedical domain to help illustrate how our abstractions relate to real-world requirements while enabling systematic reuse and interoperability. We introduce DELVE (Document ExpLoration and Visualization Engine), our framework for developing interactive visualizations as modular Web-applications in order to assist researchers with exploratory literature search. We show how facets relate to and control visualizations; we give three examples of text visualizations that either contain or interact with facets. We show how each of these visualizations can be represented with our model and demonstrate how our model directly informs implementation. With our general framework for communicating consistently about facets at a high level of abstraction, we enable the construction of interoperable interfaces and enable the intelligent reuse of both existing and future efforts

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282