Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log^2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Groebner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp. 619-628. For source code and experimental results, see http://www.ics.uci.edu/~eppstein/projects/pairs

Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute m eigenvalues of the generalized symmetric eigenvalue problem in $\mathcal{O}(n m \log^\alpha n)$ operations, where $\alpha>0$ is a small constant

Modeling relation paths for knowledge base completion via joint adversarial training

Knowledge Base Completion (KBC), which aims at determining the missing relations between entity pairs, has received increasing attention in recent years. Most existing KBC methods focus on either embedding the Knowledge Base (KB) into a specific semantic space or leveraging the joint probability of Random Walks (RWs) on multi-hop paths. Only a few unified models take both semantic and path-related features into consideration with adequacy. In this paper, we propose a novel method to explore the intrinsic relationship between the single relation (i.e. 1-hop path) and multi-hop paths between paired entities. We use Hierarchical Attention Networks (HANs) to select important relations in multi-hop paths and encode them into low-dimensional vectors. By treating relations and multi-hop paths as two different input sources, we use a feature extractor, which is shared by two downstream components (i.e. relation classifier and source discriminator), to capture shared/similar information between them. By joint adversarial training, we encourage our model to extract features from the multi-hop paths which are representative for relation completion. We apply the trained model (except for the source discriminator) to several large-scale KBs for relation completion. Experimental results show that our method outperforms existing path information-based approaches. Since each sub-module of our model can be well interpreted, our model can be applied to a large number of relation learning tasks.Comment: Accepted by Knowledge-Based System

Forward-secure hierarchical predicate encryption

Secrecy of decryption keys is an important pre-requisite for security of any encryption scheme and compromised private keys must be immediately replaced. \emph{Forward Security (FS)}, introduced to Public Key Encryption (PKE) by Canetti, Halevi, and Katz (Eurocrypt 2003), reduces damage from compromised keys by guaranteeing confidentiality of messages that were encrypted prior to the compromise event. The FS property was also shown to be achievable in (Hierarchical) Identity-Based Encryption (HIBE) by Yao, Fazio, Dodis, and Lysyanskaya (ACM CCS 2004). Yet, for emerging encryption techniques, offering flexible access control to encrypted data, by means of functional relationships between ciphertexts and decryption keys, FS protection was not known to exist.\smallskip In this paper we introduce FS to the powerful setting of \emph{Hierarchical Predicate Encryption (HPE)}, proposed by Okamoto and Takashima (Asiacrypt 2009). Anticipated applications of FS-HPE schemes can be found in searchable encryption and in fully private communication. Considering the dependencies amongst the concepts, our FS-HPE scheme implies forward-secure flavors of Predicate Encryption and (Hierarchical) Attribute-Based Encryption.\smallskip Our FS-HPE scheme guarantees forward security for plaintexts and for attributes that are hidden in HPE ciphertexts. It further allows delegation of decrypting abilities at any point in time, independent of FS time evolution. It realizes zero-inner-product predicates and is proven adaptively secure under standard assumptions. As the ``cross-product" approach taken in FS-HIBE is not directly applicable to the HPE setting, our construction resorts to techniques that are specific to existing HPE schemes and extends them with what can be seen as a reminiscent of binary tree encryption from FS-PKE

Bayesian Speaker Adaptation Based on a New Hierarchical Probabilistic Model

In this paper, a new hierarchical Bayesian speaker adaptation method called HMAP is proposed that combines the advantages of three conventional algorithms, maximum a posteriori (MAP), maximum-likelihood linear regression (MLLR), and eigenvoice, resulting in excellent performance across a wide range of adaptation conditions. The new method efficiently utilizes intra-speaker and inter-speaker correlation information through modeling phone and speaker subspaces in a consistent hierarchical Bayesian way. The phone variations for a specific speaker are assumed to be located in a low-dimensional subspace. The phone coordinate, which is shared among different speakers, implicitly contains the intra-speaker correlation information. For a specific speaker, the phone variation, represented by speaker-dependent eigenphones, are concatenated into a supervector. The eigenphone supervector space is also a low dimensional speaker subspace, which contains inter-speaker correlation information. Using principal component analysis (PCA), a new hierarchical probabilistic model for the generation of the speech observations is obtained. Speaker adaptation based on the new hierarchical model is derived using the maximum a posteriori criterion in a top-down manner. Both batch adaptation and online adaptation schemes are proposed. With tuned parameters, the new method can handle varying amounts of adaptation data automatically and efficiently. Experimental results on a Mandarin Chinese continuous speech recognition task show good performance under all testing conditions