Edit distance

About: Edit distance is a research topic. Over the lifetime, 2887 publications have been published within this topic receiving 71491 citations.

Computing atom mappings for biochemical reactions without subgraph isomorphism.

Abstract: The ability to trace the fate of individual atoms through the metabolic pathways is needed in many applications of systems biology and drug discovery. However, this information is not immediately available from the most common metabolome studies and needs to be separately acquired. Automatic discovery of correspondence of atoms in biochemical reactions is called the "atom mapping problem." We suggest an efficient approach for solving the atom mapping problem exactly--finding mappings of minimum edge edit distance. The algorithm is based on A* search equipped with sophisticated heuristics for pruning the search space. This approach has clear advantages over the commonly used heuristic approach of iterative maximum common subgraph (MCS) algorithm: we explicitly minimize an objective function, and we produce solutions that typically require less manual curation. The two methods are similar in computational resource demands. We compare the performance of the proposed algorithm against several alternatives on data obtained from the KEGG LIGAND and RPAIR databases: greedy search, bi-partite graph matching, and the MCS approach. Our experiments show that alternative approaches often fail in finding mappings with minimum edit distance.

Learnable similarity functions and their application to record linkage and clustering

Abstract: Many machine learning and data mining tasks depend on functions that estimate similarity between instances. Similarity computations are particularly important in clustering and information integration applications, where pairwise distances play a central role in many algorithms. Typically, algorithms for these tasks rely on pre-defined similarity measures, such as edit distance or cosine similarity for strings, or Euclidean distance for vector-space data. However, standard distance functions are frequently suboptimal as they do not capture the appropriate notion of similarity for a particular domain, dataset, or application. In this thesis, we present several approaches for addressing this problem by employing learnable similarity functions. Given supervision in the form of similar or dis-similar pairs of instances, learnable similarity functions can be trained to provide accurate estimates for the domain and task at hand. We study the problem of adapting similarity functions in the context of several tasks: record linkage, clustering, and blocking. For each of these tasks, we present learnable similarity functions and training algorithms that lead to improved performance. In record linkage, also known as duplicate detection and entity matching, the goal is to identify database records referring to the same underlying entity. This requires estimating similarity between corresponding field values of records, as well as overall similarity between records. For computing field-level similarity between strings, we describe two learnable variants of edit distance that lead to improvements in linkage accuracy. For learning record-level similarity functions, we employ Support Vector Machines to combine similarities of individual record fields in proportion to their relative importance, yielding a high-accuracy linkage system. We also investigate strategies for efficient collection of training data which can be scarce due to the pairwise nature of the record linkage task. In clustering, similarity functions are essential as they determine the grouping of instances that is the goal of clustering. We describe a framework for integrating learnable similarity functions within a probabilistic model for semi-supervised clustering based on Hidden Markov Random Fields (HMRFs). The framework accommodates learning various distance measures, including those based on Bregman divergences (e.g., parameterized Mahalanobis distance and parameterized KL-divergence), as well as directional measures (e.g., cosine similarity). Thus, it is applicable to a wide range of domains and data representations. Similarity functions are learned within the HMRF-KMEANS algorithm derived from the framework, leading to significant improvements in clustering accuracy. The third application we consider, blocking, is critical in making record linkage and clustering algorithms scalable to large datasets, as it facilitates efficient selection of approximately similar instance pairs without explicitly considering all possible pairs. Previously proposed blocking methods require manually constructing a similarity function or a set of similarity predicates, followed by hand-tuning of parameters. We propose learning blocking functions automatically from linkage and semi-supervised clustering supervision, which allows automatic construction of blocking methods that are efficient and accurate. This approach yields computationally cheap learnable similarity functions that can be used for scaling up in a variety of tasks that rely on pairwise distance computations, including record linkage and clustering.

The Dyck Language Edit Distance Problem in Near-Linear Time

Abstract: Given a string σ over alphabet Σ and a grammar G defined over the same alphabet, how many minimum number of repairs (insertions, deletions and substitutions) are required to map σ into a valid member of G? The seminal work of Aho and Peterson in 1972 initiated the study of this language edit distance problem providing a dynamic programming algorithm for context free languages that runs in O(|G|2n3) time, where n is the string length and |G| is the grammar size. While later improvements reduced the running time to O(|G|n3), the cubic time complexity on the input length held a major bottleneck for applying these algorithms to their multitude of applications. In this paper, we study the language edit distance problem for a fundamental context free language, DYCK(s) representing the language of well-balanced parentheses of s different types, that has been pivotal in the development of formal language theory. We provide the very first it near-linear time} algorithm to tightly approximate the DYCK(s) language edit distance problem for any arbitrary s. DYCK(s) language edit distance significantly generalizes the well-studied string edit distance problem, and appears in most applications of language edit distance ranging from data quality in databases, generating automated error-correcting parsers in compiler optimization to structure prediction problems in biological sequences. Its nondeterministic counterpart is known as the hardest context free language. Our main result is an algorithm for edit distance computation to DYCK(s) for any positive integer s that runs in O(n1+ e polylog(n)) time and achieves an approximation factor of O(1/eβ(n)log|OPT|), for any e > 0. Here OPT is the optimal edit distance to DYCK(s) and β(n) is the best approximation factor known for the simpler problem of string edit distance running in analogous time. If we allow O(n1+e+|OPT|2ne) time, then the approximation factor can be reduced to O(1/e log|OPT|). Since the best known near-linear time algorithm for the string edit distance problem has β(n) = polylog(n), under near-linear time computation model both DYCK(s) language and string edit distance problems have polylog(n) approximation factors. This comes as a surprise since the former is a significant generalization of the latter and their exact computations via dynamic programming show a stark difference in time complexity. Rather less surprisingly, we show that the framework for efficiently approximating edit distance to DYCK(s) can be utilized for many other languages. We illustrate this by considering various memory checking languages (studied extensively under distributed verification) such as stack, queue, PQ and DEQUE which comprise of valid transcripts of stacks, queues, priority queues and double-ended queues respectively. Therefore, any language that can be recognized by these data structures, can also be repaired efficiently by our algorithm.