A self-index is a compressed data structure that supports locate queries-reporting all positions where a given pattern occurs in a string while maintaining the string in compressed form. While many self-indexes have been proposed, developing dynamically updatable ones supporting string insertions and deletions remains a challenge. The r-index (Gagie et al., JACM'20) is a representative static self-index based on the run-length Burrows-Wheeler transform (RLBWT), designed for highly repetitive strings. We present the dynamic r-index, a dynamic extension of the r-index that achieves updates in LCP-bounded time. The dynamic r-index supports count queries in$\mathcal{O}(m \log r / \log \log r)$time and locate queries in$\mathcal{O}(m \log r / \log \log r+$occ$\log r)$time, using$\mathcal{O}(r)$words of space, where$m$is the length of a query with occ occurrences and$r$is the number of runs in the RLBWT. Crucially, update operations are supported in$\mathcal{O}\left(\left(m+L_{\max}\right) \log n\right)$time for a substring of length$m$, where$n$is the text length and$L_{\max}$is the maximum LCP value; the average running time is$\mathcal{O}\left(\left(m+L_{\text{avg}}\right) \log n\right)$, where$L_{\text{avg}}$is the average LCP value. This LCP-bounded complexity is particularly advantageous for highly repetitive strings where LCP values are typically small. We experimentally demonstrate the practical efficiency of the dynamic r-index on various highly repetitive datasets.

We propose a novelstatistical approachto evaluate thestatistical significance(reliability) of the results from discriminative sub-trajectory mining, which we callStatistically Discriminative Sub-trajectory Mining (Stat-DSM). Given two groups of trajectories, the goal of Stat-DSM is to extract moving patterns in the form of sub-trajectories that occur statistically significantly more often in one group than in the other. An advantage of the proposed method is that the statistical significance of the extracted sub-trajectories are properly controlled in the sense that the probability of finding a falsely discriminative sub-trajectory is smaller than a specified significance threshold$\alpha$(e.g., 0.05), which is crucial when the method is used in scientific or social science studies under noisy environments. Finding such statistically discriminative sub-trajectories from a massive trajectory dataset is both computationally and statistically challenging. In the Stat-DSM method, we address these difficulties by introducing a tree representation of sub-trajectories, and applying an efficient permutation-based statistical inference method to the tree. To the best of our knowledge, Stat-DSM is the first method that provides a statistical approach to quantify the reliability of discriminative sub-trajectory mining results. We illustrate the effectiveness and scalability of the Stat-DSM method by applying it to a real-world dataset containing 1,000,000 trajectories.

Trajectory analysis has been a central problem in applications of location tracking systems. Recently, the (discrete) Fréchet distance becomes a popular approach for measuring the similarity of two trajectories because of its high feature extraction capability. Despite its importance, the Fréchet distance has several limitations: (i) sensitive to noise as a trade-off for its high feature extraction capability; and (ii) it cannot be incorporated into machine learning frameworks due to its non-smooth functions. To address these problems, we propose the Fréchet kernel (FRK), which is associated with a smoothed Fréchet distance using a combination of two approximation techniques. FRK can adaptively acquire appropriate extraction capability from trajectories while retaining robustness to noise. Theoretically, we find that FRK has a positive definite property, hence FRK can be incorporated into the kernel method. We also provide an efficient algorithm to calculate FRK. Experimentally, FRK outperforms other methods, including other kernel methods and neural networks, in various noisy real-data classification tasks.

Massive datasets of spatial trajectories representing the mobility of a diversity of moving objects are ubiquitous in research and industry. Similarity search of a large collection of trajectories is indispensable for turning these datasets into knowledge. Locality sensitive hashing (LSH) is a powerful technique for fast similarity searches. Recent methods employ LSH and attempt to realize an efficient similarity search of trajectories; however, those methods are inefficient in terms of search time and memory when applied to massive datasets. To address this problem, we present the trajectory-indexing succinct trit-array trie (tSTAT), which is a scalable method leveraging LSH for trajectory similarity searches. tSTAT quickly performs the search on a tree data structure called trie. We also present two novel techniques that enable to dramatically enhance the memory efficiency of tSTAT. One is a node reduction technique that substantially omits redundant trie nodes while maintaining the time performance. The other is a space-efficient representation that leverages the idea behind succinct data structures (i.e., a compressed data structure supporting fast data operations). We experimentally test tSTAT on its ability to retrieve similar trajectories for a query from large collections of trajectories and show that tSTAT performs superiorly in comparison to state-of-the-art similarity search methods.

Similarity-preserving hashing is a core technique for fast similarity searches, and it randomly maps data points in a metric space to strings of discrete symbols (i.e., sketches) in the Hamming space. While traditional hashing techniques produce binary sketches, recent ones produce integer sketches for preserving various similarity measures. However, most similarity search methods are designed for binary sketches and inefficient for integer sketches. Moreover, most methods are either inapplicable or inefficient for dynamic datasets, although modern real-world datasets are updated over time. We propose dynamic filter trie (DyFT), a dynamic similarity search method for both binary and integer sketches. An extensive experimental analysis using large real-world datasets shows that DyFT performs superiorly with respect to scalability, time performance, and memory efficiency. For example, on a huge dataset of 216 million data points, DyFT performs a similarity search 6,000 times faster than a state-of-the-art method while reducing to one-thirteenth in memory.

Abstract String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit-sensitive parsing and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses. The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications. We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.

Abstract Here, we present a novel algorithm for frequent itemset mining in streaming data (FIM-SD). For the past decade, various FIM-SD methods in one-pass approximation settings that allow to approximate the support of each itemset have been proposed. They can be categorized into two approximation types: parameter-constrained (PC) mining and resource-constrained (RC) mining. PC methods control the maximum error that can be included in the approximate support based on a pre-defined parameter. In contrast, RC methods limit the maximum memory consumption based on resource constraints. However, the existing PC methods can exponentially increase the memory consumption, while the existing RC methods can rapidly increase the maximum error. In this study, we address this problem by introducing a hybrid approach of PC-RC approximations, called PARASOL. For any streaming data, PARASOL ensures to provide a condensed representation, called a Δ-covered set, which is regarded as an extension of the closedness compression; when Δ = 0, the solution corresponds to the ordinary closed itemsets. PARASOL searches for such approximate closed itemsets that can restore the frequent itemsets and their supports while the maximum error is bounded by an integer, Δ. Then, we empirically demonstrate that the proposed algorithm significantly outperforms the state-of-the-art PC and RC methods for FIM-SD.

Recently, randomly mapping vectorial data to strings of discrete symbols (i.e., sketches) for fast and space-efficient similarity searches has become popular. Such random mapping is called similarity-preserving hashing and approximates a similarity metric by using the Hamming distance. Although many efficient similarity searches have been proposed, most of them are designed for binary sketches. Similarity searches on integer sketches are in their infancy. In this paper, we present a novel space-efficient trie named b-bit sketch trie on integer sketches for scalable similarity searches by leveraging the idea behind succinct data structures (i.e., space-efficient data structures while supporting various data operations in the compressed format) and a favorable property of integer sketches as fixed-length strings. Our experimental results obtained using real-world datasets show that a trie-based index is built from integer sketches and efficiently performs similarity searches on the index by pruning useless portions of the search space, which greatly improves the search time and space-efficiency of the similarity search. The experimental results show that our similarity search is at most one order of magnitude faster than state-of-the-art similarity searches. Besides, our method needs only 10 GiB of memory on a billion-scale database, while state-of-the-art similarity searches need 29 GiB of memory.

Lossless data compression has been widely studied in computer science. One of the most widely used lossless data compressions is Lempel-Ziv (LZ) 77 parsing, which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing is a lossless data compression and computes a sequence of phrases copied from another substring (target phrase) on either the left or the right position in an input string. Gagie et al. (LATIN 2018) recently showed that a large gap exists between the number of smallest bidirectional phrases of a given string and that of LZ77 phrases. In addition, finding the smallest bidirectional parse of a given text is NP-complete. Several variants of bidirectional parsing have been proposed thus far, but no prior work for bidirectional parsing has achieved high compression that is smaller than that of LZ77 phrasing for any string. In this paper, we present the first practical bidirectional parsing named LZ77 parsing with right reference (LZRR), in which the number of LZRR phrases is theoretically guaranteed to be smaller than the number of LZ77 phrases. Experimental results using benchmark strings show the number of LZRR phrases is approximately five percent smaller than that of LZ77 phrases.

We propose a novel statistical approach to evaluate the statistical significance (reliability) of the findings in the discriminative sub-trajectory mining problem, called Statistically Discriminative Sub-trajectory Mining (Stat-DSM). Given two groups of trajectories, the goal is to extract moving patterns in the form of sub-trajectories that occur statistically significantly more often in one group than in the other. An advantage of the Stat-DSM method is that the statistical significance of the extracted sub-trajectories are properly controlled in the sense that the probability of finding a false discriminative sub-trajectory is smaller than a specified significance threshold a (e.g., 0.05). We conduct experiments on real-world datasets to demonstrate the effectiveness of the Stat-DSM method.

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs). The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors. Thus, we present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.

We present a novel compressed dynamic self-index for highly repetitive text collections. Signature encoding, an existing self-index of this type, has a large disadvantage of slow pattern search for short patterns. We obtain faster pattern search by leveraging the idea behind a truncated suffix tree (TST) to develop the first compressed dynamic self-index, called the TST-index, that supports not only fast pattern search but also dynamic update operations for highly repetitive texts. Experiments with a benchmark dataset show that the pattern search performance of the TST-index is significantly improved.

Building sparse combinatorial model with non-negative constraint is essential in solving real-world problems such as in biology, in which the target response is often formulated by additive linear combination of features variables. This paper presents a solution to this problem by combining itemset mining with non-negative least squares. However, once incorporation of modern regularization is considered, then a naive solution requires to solve expensive enumeration problem many times for every regularization parameter. In this paper, we devise a regularization path tracking algorithm such that combinatorial feature is searched and included one by one to the solution set. Our contribution is a proposal of novel bounds specifically designed for the feature search problem. In synthetic dataset, the proposed method is demonstrated to run orders of magnitudes faster than a naive counterpart which does not employ tree pruning. We also empirically show that non-negativity constraints can reduce the number of active features much less than that of LASSO, leading to significant speed-ups in pattern search. In experiments using HIV-1 drug resistance dataset, the proposed method could successfully model the rapidly increasing drug resistance triggered by accumulation of mutations in HIV-1 genetic sequences. We also demonstrate the effectiveness of non-negativity constraints in suppressing false positive features, resulting in a model with smaller number of features and thereby improved interpretability.

With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge is the ability to learn statistical models with high interpretability. Current methods for learning statistical models either produce models that are not interpretable or have prohibitive computational costs when applied to massive data. In this paper we address this need by presenting a scalable algorithm for partial least squares regression (PLS), which we call compression-based PLS (cPLS), to learn predictive linear models with a high interpretability from massive high-dimensional data. We propose a novel grammar-compressed representation of data matrices that supports fast row and column access while the data matrix is in a compressed form. The original data matrix is grammar-compressed and then the linear model in PLS is learned on the compressed data matrix, which results in a significant reduction in working space, greatly improving scalability. We experimentally test cPLS on its ability to learn linear models for classification, regression and feature extraction with various massive high-dimensional data, and show that cPLS performs superiorly in terms of prediction accuracy, computational efficiency, and interpretability.

We describe a data structure that stores a strings in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data structures, such as compressed trees and graphs. We show that our data structure can be built in a scalable manner and is both small and fast in practice compared to other data structures supporting such queries.

We present novel variants of fully online LCA (FOLCA), a fully online grammar compression that builds a straight line program (SLP) and directly encodes it into a succinct representation in an online manner. FOLCA enables a direct encoding of an SLP into a succinct representation that is asymptotically equivalent to an information theoretic lower bound for representing an SLP (Maruyama et al., SPIRE'13). The compression of FOLCA takes linear time proportional to the length of an input text and its working space depends only on the size of the SLP, which enables us to apply FOLCA to large-scale repetitive texts. Recent repetitive texts, however, include some noise. For example, current sequencing technology has significant error rates, which embeds noise into genome sequences. For such noisy repetitive texts, FOLCA working in the SLP size consumes a large amount of memory. We present two variants of FOLCA working in constant space by leveraging the idea behind stream mining techniques. Experiments using 100 human genomes corresponding to about 300GB from the 1000 human genomes project revealed the applicability of our method to large-scale, noisy repetitive texts.

Analyzing functional interactions between small compounds and proteins is indispensable in genomic drug discovery. Since rich information on various compound-protein inter- actions is available in recent molecular databases, strong demands for making best use of such databases require to in- vent powerful methods to help us find new functional compound-protein pairs on a large scale. We present the succinct interval-splitting tree algorithm (SITA) that efficiently per- forms similarity search in databases for compound-protein pairs with respect to both binary fingerprints and real-valued properties. SITA achieves both time and space efficiency by developing the data structure called interval-splitting trees, which enables to efficiently prune the useless portions of search space, and by incorporating the ideas behind wavelet tree, a succinct data structure to compactly represent trees. We experimentally test SITA on the ability to retrieve similar compound-protein pairs/substrate-product pairs for a query from large databases with over 200 million compound- protein pairs/substrate-product pairs and show that SITA performs better than other possible approaches.

Similarity search in databases of labeled graphs is a fundamental task in managing graph data such as XML, chemical compounds and social networks. Typically, a graph is decomposed to a set of substructures (e.g., paths, trees and subgraphs) and a similarity measure is defined via the number of common substructures. Using the representation, graphs can be stored in a document database by regarding graphs as documents and substructures as words. A graph similarity query then translates to a semi-conjunctive query that retrieves graphs sharing at least k substructures in common with the query graph. We argue that this kind of query cannot be solved efficiently by conventional inverted indexes, and develop a novel recursive search algorithm on wavelet trees (Grossi et al., SODA'03). Unlike gIndex, it does not require frequent subgraph mining for indexing. In experiments, our method was successfully applied to 25 million chemical compounds.