Constraint-based Sequential Pattern Mining with Decision Diagrams

Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.Comment: AAAI201

On Range Searching with Semialgebraic Sets II

Let $P$ be a set of $n$ points in $\R^d$. We present a linear-size data structure for answering range queries on $P$ with constant-complexity semialgebraic sets as ranges, in time close to $O(n^{1-1/d})$. It essentially matches the performance of similar structures for simplex range searching, and, for $d\ge 5$, significantly improves earlier solutions by the first two authors obtained in~1994. This almost settles a long-standing open problem in range searching. The data structure is based on the polynomial-partitioning technique of Guth and Katz [arXiv:1011.4105], which shows that for a parameter $r$, $1 < r \le n$, there exists a $d$-variate polynomial $f$ of degree $O(r^{1/d})$ such that each connected component of $\R^d\setminus Z(f)$ contains at most $n/r$ points of $P$, where $Z(f)$ is the zero set of $f$. We present an efficient randomized algorithm for computing such a polynomial partition, which is of independent interest and is likely to have additional applications

High-dimensional approximate nearest neighbor: k-d Generalized Randomized Forests

We propose a new data-structure, the generalized randomized kd forest, or kgeraf, for approximate nearest neighbor searching in high dimensions. In particular, we introduce new randomization techniques to specify a set of independently constructed trees where search is performed simultaneously, hence increasing accuracy. We omit backtracking, and we optimize distance computations, thus accelerating queries. We release public domain software geraf and we compare it to existing implementations of state-of-the-art methods including BBD-trees, Locality Sensitive Hashing, randomized kd forests, and product quantization. Experimental results indicate that our method would be the method of choice in dimensions around 1,000, and probably up to 10,000, and pointsets of cardinality up to a few hundred thousands or even one million; this range of inputs is encountered in many critical applications today. For instance, we handle a real dataset of $10^6$ images represented in 960 dimensions with a query time of less than $1$sec on average and 90\% responses being true nearest neighbors

Single image example-based super-resolution using cross-scale patch matching and Markov random field modelling

Example-based super-resolution has become increasingly popular over the last few years for its ability to overcome the limitations of classical multi-frame approach. In this paper we present a new example-based method that uses the input low-resolution image itself as a search space for high-resolution patches by exploiting self-similarity across different resolution scales. Found examples are combined in a high-resolution image by the means of Markov Random Field modelling that forces their global agreement. Additionally, we apply back-projection and steering kernel regression as post-processing techniques. In this way, we are able to produce sharp and artefact-free results that are comparable or better than standard interpolation and state-of-the-art super-resolution techniques