In the context of mining for frequent patterns using the standard levelwise algorithm, the following question arises: given the current level and the current set of frequent patterns, what is the maximal number of candidate patterns that can be generated on the next level? We answer this question by providing a tight upper bound, derived from a combinatorial result from the sixties by Kruskal and Katona. Our result is useful to reduce the number of database scans.
One of the first optimizations was the DHP algorithm proposed by @cite_25 . This algorithm uses a hashing scheme to collect upper bounds on the frequencies of the candidate patterns for the following pass. Patterns of which it is already known that they will turn up infrequent can then be eliminated from further consideration. The effectiveness of this technique only showed for the first few passes. Since our upper bound can be used to eliminate passes at the end, both techniques can be combined in the same algorithm.
@cite_25
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We propose a novel unsupervised method for discovering recurring patterns from a single view. A key contribution of our approach is the formulation and validation of a joint assignment optimization problem where multiple visual words and object instances of a potential recurring pattern are considered simultaneously. The optimization is achieved by a greedy randomized adaptive search procedure (GRASP) with moves specifically designed for fast convergence. We have quantified systematically the performance of our approach under stressed conditions of the input (missing features, geometric distortions). We demonstrate that our proposed algorithm outperforms state of the art methods for recurring pattern discovery on a diverse set of 400+ real world and synthesized test images. In this paper, we propose a new deep hashing (DH) approach to learn compact binary codes for large scale visual search. Unlike most existing binary codes learning methods which seek a single linear projection to map each sample into a binary vector, we develop a deep neural network to seek multiple hierarchical non-linear transformations to learn these binary codes, so that the nonlinear relationship of samples can be well exploited. Our model is learned under three constraints at the top layer of the deep network: 1) the loss between the original real-valued feature descriptor and the learned binary vector is minimized, 2) the binary codes distribute evenly on each bit, and 3) different bits are as independent as possible. To further improve the discriminative power of the learned binary codes, we extend DH into supervised DH (SDH) by including one discriminative term into the objective function of DH which simultaneously maximizes the inter-class variations and minimizes the intra-class variations of the learned binary codes. Experimental results show the superiority of the proposed approach over the state-of-the-arts. Mining discrete patterns in binary data is important for subsampling, compression, and clustering. We consider rank-one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds. We study a fundamental tradeoff issue in designing a distributed hash table (DHT) in peer-to-peer (P2P) networks: the size of the routing table versus the network diameter. Observing that existing DHT schemes have either 1) a routing table size and network diameter both of O(log sub 2 n), or 2) a routing table of size d and network diameter of O(n sup 1 d ), S. (2001) asked whether this represents the best asymptotic "state-efficiency" tradeoffs. We show that some straightforward routing algorithms achieve better asymptotic tradeoffs. However, such algorithms all cause severe congestion on certain network nodes, which is undesirable in a P2P network. We rigorously define the notion of "congestion" and conjecture that the above tradeoffs are asymptotically optimal for a congestion-free network. The answer to this conjecture is negative in the strict sense. However, it becomes positive if the routing algorithm is required to eliminate congestion in a "natural" way by being uniform. We also prove that the tradeoffs are asymptotically optimal for uniform algorithms. Furthermore, for uniform algorithms, we find that the routing table size of O(log sub 2 n) is a magic threshold point that separates two different "state-efficiency" regions. Our third result is to study the exact (instead of asymptotic) optimal tradeoffs for uniform algorithms. We propose a new routing algorithm that reduces the routing table size and the network diameter of Chord both by 21.4 without introducing any other protocol overhead, based on a novel number-theory technique. Our final result is to present Ulysses, a congestion-free nonuniform algorithm that achieves a better asymptotic "state-efficiency" tradeoff than existing schemes in the probabilistic sense, even under dynamic node joins leaves.