In this paper, we strengthen the competitive analysis results obtained for a fundamental online streaming problem, the Frequent Items Problem. Additionally, we contribute with a more detailed analysis of this problem, using alternative performance measures, supplementing the insight gained from competitive analysis. The results also contribute to the general study of performance measures for online algorithms. It has long been known that competitive analysis suffers from drawbacks in certain situations, and many alternative measures have been proposed. However, more systematic comparative studies of performance measures have been initiated recently, and we continue this work, using competitive analysis, relative interval analysis, and relative worst order analysis on the Frequent Items Problem.
We present a message-passing based parallel version of the Space Saving algorithm designed to solve the $k$--majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given threshold, and is therefore useful for iceberg queries and many other different contexts. We apply our algorithm to the detection of frequent items in both real and synthetic datasets whose probability distribution functions are a Hurwitz and a Zipf distribution respectively. Also, we compare its parallel performances and accuracy against a parallel algorithm recent…
Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured using the $L_p$ norm, which sums the differences between the two functions over all items in the domain. Although useful in many applications, the drawback of this error measure is that it treats approximation errors of all items in the same way, irrespective of whether the mass of an item is important for the downstream application that uses the approximatio…
Many problems on data streams have been studied at two extremes of difficulty: either allowing randomized algorithms, in the static setting (where they should err with bounded probability on the worst case stream); or when only deterministic and infallible algorithms are required. Some recent works have considered the adversarial setting, in which a randomized streaming algorithm must succeed even on data streams provided by an adaptive adversary that can see the intermediate outputs of the algorithm. In order to better understand the differences between these models, we study a streaming task…
Data mining techniques have been widely used in various applications. Binary search tree based frequent items is an effective method for automatically recognize the most frequent items, least frequent items and average frequent items. This paper presents a new approach in order to find out frequent items. The word frequent item refers to how many times the item appeared in the given input. This approach is used to find out item sets in any order using familiar approach binary search tree. The method adapted here is in order to find out frequent items by comparing and incrementing the counter v…
Here, we present a novel algorithm for frequent itemset mining for streaming data (FIM-SD). For the past decade, various FIM-SD methods in one-pass approximation settings have been developed to approximate the frequency of each itemset. These approaches 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 frequency based on a pre-defined parameter. In contrast, RC methods limit the maximum memory consumption based on resource constraints. However, the existing PC…
Detecting frequent elements is among the oldest and most-studied problems in the area of data streams. Given a stream of $m$ data items in $\{1, 2, \dots, n\}$, the objective is to output items that appear at least $d$ times, for some threshold parameter $d$, and provably optimal algorithms are known today. However, in many applications, knowing only the frequent elements themselves is not enough: For example, an Internet router may not only need to know the most frequent destination IP addresses of forwarded packages, but also the timestamps of when these packages appeared or any other meta-d…
Frequent Item-set Mining (FIM), sometimes called Market Basket Analysis (MBA) or Association Rule Learning (ARL), are Machine Learning (ML) methods for creating rules from datasets of transactions of items. Most methods identify items likely to appear together in a transaction based on the support (i.e. a minimum number of relative co-occurrence of the items) for that hypothesis. Although this is a good indicator to measure the relevance of the assumption that these items are likely to appear together, the phenomenon of very frequent items, referred to as ubiquitous items, is not addressed in …
The Expiration Streaming Model: Diameter, $k$-Center, Counting, Sampling, and Friends
University of Bonn（波恩大学）；University of Ljubljana（卢布尔雅那大学）；Institute of Mathematics, Physics and Mechanics（数学、物理和力学研究所）；University of Maryland, College Park（马里兰大学帕克分校）；Weizmann Institute of Science（魏茨曼科学研究所）；Microsoft Research（微软研究院）；Université Côte d’Azur（蔚蓝海岸大学）
Large scale decentralized systems, such as P2P, sensor or IoT device networks are becoming increasingly common, and require robust protocols to address the challenges posed by the distribution of data and the large number of peers belonging to the network. In this paper, we deal with the problem of mining frequent items in unstructured P2P networks. This problem, of practical importance, has many useful applications. We design P2PSS, a fully decentralized, gossip--based protocol for frequent items discovery, leveraging the Space-Saving algorithm. We formally prove the correctness and theoretic…
Estimating frequencies of items over data streams is a common building block in streaming data measurement and analysis. Misra and Gries introduced their seminal algorithm for the problem in 1982, and the problem has since been revisited many times due its practicality and applicability. We describe a highly optimized version of Misra and Gries' algorithm that is suitable for deployment in industrial settings. Our code is made public via an open source library called DataSketches that is already used by several companies and production systems. Our algorithm improves on two theoretical and pra…
We present FDCMSS, a new sketch-based algorithm for mining frequent items in data streams. The algorithm cleverly combines key ideas borrowed from forward decay, the Count-Min and the Space Saving algorithms. It works in the time fading model, mining data streams according to the cash register model. We formally prove its correctness and show, through extensive experimental results, that our algorithm outperforms $λ$-HCount, a recently developed algorithm, with regard to speed, space used, precision attained and error committed on both synthetic and real datasets.
We introduce and study the problem of computing the similarity self-join in a streaming context (SSSJ), where the input is an unbounded stream of items arriving continuously. The goal is to find all pairs of items in the stream whose similarity is greater than a given threshold. The simplest formulation of the problem requires unbounded memory, and thus, it is intractable. To make the problem feasible, we introduce the notion of time-dependent similarity: the similarity of two items decreases with the difference in their arrival time. By leveraging the properties of this time-dependent similar…
In this paper, we propose the first deterministic algorithms to solve the frequency estimation and frequent item problems in the bounded deletion model. We establish the space lower bound for solving the deterministic frequent items problem in the bounded deletion model, and propose the Lazy SpaceSaving$^\pm$ and SpaceSaving$^\pm$ algorithms with optimal space bound. We then develop an efficient implementation of the SpaceSaving$^\pm$ algorithm that minimizes the latency of update operations using novel data structures. The experimental evaluations testify that SpaceSaving$^\pm$ has accurate f…
We generalize the continuous observation privacy setting from Dwork et al. '10 and Chan et al. '11 by allowing each event in a stream to be a subset of some (possibly unknown) universe of items. We design differentially private (DP) algorithms for histograms in several settings, including top-$k$ selection, with privacy loss that scales with polylog$(T)$, where $T$ is the maximum length of the input stream. We present a meta-algorithm that can use existing one-shot top-$k$ DP algorithms as a subroutine to continuously release private histograms from a stream. Further, we present more practical…
Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the $k$-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as it provides a compact summary of the characteristics of the graph. However, the task is challenging, even more so for evolving graphs due to the streaming nature of the input and the exponential time complexity of the problem. In this paper, we initiate the study of the approximate FSM problem in both incremental and fully-dynamic streaming settings, where …
Frequent itemset mining has emerged as a fundamental problem in data mining and plays an important role in many data mining tasks, such as association analysis, classification, etc. In the framework of frequent itemset mining, the results are itemsets that are frequent in the whole database. However, in some applications, such recommendation systems and social networks, people are more interested in finding out the items that occur with some user-specified itemsets (query itemsets) most frequently in a database. In this paper, we address the problem by proposing a new mining task named top-k c…
We introduce and study a new data sketch for processing massive datasets. It addresses two common problems: 1) computing a sum given arbitrary filter conditions and 2) identifying the frequent items or heavy hitters in a data set. For the former, the sketch provides unbiased estimates with state of the art accuracy. It handles the challenging scenario when the data is disaggregated so that computing the per unit metric of interest requires an expensive aggregation. For example, the metric of interest may be total clicks per user while the raw data is a click stream with multiple rows per user.…
BESTMOD Laboratory（BESTMOD实验室）；Institut Supérieur de Gestion（高等管理学院）
Mining association rules is a task of data mining, which extracts knowledge in the form of significant implication relation of useful items (objects) from a database. Mining multilevel association rules uses concept hierarchies, also called taxonomies and defined as relations of type 'is-a' between objects, to extract rules that items belong to different levels of abstraction. These rules are more useful, more refined and more interpretable by the user. Several algorithms have been proposed in the literature to discover the multilevel association rules. In this article, we are interested in th…
Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A recently-introduced framework, named \emph{maximum submodular ranking} (MSR), tackles a family of ranking problems that arise naturally when resources are shared among multiple demands with different budgets. For example, the MSR framework can be used to rank web pages for multiple user intents. In this paper, we extend the MSR framework in the streaming setting. In par…
The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible. Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ fr…
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of pro…
Streaming computation plays an important role in large-scale data analysis. The sliding window model is a model of streaming computation which also captures the recency of the data. In this model, data arrives one item at a time, but only the latest $W$ data items are considered for a particular problem. The goal is to output a good solution at the end of the stream by maintaining a small summary during the stream. In this work, we propose a new algorithmic framework for designing efficient sliding window algorithms via bucketing-based sketches. Based on this new framework, we develop space-ef…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low dimensional LP-type problems appear frequently in various machine learning tasks such as robust regression, support vector machines, and core vector machines. As supporting large-scale machine learning queries in database systems has become an important direction for database research, obtaining efficient algorithms for low dimensional LP-type problems on m…
Set intersection is the core in a variety of problems, e.g. frequent itemset mining and sparse boolean matrix multiplication. It is well-known that large speed gains can, for some computational problems, be obtained by using a graphics processing unit (GPU) as a massively parallel computing device. However, GPUs require highly regular control flow and memory access patterns, and for this reason previous GPU methods for intersecting sets have used a simple bitmap representation. This representation requires excessive space on sparse data sets. In this paper we present a novel data layout, "BatM…
While there has been a lot of work on finding frequent itemsets in transaction data streams, none of these solve the problem of finding similar pairs according to standard similarity measures. This paper is a first attempt at dealing with this, arguably more important, problem. We start out with a negative result that also explains the lack of theoretical upper bounds on the space usage of data mining algorithms for finding frequent itemsets: Any algorithm that (even only approximately and with a chance of error) finds the most frequent k-itemset must use space Omega(min{mb,n^k,(mb/phi)^k}) bi…
The probabilistic-stream model was introduced by Jayram et al. \cite{JKV07}. It is a generalization of the data stream model that is suited to handling ``probabilistic'' data where each item of the stream represents a probability distribution over a set of possible events. Therefore, a probabilistic stream determines a distribution over potentially a very large number of classical "deterministic" streams where each item is deterministically one of the domain values. The probabilistic model is applicable for not only analyzing streams where the input has uncertainties (such as sensor data strea…
The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High quality approximations of FI's and AR's are sufficient for most practical uses, and a number of recent works explored the application of sampling for fast discovery of approximate solutions to the problems. However, these works do not provide satisfactory performance gua…
Hong Kong University of Science and Technology（香港科技大学）；University of Warwick（华威大学）
We study the fundamental problem of frequency estimation under both privacy and communication constraints, where the data is distributed among $k$ parties. We consider two application scenarios: (1) one-shot, where the data is static and the aggregator conducts a one-time computation; and (2) streaming, where each party receives a stream of items over time and the aggregator continuously monitors the frequencies. We adopt the model of multiparty differential privacy (MDP), which is more general than local differential privacy (LDP) and (centralized) differential privacy. Our protocols achieve …
