Simple and deterministic matrix sketching

Liberty, Edo

doi:10.1145/2487575.2487623

Cited by 242 publications

(282 citation statements)

References 33 publications

(30 reference statements)

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“…3. MatrixSketching [11] clustering results (recorded in NMI) on 20NG-10 dataset, which is a subset of 20Newsgroups with 10 clusters. We ran the algorithm 20 times and every time we shuffled the input order randomly.…”

Section: Discussionmentioning

confidence: 99%

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Diverse Power Iteration Embeddings and Its Applications

Huang

Yoo

et al. 2014

2014 IEEE International Conference on Data Mining

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Spectral Embedding is one of the most effective dimension reduction algorithms in data mining. However, its computation complexity has to be mitigated in order to apply it for real-world large scale data analysis. Many researches have been focusing on developing approximate spectral embeddings which are more efficient, but meanwhile far less effective. This paper proposes Diverse Power Iteration Embeddings (DPIE), which not only retains the similar efficiency of power iteration methods but also produces a series of diverse and more effective embedding vectors. We test this novel method by applying it to various data mining applications (e.g. clustering, anomaly detection and feature selection) and evaluating their performance improvements. The experimental results show our proposed DPIE is more effective than popular spectral approximation methods, and obtains the similar quality of classic spectral embedding derived from eigen-decompositions. Moreover it is extremely fast on big data applications. For example in terms of clustering result, DPIE achieves as good as 95% of classic spectral clustering on the complex datasets but 4000+ times faster in limited memory environment.

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Section: Discussionmentioning

confidence: 99%

“…To overcome these limitations, several methods are proposed such as [13] [26] [11]. Among them, Power Iteration Clustering (PIC) [13] is one of the most promising candidates due to its speed, small memory requirements and yet effectiveness in obtaining clustering results for datasets with small number of clusters.…”

Section: Introductionmentioning

confidence: 99%

Diverse Power Iteration Embeddings and Its Applications

Huang

Yoo

et al. 2014

2014 IEEE International Conference on Data Mining

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“…Introduced in [47] and further analyzed in a series of papers culminating with [32], Frequent Directions sketches are easily maintained in a single-pass column stream of A.…”

Section: General Approachmentioning

confidence: 99%

Input Sparsity Time Low-rank Approximation via Ridge Leverage Score Sampling

Cohen

Musco

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present a new algorithm for finding a near optimal low-rank approximation of a matrix A in O(nnz(A)) time. Our method is based on a recursive sampling scheme for computing a representative subset of A's columns, which is then used to find a low-rank approximation.This approach differs substantially from prior O(nnz(A)) time algorithms, which are all based on fast Johnson-Lindenstrauss random projections.Our algorithm matches the guarantees of the random projection methods while offering a number of advantages.In addition to better performance on sparse and structured data, sampling algorithms can be applied in settings where random projections cannot. For example, we give new streaming algorithms for the column subset selection and projection-cost preserving sample problems. Our method has also been used in the fastest algorithms for provably accurate Nyström approximation of kernel matrices [56].

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“…Figure 1: Matrix sketching algorithm by Liberty (2013). In the output, X ∈ R n×d denotes the data matrix with rows x 1 .…”

Section: Deterministic Matrix Sketchingmentioning

confidence: 99%

Scalable Semi-Supervised Query Classification Using Matrix Sketching

Kim

Stratos

Sarikaya

2016

Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)

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The enormous scale of unlabeled text available today necessitates scalable schemes for representation learning in natural language processing. For instance, in this paper we are interested in classifying the intent of a user query. While our labeled data is quite limited, we have access to virtually an unlimited amount of unlabeled queries, which could be used to induce useful representations: for instance by principal component analysis (PCA). However, it is prohibitive to even store the data in memory due to its sheer size, let alone apply conventional batch algorithms. In this work, we apply the recently proposed matrix sketching algorithm to entirely obviate the problem with scalability (Liberty, 2013). This algorithm approximates the data within a specified memory bound while preserving the covariance structure necessary for PCA. Using matrix sketching, we significantly improve the user intent classification accuracy by leveraging large amounts of unlabeled queries.

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Simple and deterministic matrix sketching

Cited by 242 publications

References 33 publications

Diverse Power Iteration Embeddings and Its Applications

Diverse Power Iteration Embeddings and Its Applications

Input Sparsity Time Low-rank Approximation via Ridge Leverage Score Sampling

Scalable Semi-Supervised Query Classification Using Matrix Sketching

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