Massive multiple-input multiple-output (MIMO) systems are vital to current-generation wireless networks and provide reliable communication at higher data rates. This advantage comes at the cost of enhanced signal processing at the receiver. This work proposes a novel rescaled Kronecker volume sampling (RKVS) based efficient multi-user data detector for uplink massive MIMO communication networks. The proposed RKVS detector has a faster asymptotic run-time than linear detectors like zero-forcing (ZF), minimum mean squared error (MMSE), and low-complexity approximations having polynomial run-time complexity. Theoretical analysis shows that the RKVS detector’s test statistic is an unbiased estimator of the ZF detector’s test statistic. Numerical results further prove that the error performance of the RKVS detector lies in close approximation to the ZF detector and is superior to detectors employing state-of-the-art sampling-based regression approximation.

Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors over categorical attributes to low-dimension discrete vectors do not provide any guarantee on the Hamming distances between the compressed representations. Here we presentFSketchto create sketches for a sparse categorical data and an estimator to estimate the pairwise Hamming distances among the uncompressed data only from their sketches. We claim that these sketches can be used in the usual data mining tasks in place of the original data without compromising the quality of the task. For that we ensure that the sketches also are categorical, sparse, and the Hamming distance estimates are reasonably precise. Both the sketch construction and the Hamming distance estimation algorithms require just a single-pass; furthermore, changes to a data point can be incorporated into its sketch in an efficient manner. The compressibility depends upon how sparse the data is and is independent of the original dimension – making our algorithm attractive for many real-life scenarios. Our claims are backed by rigorous theoretical analysis of the properties ofFSketchand supplemented by extensive comparative evaluations with related algorithms on some real-world datasets. We show thatFSketchis significantly faster, and the accuracy obtained by using its sketches are among the top for the standard unsupervised tasks of$\mathrm{RMSE}$, clustering and similarity search.

Representation learning using network embedding has received tremendous attention due to its efficacy to solve downstream tasks. Popular embedding methods (such as deepwalk,node2vec,LINE) are based on a neural architecture, thus unable to scale on large networks both in terms of time and space usage. Recently, we proposed BinSketch, a sketching technique for compressing binary vectors to binary vectors. In this paper, we show how to extend BinSketch and use it for network hashing. Our proposal named QUINT is built upon BinSketch, and it embeds nodes of a sparse network onto a low-dimensional space using simple bit-wise operations. QUINT is the first of its kind that provides tremendous gain in terms of speed and space usage without compromising much on the accuracy of the downstream tasks. Extensive experiments are conducted to compare QUINT with seven state-of-the-art network embedding methods for two end tasks link prediction and node classification. We observe huge performance gain for QUINT in terms of speedup (up to 7000) and space saving (up to 800) due to its bit-wise nature to obtain node embedding.Moreover, QUINT is a consistent top-performer for both the tasks among the baselines across all the datasets. Our empirical observations are backed by rigorous theoretical analysis to justify the effectiveness of QUINT.

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering problems, the input is a set of points in some metric space, and a common goal is to compute a set of centers in some other space (points, lines) that will minimize the sum of distances to these points. In database queries, we may need to compute such a some for a specific query set of $k$ centers. However, traditional algorithms cannot handle modern systems that require parallel real-time computations of infinite distributed streams from sensors such as GPS, audio or video that arrive to a cloud, or networks of weaker devices such as smartphones or robots. Core-set is a "small data" summarization of the input "big data", where every possible query has approximately the same answer on both data sets. Generic techniques enable efficient coreset \changed{maintenance} of streaming, distributed and dynamic data. Traditional algorithms can then be applied on these coresets to maintain the approximated optimal solutions. The challenge is to design coresets with provable tradeoff between their size and approximation error. This survey summarizes such constructions in a retrospective way, that aims to unified and simplify the state-of-the-art.

Computing the angular similarity between pairs of vectors is a core part of various machine learning algorithms. The seminal work of Charikar (a.k.a. Sign-Random-Projection (SRP) or SimHash) provides an unbiased estimate for the same. However, SRP suffers from the following limitations: (i) large variance in the similarity estimation, (ii) and high running time while computing the sketch. There are improved variants that address these limitations. However, they are known to improve on only one aspect in their proposal, for e.g. Yu et al. suggest a faster algorithm, Ji et al., Kang and Wong, provide estimates with a smaller variance. In this work, we propose a sketching algorithm that addresses both aspects in one algorithm – a faster algorithm along with a smaller variance in the similarity estimation. Moreover, our algorithm is space-efficient as well. We present a rigorous theoretical analysis of our proposal and complement it via experiments on synthetic and real-world datasets.

Feature hashing algorithms [14], [21] are well-known algorithmic techniques for handling large dimensionality of the datasets. These methods reduce the dimensionality of data points while preserving the pairwise distance, or similarity between them. However, to the best of our knowledge, these feature hashing algorithms are not adaptable to the dynamic insertion and deletion of features. In this work, we suggest algorithms using which the existing feature hashing algorithms can be made adapted to dynamic feature insertion and deletion. Our algorithms fit in the framework of both real-valued [21], and binary [14] feature hashing algorithms. We show a theoretical analysis of our algorithms, and complement it with experiments on real-world datasets. Our algorithms suggest comparable accuracy w.r.t. baselines while simultaneously offering a significant speed-up in the running time. Our proposal is easy to implement and can be adopted in practice.

Generating succinct summaries (also known as sketches) of massive data streams is becoming increasingly important. Such a task typically requires fast, accurate, and small space algorithms in order to support the downstream applications, mainly in areas such as data analysis, machine learning and data mining. A fundamental and well-studied problem in this context is that of estimating the frequencies of the items appearing in a data stream. The Count-Min-Sketch (Cormode and Muthukrishnan, J. Algorithms, 55(1):58–75, 2005) and Count-Sketch (Charikar et al., Theor. Comput. Sci., 312(1):3–15, 2004) are two known classical algorithms for this purpose. However, a limitation of these techniques is that the variance of their estimate tends to be large. In this work, we address this problem and suggest a technique that reduces the variance in their respective estimates, at the cost of little computational overhead. Our technique relies on the classical Control-Variate trick (Lavenberg and Welch, Manage. Sci., 27:322–335, 1981) used for reducing variance in Monte-Carlo simulation. We present a theoretical analysis of our proposal by carefully choosing the control variates and complement them with experiments on synthetic as well as real-world datasets.

The seminal work of (Charikar, 2002) gives a space efficient sketching algorithm (Simhash) which compresses real-valued vectors to binary vectors while maintaining an estimate of the Cosine similarity between any pairs of original real-valued vectors. In this work, we propose a sketching algorithm – Simsketch – that can be applied on top of the results obtained from Simhash. This further reduces the data dimension while maintaining an estimate of the Cosine similarity between original real-valued vectors. As a consequence, it helps in scaling up the performance of Simhash. We present theoretical bounds of our result and complement it with experimentation on public datasets. Our proposed algorithm is simple, efficient, and therefore can be adopted in practice.

We present sketching algorithms for sparse binary datasets, which maintain binary version of the dataset after sketching, while simultaneously preserving multiple similarity measures such as Jaccard Similarity, Cosine Similarity, Inner Product, and Hamming Distance, on the same sketch. A major advantage of our algorithms is that they are randomness efficient, and require significantly less number of random bits for sketching – logarithmic in dimension, while other competitive algorithms require linear in dimension. Our proposed algorithms are efficient, offer a compact sketch of the dataset, and can be efficiently deployed in a distributive setting. We present a theoretical analysis of our approach and complement them with extensive experimentations on public datasets. For analysis purposes, our algorithms require a natural assumption on the dataset. We empirically verify the assumption and notice that it holds on several real-world datasets.

Massive biometric deployments are pervasive in today's world. But despite the high accuracy of biometric systems, their computational efficiency degrades drastically with an increase in the database size. Thus, it is essential to index them. Here, in this paper, we propose an iris indexing scheme using real-valued deep iris features binarized to iris bar codes (IBC) compatible with the indexing structure. Firstly, for extracting robust iris features, we have designed a network utilizing the domain knowledge of ordinal filtering and learning their nonlinear combinations. Later these real-valued features are binarized. Finally, for indexing the iris dataset, we have proposed a Mcomloss that can transform the binary feature into an improved feature compatible with the Multi-Index Hashing scheme. This Mcomloss function ensures the equal distribution of Hamming distance among all the contiguous disjoint sub-strings. To the best of our knowledge, this is the first work in the iris indexing domain that presents an end-to-end iris indexing structure. Experimental results on four datasets are presented to depict the efficacy of the proposed approach.

A good seeding or initialization of cluster centers for the $k$-means method is important from both theoretical and practical standpoints. The $k$-means objective is inherently non-robust and sensitive to outliers. A popular seeding such as the $k$-means++ [3] that is more likely to pick outliers in the worst case may compound this drawback, thereby affecting the quality of clustering on noisy data.For any $0 < \delta \leq 1$, we show that using a mixture of $D^{2}$ [3] and uniform sampling, we can pick $O(k/\delta)$ candidate centers with the following guarantee: they contain some $k$ centers that give $O(1)$-approximation to the optimal robust $k$-means solution while discarding at most $\delta n$ more points than the outliers discarded by the optimal solution. That is, if the optimal solution discards its farthest $\beta n$ points as outliers, our solution discards its $(\beta + \delta) n$ points as outliers. The constant factor in our $O(1)$-approximation does not depend on $\delta$. This is an improvement over previous results for $k$-means with outliers based on LP relaxation and rounding [7] and local search [17]. The $O(k/\delta)$ sized subset can be found in time $O(ndk)$. Our \emph{robust} $k$-means++ is also easily amenable to scalable, faster, parallel implementations of $k$-means++ [5]. Our empirical results show a comparison of the above \emph{robust} variant of $k$-means++ with the usual $k$-means++, uniform random seeding, threshold $k$-means++ [6] and local search on real world and synthetic data.

Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic tasks such as clustering, classification, ranking, nearest neighbour search, etc. scale poorly with the dimension of the dataset. In this work, we address this problem and propose a sketching (alternatively, dimensionality reduction) algorithm - BinSketch (Binary Data Sketch) - for sparse binary datasets. BinSketch preserves the binary version of the dataset after sketching and maintains estimates for multiple similarity measures such as Jaccard, Cosine, Inner-Product similarities, and Hamming distance, on the same sketch. We present a theoretical analysis of our algorithm and complement it with extensive experimentation on several real-world datasets. We compare the performance of our algorithm with the state-of-the-art algorithms on the task of mean-square-error and ranking. Our proposed algorithm offers a comparable accuracy while suggesting a significant speedup in the dimensionality reduction time, with respect to the other candidate algorithms. Our proposal is simple, easy to implement, and therefore can be adopted in practice.

The Spherical $k$-means algorithm proposed by (Dhillon and Modha, 2001) is a popular algorithm for clustering high dimensional datasets. Although their algorithm is simple and easy to implement, a drawback of the same is that it doesn’t provide any provable guarantee on the clustering result. (Endo and Miyamoto, 2015) suggest an adaptive sampling based algorithm (Spherical $k$-means$++$) which gives near optimal results, with high probability. However, their algorithm requires $k$ sequential passes over the entire dataset, which may not be feasible when the dataset and/or the values of $k$ are large. In this work, we propose a Markov chain based sampling algorithm that takes only one pass over the data, and gives close to optimal clustering similar to Spherical $k$-means$++$, i.e., a faster algorithm while maintaining almost the same approximation. We present a theoretical analysis of the algorithm, and complement it with rigorous experiments on real-world datasets. Our proposed algorithm is simple and easy to implement, and can be easily adopted in practice.

We propose a dimensionality reduction (sketching) algorithm for high dimensional, sparse, binary data. Our proposed algorithm provides a single sketch which simultaneously preserves multiple similarity measures including Hamming distance, Inner product, and Jaccard Similarity [12]. In contrast to the "local projection" strategy used by most of the earlier algorithms [6], [4], [7], our approach exploits sparsity and combines the following two strategies: 1. partitioning the dimensions into several buckets, 2. obtaining "global linear summaries" within those buckets. Our algorithm is faster than the existing state-of-the-art, and it preserves the binary format of the data after the dimensionality reduction, which makes the sketch space efficient. Our algorithm can also be easily adapted in streaming and incremental learning frameworks. We give a rigorous theoretical analysis of the dimensionality reduction bounds and complement it with extensive experiments. Our proposed algorithm is simple and easy to implement in practice.