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906
Entropybased Subspace Clustering for Mining Numerical Data
, 1999
"... Mining numerical data is a relatively difficult problem in data mining. Clustering is one of the techniques. We consider a database with numerical attributes, in which each transaction is viewed as a multidimensional vector. By studying the clusters formed by these vectors, we can discover certain ..."
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Cited by 111 (1 self)
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Mining numerical data is a relatively difficult problem in data mining. Clustering is one of the techniques. We consider a database with numerical attributes, in which each transaction is viewed as a multidimensional vector. By studying the clusters formed by these vectors, we can discover certain behaviors hidden in the data. Traditional clustering algorithms find clusters in the full space of the data sets. This results in high dimensional clusters, which are poorly comprehensible to human. One important task in this setting is the ability to discover clusters embedded in the subspaces of a highdimensional data set. This problem is known as subspace clustering. We follow the basic assumptions of previous work CLIQUE. It is found that the number of subspaces with clustering is very large, and a criterion called the coverage is proposed in CLIQUE for the pruning. In addition to coverage, we identify new useful criteria for this problem and propose an entropybased algorithm called ENC...
Capacity bounds via duality with applications to multipleantenna systems on flatfading channels
 IEEE Trans. Inform. Theory
, 2003
"... A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relativ ..."
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Cited by 101 (36 self)
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A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relative entropy) over distributions on the channel output alphabet. Every choice of an output distribution — even if not the channel image of some input distribution — leads to an upper bound on mutual information. The proposed approach is used in order to study multiantenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown (or only partially known) at the receiver. It is demonstrated that, for high signaltonoise ratio (SNR), the capacity of such channels typically grows only doublelogarithmically in the SNR. This is in stark contrast to the case with perfect receiver side information where capacity grows logarithmically in the SNR. To better understand this phenomenon
InformationTheoretic Determination of Minimax Rates of Convergence
 Ann. Stat
, 1997
"... In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain informationtheoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence. ..."
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Cited by 95 (19 self)
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In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain informationtheoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.
A ratesplitting approach to the Gaussian multipleaccess channel
 IEEE TRANS. INFORM. THEORY
, 1996
"... It is shown that any point in the capacity region of a Gaussian multipleaccess channel is achievable by singleuser coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multipleaccess technique called rat ..."
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Cited by 87 (2 self)
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It is shown that any point in the capacity region of a Gaussian multipleaccess channel is achievable by singleuser coding without requiring synchronization among users, provided that each user “splits” data and signal into two parts. Based on this result, a new multipleaccess technique called ratesplitting multiple accessing (RSMA) is proposed. RSMA is a codedivision multipleaccess scheme for the Muser Gaussian multipleaccess channel for which the effort of finding the codes for the M users, of encoding, and of decoding is that of at most 2M  1 independent pointtopoint Gaussian channels. The effects of bursty sources, multipath fading, and intercell interference are discussed and directions for further research are indicated.
Universal Portfolios with Side Information
 IEEE Transactions on Information Theory
, 1996
"... We present a sequential investment algorithm, the ¯weighted universal portfolio with sideinformation, which achieves, to first order in the exponent, the same wealth as the best sideinformation dependent investment strategy (the best stateconstant rebalanced portfolio) determined in hindsight fr ..."
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Cited by 85 (3 self)
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We present a sequential investment algorithm, the ¯weighted universal portfolio with sideinformation, which achieves, to first order in the exponent, the same wealth as the best sideinformation dependent investment strategy (the best stateconstant rebalanced portfolio) determined in hindsight from observed market and sideinformation outcomes. This is an individual sequence result which shows that the difference between the exponential growth rates of wealth of the best stateconstant rebalanced portfolio and the universal portfolio with sideinformation is uniformly less than (d=(2n)) log(n + 1) + (k=n) log 2 for every stock market and sideinformation sequence and for all time n. Here d = k(m \Gamma 1) is the number of degrees of freedom in the stateconstant rebalanced portfolio with k states of sideinformation and m stocks. The proof of this result establishes a close connection between universal investment and universal data compression. Keywords: Universal investment, univ...
The Rate Loss in the WynerZiv Problem
 IEEE Trans. Inform. Theory
, 1996
"... The ratedistortion function for source coding with side information at the decoder (the "WynerZiv problem") is given in terms of an auxiliary random variable, which forms a Markov chain with the source and the side information. This Markov chain structure, typical to the solution of mult ..."
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Cited by 78 (15 self)
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The ratedistortion function for source coding with side information at the decoder (the "WynerZiv problem") is given in terms of an auxiliary random variable, which forms a Markov chain with the source and the side information. This Markov chain structure, typical to the solution of multiterminal source coding problems, corresponds to a loss in coding rate with respect to the conditional ratedistortion function, i.e., to the case where the encoder is fully informed. We show that for difference (or balanced) distortion measures, this loss is bounded by a universal constant, which is the minimax capacity of a suitable additive noise channel. Furthermore, in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise "test" channel. For example, the loss in the WynerZiv problem is less than 0:5 bit per sample in the squarederror distortion case, and it is less than 0:22 bits for a binary source with Hammingdistance. These resul...
Computation over MultipleAccess Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 74 (19 self)
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The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separationbased strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multipleaccess channel with a joint sourcechannel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multipleaccess networks, thus linking them to network coding.
InformationTheoretic Considerations for Symmetric, Cellular, MultipleAccess Fading Channels  Part II
, 1997
"... A simple idealized linear (and planar) uplink, cellular, multipleaccess communication model, where only adjacent cell interference is present and all signals may experience fading is considered. Shannon theoretic arguments are invoked to gain insight into the implications on performance of the main ..."
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Cited by 69 (1 self)
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A simple idealized linear (and planar) uplink, cellular, multipleaccess communication model, where only adjacent cell interference is present and all signals may experience fading is considered. Shannon theoretic arguments are invoked to gain insight into the implications on performance of the main system parameters and multipleaccess techniques. The model treated in Part I [1] is extended here to account for cellsite receivers that may process also the received signal at an adjacent cell site, compromising thus between the advantage of incorporating additional information from other cell sites on one hand and the associated excess processing complexity on the other. Various settings which include fading, timedivision multiple access (TDMA), wideband (WB), and (optimized) fractional intercell time sharing (ICTS) protocols are investigated and compared. In this case and for the WB approach and a large number of users per cell it is found, surprisingly, that fading may enhance performance in terms of Shannon theoretic achievable rates. The linear model is extended to account for general linear and planar configurations. The effect of a random number of users per cell is investigated and it is demonstrated that randomization is beneficial. Certain aspects of diversity as well as some features of TDMA and orthogonal codedivision multiple access (CDMA) techniques in the presence of fading are studied in an isolated cell scenario.
On the Size of Shares for Secret Sharing Schemes
 Journal of Cryptology
"... A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. The set of all qualified subsets defines the access structure to the se ..."
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Cited by 65 (7 self)
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A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. The set of all qualified subsets defines the access structure to the secret. Sharing schemes are useful in the management of cryptographic keys and in multyparty secure protocols. We analyze the relationships among the entropies of the sample spaces from which the shares and the secret are chosen. We show that there are access structures with 4 participants for which any secret sharing scheme must give to a participant a share at least 50% greater than the secret size. This is the first proof that there exist access structures for which the best achievable information rate (i.e., the ratio between the size of the secret and that of the largest share) is bounded away from 1. The bound is the best possible, as we construct a secret sharing scheme for the above a...