Targeted matrix completion

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods depends on the number of observed entries and the rank of the matrix; the larger the rank, the more entries need to be observed in order to accurately complete the matrix. In this paper, we deal with matrices that are not necessarily low rank themselves, but rather they contain low-rank submatrices. We propose Targeted, which is a general framework for completing such matrices. In this framework, we first extract the low-rank submatrices and then apply a matrix-completion algorithm to these low-rank submatrices as well as the remainder matrix separately. Although for the completion itself we use state-of-the-art completion methods, our results demonstrate that Targeted achieves significantly smaller reconstruction errors than other classical matrix-completion methods. One of the key technical contributions of the paper lies in the identification of the low-rank submatrices from the input partially-observed matrices.Comment: Proceedings of the 2017 SIAM International Conference on Data Mining (SDM

The requirement of matrix ATP for the import of precursor proteins into the mitochondrial matrix and intermembrane space

The role of ATP in the matrix for the import of precursor proteins into the various mitochondrial subcompartments was investigated by studying protein translocation at experimentally defined ATP levels. Proteins targeted to the matrix were neither imported or processed when matrix ATP was depleted. Import and processing of precytochrome b2, (pb2), a precursor carrying a bipartite presequence, into the intermembrane space was also strongly dependent on matrix ATP. Preproteins, consisting of 220 or more residues of pb2 fused to dihydrofolate reductase, showed the same requirement for matrix ATP, whereas the import of shorter fusion proteins (up to 167 residues of pb2) was largely independent of matrix ATP. For those intermembrane-space-targeted proteins that did need matrix ATP, the dependence could be relieved either by unfolding these proteins prior to import or by introducing a deletion into the mature portion of the protein thereby impairing the tight folding of the cytochrome b5 domain. These results suggest the following: (a) The import of matrix-targeted preproteins, in addition to a membrane potential ΔΨ, requires matrix ATP [most likely to facilitate reversible binding of mitochondrial heat-shock protein 70 (mt-Hsp70) to incoming precursors], for two steps, securing the presequence on the matrix side of the inner membrane and for the completion of translocation; (b) in the case of intermembrane-space-targeted precursors with bipartite signals, the function of ATP/mt-Hsp70 is not obligatory, as components of the intermembrane-space-sorting pathway may substitute for ATP/mt-Hsp70 function (however, if a tightly folded domain is present in the precursor, ATP/mt-Hsp70 is indispensable); (c) unfolding on the mitochondrial surface of tightly folded segments of preproteins is facilitated by matrix-ATP/mt-Hsp70

Generalized Instantly Decodable Network Coding for Relay-Assisted Networks

In this paper, we investigate the problem of minimizing the frame completion delay for Instantly Decodable Network Coding (IDNC) in relay-assisted wireless multicast networks. We first propose a packet recovery algorithm in the single relay topology which employs generalized IDNC instead of strict IDNC previously proposed in the literature for the same relay-assisted topology. This use of generalized IDNC is supported by showing that it is a super-set of the strict IDNC scheme, and thus can generate coding combinations that are at least as efficient as strict IDNC in reducing the average completion delay. We then extend our study to the multiple relay topology and propose a joint generalized IDNC and relay selection algorithm. This proposed algorithm benefits from the reception diversity of the multiple relays to further reduce the average completion delay in the network. Simulation results show that our proposed solutions achieve much better performance compared to previous solutions in the literature.Comment: 5 pages, IEEE PIMRC 201

Stability of matrix factorization for collaborative filtering

We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as a subspace fitting problem and analyze the difference between the solution subspace and the ground truth; (III) we analyze the prediction error of individual users based on the subspace stability. We apply these results to the problem of collaborative filtering under manipulator attack, which leads to useful insights and guidelines for collaborative filtering system design.Comment: ICML201

On Throughput and Decoding Delay Performance of Instantly Decodable Network Coding

In this paper, a comprehensive study of packet-based instantly decodable network coding (IDNC) for single-hop wireless broadcast is presented. The optimal IDNC solution in terms of throughput is proposed and its packet decoding delay performance is investigated. Lower and upper bounds on the achievable throughput and decoding delay performance of IDNC are derived and assessed through extensive simulations. Furthermore, the impact of receivers' feedback frequency on the performance of IDNC is studied and optimal IDNC solutions are proposed for scenarios where receivers' feedback is only available after and IDNC round, composed of several coded transmissions. However, since finding these IDNC optimal solutions is computational complex, we further propose simple yet efficient heuristic IDNC algorithms. The impact of system settings and parameters such as channel erasure probability, feedback frequency, and the number of receivers is also investigated and simple guidelines for practical implementations of IDNC are proposed.Comment: This is a 14-page paper submitted to IEEE/ACM Transaction on Networking. arXiv admin note: text overlap with arXiv:1208.238

From Instantly Decodable to Random Linear Network Coding

Our primary goal in this paper is to traverse the performance gap between two linear network coding schemes: random linear network coding (RLNC) and instantly decodable network coding (IDNC) in terms of throughput and decoding delay. We first redefine the concept of packet generation and use it to partition a block of partially-received data packets in a novel way, based on the coding sets in an IDNC solution. By varying the generation size, we obtain a general coding framework which consists of a series of coding schemes, with RLNC and IDNC identified as two extreme cases. We then prove that the throughput and decoding delay performance of all coding schemes in this coding framework are bounded between the performance of RLNC and IDNC and hence throughput-delay tradeoff becomes possible. We also propose implementations of this coding framework to further improve its throughput and decoding delay performance, to manage feedback frequency and coding complexity, or to achieve in-block performance adaption. Extensive simulations are then provided to verify the performance of the proposed coding schemes and their implementations.Comment: 30 pages with double space, 14 color figure

On Minimizing the Maximum Broadcast Decoding Delay for Instantly Decodable Network Coding

In this paper, we consider the problem of minimizing the maximum broadcast decoding delay experienced by all the receivers of generalized instantly decodable network coding (IDNC). Unlike the sum decoding delay, the maximum decoding delay as a definition of delay for IDNC allows a more equitable distribution of the delays between the different receivers and thus a better Quality of Service (QoS). In order to solve this problem, we first derive the expressions for the probability distributions of maximum decoding delay increments. Given these expressions, we formulate the problem as a maximum weight clique problem in the IDNC graph. Although this problem is known to be NP-hard, we design a greedy algorithm to perform effective packet selection. Through extensive simulations, we compare the sum decoding delay and the max decoding delay experienced when applying the policies to minimize the sum decoding delay [1] and our policy to reduce the max decoding delay. Simulations results show that our policy gives a good agreement among all the delay aspects in all situations and outperforms the sum decoding delay policy to effectively minimize the sum decoding delay when the channel conditions become harsher. They also show that our definition of delay significantly improve the number of served receivers when they are subject to strict delay constraints