The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging of clusters. In this paper, we present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points. We perform a detailed theoretical analysis, showing that under mild separability conditions our algorithm can not only recover the optimal flat partition but also provide a two-approximation to non-parametric DP-Means objective. This introduces a novel application of hierarchical clustering as an approximation algorithm for the non-parametric clustering objective. We additionally relate our algorithm to the classic hierarchical agglomerative clustering method. We perform extensive empirical experiments in both hierarchical and flat clustering settings and show that our proposed approach achieves state-of-the-art results on publicly available clustering benchmarks. Finally, we demonstrate our method's scalability by applying it to a dataset of 30 billion queries. Human evaluation of the discovered clusters show that our method finds better quality of clusters than the current state-of-the-art.

In this work, we study a communication scheme in which nodes transmit sufficient statistics of their observations over non-orthogonal medium access channels for distributed estimation. This scheme unifies and generalizes several multiple access schemes such as uncoded transmissions of Gaussian observations and type-based multiple access. For the exponential family of distributions, we show that the sufficient-statistic based multiple access (SSBMA) achieves the Cramer-Rao bound on the estimation error asymptotically. Further, we argue that such an optimality result only applies to the exponential family of distributions. In addition, we present a simplified and unified analysis of asymptotic distribution of estimation error for a very general class of communication schemes and estimators. The proposed analysis method reduces the computation of asymptotic estimation error to mere calculation of derivatives. With the proposed technique, we analyze the performance of various communication schemes with optimal and suboptimal estimators and with i.i.d. (independent and identically distributed) data.

In this paper we study the maximum asymptotic stable throughput of an opportunistic slotted ALOHA protocol. We provide a characterization of the maximum stable throughput as the number of users in the system goes to infinity. We then apply our findings to CDMA networks with the signal-to-interference-ratio (SIR) threshold model. It is shown that the slotted ALOHA protocol with the power/transmission control rule that equalizes the reception powers achieves 1 - O(logN/radicN) channel utilization, which is defined as the throughput divided by the optimal throughput N achieved by scheduling. This implies that the slotted ALOHA is asymptotically optimal in the sense that its channel utilization converges to 1 as the spreading gain goes to infinity

Sensor network with mobile access (SENMA) is an architecture in which randomly deployed low-power sensors are orchestrated by a few powerful mobile access points. This paper considers SENMA from energy-efficiency and information-theoretic perspectives. By allowing sensors to propagate data directly to mobile access points over multiaccess channels and relieving sensors from energy-consuming network functions, SENMA has the potential of offering orders of magnitude of improvement in energy efficiency over the multihop ad hoc architecture, as demonstrated by our analysis on scalability. Optimization configurations of SENMA such as the altitude, the trajectory, and the coverage of access points are considered next, using the sum-rate as the performance metric. Optimal strategies for single and multiple access points are determined. For multiple access points, the possibility of and the gain due to cooperation (i.e., joint decoding of signals received at different access points) are investigated.

Sensor network with mobile access (SENMA) is an architecture in which randomly deployed low-power sensors are orchestrated by a few powerful mobile access points (APs). This paper considers SENMA from energy-efficiency and information-theoretic perspectives. By allowing sensors to propagate data directly to mobile APs over multiaccess channels, and relieving sensors from energy-consuming network functions, SENMA has the potential of offering orders of magnitude of improvement in energy efficiency over the multihop ad hoc architecture, as demonstrated by our analysis on scalability. Optimization configurations of SENMA such as the altitude, the trajectory, and the coverage of APs are considered next, using the sum-rate as the performance metric. Optimal strategies for single and multiple APs are determined. For multiple APs, the possibility of and the gain due to cooperation (i.e., joint decoding of signals received at different APs) are investigated

Cooperative broadcast aims to deliver a source message to a locally connected network by means of collaborating nodes. In traditional architectures, node cooperation has been at the network layer. Recently, physical layer cooperative schemes have been shown to offer several advantages over the network layer approaches. This form of cooperation employs distributed transmission resources at the physical layer as a single radio with spatial diversity. In decentralized cooperation schemes, collaborating nodes make transmission decisions based on the quality of the received signal, which is the only parameter available locally. In this case, critical parameters that influence the broadcast performance include the source/relay transmission powers and the decoding threshold (the minimum signal-to-noise ratio (SNR) required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show that there exists a phase transition in the network behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes is reached, which is proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions that are accurate when the network density is high.

We study the problem of communicating sensor readings over a multiaccess channel. Previous works focused on the approach that each sensor is allocated an orthogonal channel to transmit its data as in TDMA (time-division multiple access). In this paper, we propose an. alternative method in which the sensors transmit simultaneously to deliver a noisy version of the type of sensor observations. We analyze the estimation/detection performance of this type-based multiple access (TBMA) approach in inferring a parameter /spl theta/. The data at different sensors are modeled as conditionally independent given /spl theta/. An asymptotic performance analysis is presented, and significant gains in estimation/detection performance and bandwidth usage are demonstrated.

We study the stability and capacity problems in regular wireless networks. In the first part of the paper, we provide a general approach to characterizing the capacity region of arbitrary networks, find an outer bound to the capacity region in terms of the transport capacity, and discuss connections between the capacity formulation and the stability of node buffers. In the second part of the paper, we obtain closed-form expressions for the capacity of Manhattan (two-dimensional grid) and ring networks (circular array of nodes). We also find the optimal (i.e., capacity-achieving) medium access and routing policies. Our objective in analyzing regular networks is to provide insights and design guidelines for general networks. The knowledge of the exact capacity enables us to quantify the loss incurred by suboptimal protocols such as slotted ALOHA medium access and random-walk-based routing. Optimal connectivity and the effects of link fading on network capacity are also investigated.

The effect of multipacket reception (MPR) on stability and delay of slotted ALOHA based random-access systems is considered. A general asymmetric MPR model is introduced and the medium-access control (MAC) capacity region is specified. An explicit characterization of the ALOHA stability region for the two-user system is given. It is shown that the stability region undergoes a phase transition from a concave region to a convex polyhedral region as the MPR capability improves. It is also shown that after this phase transition, slotted ALOHA is optimal i.e., the ALOHA stability region coincides with the MAC capacity region. Further, it is observed that there is no need for transmission control when ALOHA is optimal i.e., ALOHA with transmission probability one is optimal. Next, these results are extended to a symmetric N>2 user ALOHA system. Finally, a complete characterization of average delay in capture channels for the two-user system is given. It is shown that in certain capture scenarios, ALOHA with transmission probability one is delay optimal for all stable arrival rates. Further, it is also shown that ALOHA with transmission probability one is optimal for stability and delay simultaneously in the two-user capture channel.