On Clustering Images Using Compression

The need for the ability to cluster unknown data to better understand its relationship to know data is prevalent throughout science. Besides a better understanding of the data itself or learning about a new unknown object, cluster analysis can help with processing data, data standardization, and outlier detection. Most clustering algorithms are based on known features or expectations, such as the popular partition based, hierarchical, density-based, grid based, and model based algorithms. The choice of algorithm depends on many factors, including the type of data and the reason for clustering, nearly all rely on some known properties of the data being analyzed. Recently, Li et al. proposed a new universal similarity metric, this metric needs no prior knowledge about the object. Their similarity metric is based on the Kolmogorov Complexity of objects, the objects minimal description. While the Kolmogorov Complexity of an object is not computable, in "Clustering by Compression," Cilibrasi and Vitanyi use common compression algorithms to approximate the universal similarity metric and cluster objects with high success. Unfortunately, clustering using compression does not trivially extend to higher dimensions. Here we outline a method to adapt their procedure to images. We test these techniques on images of letters of the alphabet.

SEP: A Stable Election Protocol for clustered heterogeneous wireless sensor networks

We study the impact of heterogeneity of nodes, in terms of their energy, in wireless sensor networks that are hierarchically clustered. In these networks some of the nodes become cluster heads, aggregate the data of their cluster members and transmit it to the sink. We assume that a percentage of the population of sensor nodes is equipped with additional energy resources-this is a source of heterogeneity which may result from the initial setting or as the operation of the network evolves. We also assume that the sensors are randomly (uniformly) distributed and are not mobile, the coordinates of the sink and the dimensions of the sensor field are known. We show that the behavior of such sensor networks becomes very unstable once the first node dies, especially in the presence of node heterogeneity. Classical clustering protocols assume that all the nodes are equipped with the same amount of energy and as a result, they can not take full advantage of the presence of node heterogeneity. We propose SEP, a heterogeneous-aware protocol to prolong the time interval before the death of the first node (we refer to as stability period), which is crucial for many applications where the feedback from the sensor network must be reliable. SEP is based on weighted election probabilities of each node to become cluster head according to the remaining energy in each node. We show by simulation that SEP always prolongs the stability period compared to (and that the average throughput is greater than) the one obtained using current clustering protocols. We conclude by studying the sensitivity of our SEP protocol to heterogeneity parameters capturing energy imbalance in the network. We found that SEP yields longer stability region for higher values of extra energy brought by more powerful nodes.

Forewarding in Mobile Opportunistic Networks

Recent advances in processor speeds, mobile communications and battery life have enabled computers to evolve from completely wired to completely mobile. In the most extreme case, all nodes are mobile and communication takes place at available opportunities – using both traditional communication infrastructure as well as the mobility of intermediate nodes. These are mobile opportunistic networks. Data communication in such networks is a difficult problem, because of the dynamic underlying topology, the scarcity of network resources and the lack of global information. Establishing end-to-end routes in such networks is usually not feasible. Instead a store-and-carry forwarding paradigm is better suited for such networks. This dissertation describes and analyzes algorithms for forwarding of messages in such networks. In order to design effective forwarding algorithms for mobile opportunistic networks, we start by first building an understanding of the set of all paths between nodes, which represent the available opportunities for any forwarding algorithm. Relying on real measurements, we enumerate paths between nodes and uncover what we refer to as the path explosion effect. The term path explosion refers to the fact that the number of paths between a randomly selected pair of nodes increases exponentially with time. We draw from the theory of epidemics to model and explain the path explosion effect. This is the first contribution of the thesis, and is a key observation that underlies subsequent results. Our second contribution is the study of forwarding algorithms. For this, we rely on trace driven simulations of different algorithms that span a range of design dimensions. We compare the performance (success rate and average delay) of these algorithms. We make the surprising observation that most algorithms we consider have roughly similar performance. We explain this result in light of the path explosion phenomenon. While the performance of most algorithms we studied was roughly the same, these algorithms differed in terms of cost. This prompted us to focus on designing algorithms with the explicit intent of reducing costs. For this, we cast the problem of forwarding as an optimal stopping problem. Our third main contribution is the design of strategies based on optimal stopping principles which we refer to as Delegation schemes. Our analysis shows that using a delegation scheme reduces cost over naive forwarding by a factor of O(√N), where N is the number of nodes in the network. We further validate this result on real traces, where the cost reduction observed is even greater. Our results so far include a key assumption, which is unbounded buffers on nodes. Next, we relax this assumption, so that the problem shifts to one of prioritization of messages for transmission and dropping. Our fourth contribution is the study of message prioritization schemes, combined with forwarding. Our main result is that one achieves higher performance by assigning higher priorities to young messages in the network. We again interpret this result in light of the path explosion effect.