The difficulty of clustering and the variety of clustering methods suggest the need for a theoretical study of clustering. Using the idea of a standard statistical framework, we propose a new framework for clustering. For a well-defined clustering goal we assume that the data to be clustered come from an underlying distribution and we aim to find a high-density cluster tree. We regard this tree as a parameter of interest for the underlying distribution. However, it is not obvious how to determine a connected subset in a discrete distribution whose support is located in a Euclidean space. Building a cluster tree for such a distribution is an open problem and presents interesting conceptual and computational challenges. We solve this problem using graph-based approaches and further parameterize clustering using the high-density cluster tree and its extension. Motivated by the connection between clustering outcomes and graphs, we propose a graph family framework. This framework plays an important role in our clustering framework. A direct application of the graph family framework is a new cluster-tree distance measure. This distance measure can be written as an inner product or kernel. It makes our clustering framework able to perform statistical assessment of clustering via simulation. Other applications such as a method for integrating partitions into a cluster tree and methods for cluster tree averaging and bagging are also derived from the graph family framework.

The difficulty of clustering and the variety of clustering methods suggest the need for a theoretical study of clustering. Using the idea of a standard statistical framework, we propose a new framework for clustering. For a well-defined clustering goal we assume that the data to be clustered come from an underlying distribution and we aim to find a high-density cluster tree. We regard this tree as a parameter of interest for the underlying distribution. However, it is not obvious how to determine a connected subset in a discrete distribution whose support is located in a Euclidean space. Building a cluster tree for such a distribution is an open problem and presents interesting conceptual and computational challenges. We solve this problem using graph-based approaches and further parameterize clustering using the high-density cluster tree and its extension. Motivated by the connection between clustering outcomes and graphs, we propose a graph family framework. This framework plays an important role in our clustering framework. A direct application of the graph family framework is a new cluster-tree distance measure. This distance measure can be written as an inner product or kernel. It makes our clustering framework able to perform statistical assessment of clustering via simulation. Other applications such as a method for integrating partitions into a cluster tree and methods for cluster tree averaging and bagging are also derived from the graph family framework.

The focus of this study is to map, classify and analyse how different risk premia strategies that are fully implementable, perform and are affected by different economic environments. The results are of interest for practitioners who currently invest in or are thinking about investing in risk premia strategies. The study also makes a theoretical contribution since there currently is a lack of publicised work on this subject. A combination of the statistical methods cluster tree, spanning tree and principal component analysis are used to first categorise the investigated risk premia strategies into different clusters based on their correlation characteristics and secondly to find the strategies’ most important return drivers. Lastly, an analysis of how the clusters of strategies perform in different macroeconomic environments, here represented by inflation and growth, is conducted. The results show that the three most important drivers for the investigated risk premia strategies are a crisis factor, an equity directional factor and an interest rate factor. These three components explained about 18 percent, 14 percent and 10 percent of the variation in the data, respectively. The results also show that all four clusters, despite containing different types of risk premia strategies, experienced positive total returns during all macroeconomic phases sampled in this study. These results can be seen as indicative of a lower macroeconomic sensitivity among the risk premia strategies and more of an “alpha-like” behaviour. / Denna studie fokuserar på att kartlägga, klassificera och analysera hur riskpremie-strategier, som är fullt implementerbara, presterar och påverkas av olika makroekonomiska miljöer. Studiens resultat är av intresse för investerare som antingen redan investerar i riskpremiestrategier eller som funderar på att investera. Studien lämnar även ett teoretiskt bidrag eftersom det i dagsläget finns få publicerade verk som behandlar detta ämne. För att analysera strategierna har en kombination av de statistiska metoderna cluster tree, spanning  tree  och  principal  component  analysis  använts.  Detta  för  att  dels  kategorisera riskpremie-strategierna i olika kluster, baserat på deras inbördes korrelation, men också för att finna de faktorer som driver riskpremiestrategiernas avkastning. Slutligen har också en analys över hur de olika strategierna presterar under olika makroekonomiska miljöer genomförts där de makroekonomiska miljöerna representeras av inflation- och tillväxtindikatorer. Resultaten  visar  att  de  tre  viktigaste  faktorerna  som  driver  riskpremiestrategiernas avkastning  är  en  krisfaktor,  en  aktiemarknadsfaktor och  en  räntefaktor.  Dessa  tre  faktorer förklarar ungefär 18 procent, 14 procent och 10 procent av den undersökta datans totala varians. Resultaten  visar  också  att  alla  fyra  kluster,  trots  att  de  innehåller  olika  typer  av riskpremiestrategier,  genererade  positiv  avkastning  under  alla  makroekonmiska  faser  som studerades. Detta resultat ses som ett tecken på en lägre makroekonomisk känslighet bland riskpremiestrategier och mer av ett alfabeteende.

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Saving energy and increasing network lifetime are significant challenges in the field of Wireless Sensor Networks (WSNs). Energy-aware routing protocols have been introduced for WSNs to overcome limitations of WSN including limited power resources and difficulties renewing or recharging sensor nodes batteries. Furthermore, the potentially inhospitable environments of sensor locations, in some applications, such as the bottom of the ocean, or inside tornados also have to be considered. ZigBee is one of the latest communication standards designed for WSNs based on the IEEE 802.15.4 standard. The ZigBee standard supports two routing protocols, the Ad hoc On-demand Distance Vector (AODV), and the cluster-tree routing protocols. These protocols are implemented to establish the network, form clusters, and transfer data between the nodes. The AODV and the cluster-tree routing protocols are two of the most efficient routing protocols in terms of reducing the control message overhead, reducing the bandwidth usage in the network, and reducing the power consumption of wireless sensor nodes compared to other routing protocols. However, neither of these protocols considers the energy level or the energy consumption rate of the wireless sensor nodes during the establishment or routing processes.