In cluster analysis, a fundamental problem is to determine the best estimate of the number of clusters, which has a deterministic effect on the clustering results. However, a limitation in current applications is that no convincingly acceptable solution to the best-number-of-clusters problem is available due to high complexity of real data sets. In this dissertation, we tackle this problem of estimating the number of clusters, which is particularly oriented at processing very complicated data which may contain multiple types of cluster structure. Two new methods of choosing the number of clusters are proposed which have been shown empirically to be highly effective given clear and distinct cluster structure in a data set. In addition, we propose a sequential type of clustering approach, called multi-layer clustering, by combining these two methods. Multi-layer clustering not only functions as an efficient method of estimating the number of clusters, but also, by superimposing a sequential idea, improves the flexibility and effectiveness of any arbitrary existing one-layer clustering method. Empirical studies have shown that multi-layer clustering has higher efficiency than one layer clustering approaches, especially in detecting clusters in complicated data sets. The multi-layer clustering approach has been successfully implemented in clustering the WTCHP microarray data and the results can be interpreted very well based on known biological knowledge. Choosing an appropriate clustering method is another critical step in clustering. K-means clustering is one of the most popular clustering techniques used in practice. However, the k-means method tends to generate clusters containing a nearly equal number of objects, which is referred to as the ``equal-size'' problem. We propose a clustering method which competes with the k-means method. Our newly defined method is aimed at overcoming the so-called ``equal-size'' problem associated with the k-means method, while maintaining its advantage of computational simplicity. Advantages of the proposed method over k-means clustering have been demonstrated empirically using simulated data with low dimensionality. / Ph. D.

A parameter specifying the number of clusters in an unsupervised clustering algorithm is often unknown. Different cluster validity indices proposed in the past have attempted to address this issue, and their performance is directly related to the accuracy of a clustering algorithm. Toe gap statistic proposed by Tibshirani (2001) was applied to k-means and hierarchical clustering algorithms for estimating the number of clusters and is shown to outperform other cluster validity measures, especially in the null model case. In our experiments, the gap statistic is applied to the Fuzzy c-Means (FCM) algorithm and compared to existing FCM cluster validity indices examined by Pal (1995). A comparison is also made between two initialization methods where centers are randomly assigned to data points or initialized using the furthest first algorithm (Hochbaum, 1985). Toe gap statistic can be applied using the FCM algorithm as long as the fuzzy partition matrix can be employed in computing the gap statistic metric, Wk . Three new methodologies are examined for computing this metric in order to apply the gap statistic to the FCM algorithm. Toe fuzzy partition matrix generated by FCM can also be thresholded based upon the maximum membership to allow computation similar to the kmeans algorithm. This is assumed to be the current method for employing the gap statistic with the FCM algorithm and is compared to the three proposed methods. In our results, the gap statistic outperformed the cluster validity indices for FCM, and one of the new methodologies introduced for computing the metric, based upon the FCM objective function, out performed the threshold method for m=2.

The goal of this project is to investigate any correlation between marketing emails and their receivers using machine learning and only a limited amount of initial data. The data consists of roughly 1200 emails and 98.000 receivers of these. Initially, the emails are grouped together based on their content using text clustering. They contain no information regarding prior labeling or categorization which creates a need for an unsupervised learning approach using solely the raw text based content as data. The project investigates state-of-the-art concepts like bag-of-words for calculating term importance and the gap statistic for determining an optimal number of clusters. The data is vectorized using term frequency - inverse document frequency to determine the importance of terms relative to the document and to all documents combined. An inherit problem of this approach is high dimensionality which is reduced using latent semantic analysis in conjunction with singular value decomposition. Once the resulting clusters have been obtained, the most frequently occurring terms for each cluster are analyzed and compared. Due to the absence of initial labeling an alternative approach is required to evaluate the clusters validity. To do this, the receivers of all emails in each cluster who actively opened an email is collected and investigated. Each receiver have different attributes regarding their purpose of using the service and some personal information. Once gathered and analyzed, conclusions could be drawn that it is possible to find distinguishable connections between the resulting email clusters and their receivers but to a limited extent. The receivers from the same cluster did show similar attributes as each other which were distinguishable from the receivers of other clusters. Hence, the resulting email clusters and their receivers are specific enough to distinguish themselves from each other but too general to handle more detailed information. With more data, this could become a useful tool for determining which users of a service should receive a particular email to increase the conversion rate and thereby reach out to more relevant people based on previous trends. / Målet med detta projekt att undersöka eventuella samband mellan marknadsföringsemail och dess mottagare med hjälp av oövervakad maskininlärning på en brgränsad mängd data. Datan består av ca 1200 email meddelanden med 98.000 mottagare. Initialt så gruperas alla meddelanden baserat på innehåll via text klustering. Meddelandena innehåller ingen information angående tidigare gruppering eller kategorisering vilket skapar ett behov för ett oövervakat tillvägagångssätt för inlärning där enbart det råa textbaserade meddelandet används som indata. Projektet undersöker moderna tekniker så som bag-of-words för att avgöra termers relevans och the gap statistic för att finna ett optimalt antal kluster. Datan vektoriseras med hjälp av term frequency - inverse document frequency för att avgöra relevansen av termer relativt dokumentet samt alla dokument kombinerat. Ett fundamentalt problem som uppstår via detta tillvägagångssätt är hög dimensionalitet, vilket reduceras med latent semantic analysis tillsammans med singular value decomposition. Då alla kluster har erhållits så analyseras de mest förekommande termerna i vardera kluster och jämförs. Eftersom en initial kategorisering av meddelandena saknas så krävs ett alternativt tillvägagångssätt för evaluering av klustrens validitet. För att göra detta så hämtas och analyseras alla mottagare för vardera kluster som öppnat något av dess meddelanden. Mottagarna har olika attribut angående deras syfte med att använda produkten samt personlig information. När de har hämtats och undersökts kan slutsatser dras kring hurvida samband kan hittas. Det finns ett klart samband mellan vardera kluster och dess mottagare, men till viss utsträckning. Mottagarna från samma kluster visade likartade attribut som var urskiljbara gentemot mottagare från andra kluster. Därav kan det sägas att de resulterande klustren samt dess mottagare är specifika nog att urskilja sig från varandra men för generella för att kunna handera mer detaljerad information. Med mer data kan detta bli ett användbart verktyg för att bestämma mottagare av specifika emailutskick för att på sikt kunna öka öppningsfrekvensen och därmed nå ut till mer relevanta mottagare baserat på tidigare resultat.

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