Capacitated Clustering Problem in Computational Biology: Combinatorial and Statistical Approach for Sibling Reconstruction The capacitated clustering problem (CCP) has been studied in a wide range of applications. In this study, we investigate a challenging CCP in computational biology, namely, sibling reconstruction problem (SRP). The goal of SRP is to establish the sibling relationship (i.e., groups of siblings) of a population from genetic data. The SRP has gained more and more interests from computational biologists over the past decade as it is an important and necessary keystone for studies in genetic and population biology. We propose a large-scale mixed integer formulation of the CCP for SRP, that is based on both combinatorial and statistical genetic concepts. The objective is not only to find the minimum number of sibling groups, but also to maximize the degree of similarity of individuals in the same sibling groups Preprint submitted to Computers and Operations Research April 28, 2011 while each sibling group is subject to genetic constraints derived from the Mendel's laws. We develop a new randomized greedy optimization algorithm to effectively and efficiently solve this SRP. The algorithm consists of two key phases: construction and enhancement. In the construction phase, a greedy approach with randomized perturbation is applied to construct multiple sibling groups iteratively. In the enhancement phase, a two-stage local search with a memory function is used to improve the solution quality with respect to the similarity measure. We demonstrate the effectiveness of the proposed algorithm using real biological data sets and compare it with state-of-the-art approaches in the literature. We also test it on larger simulated data sets.The experimental results show that the proposed algorithm provide the best reconstruction solutions. The capacitated clustering problem (CCP) has been one of the most challenging problems in clustering research. Several variants of CCP have been studied in the literature including a capacitated centred clustering problem (CCCP) as well as a capacitated p-median problem (CPMP). The CCP can be formally defined as follows. Given a set of data points with associated weights (or features), the CCP is to partition the data points into clusters such that the total weight of data points in each cluster does not exceed the capacity limit of the cluster. In general, the objective of CCP is to maximize the homogeneity (similarity) of the data points in each cluster or to maximize the separation (dissimilarity) among different clusters (Hansen and Jaumard, 1997) . Although clustering techniques have been essential tools to solve many practical problems, previous studies on the CCP are mostly applied to facility location problems and they often focus on the development of solution algorithms. In this study, we consider an application of the CCP in computational biology to solve the sibling reconstruction problem (SRP). The SRP is one of the most important problems in genetic biology (Blouin, 2003) . The knowledge of sibling relationships allows biologists to understand the fundamental biological phenomena including mating systems, ecological behaviors and evolutions, social organizations, etc. The SRP can be formally defined as follows. Given a population (or set) of individuals (or data points) with associated genetic features (or weights), the SRP is to partition individuals into sibling groups (or clusters) such that the combination of features in each sibling group does not violate the genetic constraints of sibling group (i.e., the Mendel's laws). The common objective of SRP is to maximize the similarity degrees of individuals in sibling groups and to minimize the number of sibling groups in the population. The genetic constraints of the sibling group make the SRP far more complicated than a standard CCP. The capacity constraint in the CCP only incorporates the total weight of data points in each cluster, which is usually one-dimensional. On the other hand, the genetic constraints of SRP are derived from the combinatorial concept of the Mendel's laws, which consider multiple pairwise genetic features of individuals. In addition, the actual number of sibling groups is not known a priori, and overlapping sibling groups are commonly seen in natural populations because wild animals are not always monogamous. In other words, an individual can be assigned to more than one sibling group simultaneously if the genetic constraints are satisfied.. To solve the SRP, most studies employ statistical likelihood techniques from genetic data (Painter, 1997; Smith et al., 2001 ; Thomas and Hill, 2002; Butler et al., 2004; Wang, 2004; Konovalov et al., 2004; Wang and Santure, 2009) , while heuristic approaches are developed to integrate statistical likelihood such as graph-based approaches (Almudevar and Field, 1999; Beyer and May, 2003; Almudevar, 2007) , simulated annealing (Almudevar, 2003) , etc. More recently, there has been an increasing degree of interest to apply combinatorial concepts to the SRP. A new optimization model with complex combinatorial constraints derived from the Mendel's laws and its computational algorithms have been proposed (Berger-Wolf et al., 2005 , 2007 Chaovalitwongse et al., 2007 Chaovalitwongse et al., , 2010 . The model is formulated in the format of a set covering problem (SCP), which is to find a minimum set of sibling groups subject to the combinatorial constraints. Note that, in those studies, only the combinatorial constraints and the concept of parsimony, which is to minimize the number of sibling groups, were considered in the model. More importantly, statistical similarity measure from genetic features of individuals can provide direct information to benefit the sibling relationships, while the combinatorial constraints give the robustness of reconstructing sibling groups.. In this study, we propose a new heuristic optimization algorithm, which has similar concept to a greedy randomized adaptive search procedure (GRASP) (Feo and Resende, 1995) , that integrates the combinatorial constraints and the concept of parsimony with a statistical similarity measure. The proposed framework involves the following phases: the construction of clusters and the enhancement of quality of clusters. In the first phase, an efficient greedy approach, proposed by Chaovalitwongse et al. (2010) , is employed repeatedly to construct a number of different possible partitions of (disjoint) sibling groups by introducing a randomized perturbation. Subsequently, among all possible partitions of sibling groups, a set covering problem (SCP) is solved to select the minimum set of sibling groups to cover the population. In the second phase, we propose a new two-stage local search with a memory function to improve the quality of sibling reconstruction based on the similarity of individuals in the sibling groups. Finally, a SCP is solved again to find the minimum number of sibling groups.. The remainder of this paper is organized as follows. In Section 2, we present the CCP and the sibling reconstruction problem with basic genetic terminologies and a mathematical representation of genetic data. The capacitated clustering formulation for the SRP is presented in detail in Section 3. The mathematical programming model with the combinatorial constraints of the Mendel's laws is formulated to integrate the statistical similarity measure of genetic data. In Section 4, we elaborate the proposed framework designed to solve the SRP. In Section 5, we demonstrate computational experiments using real biological data sets and simulated data sets, and show the effectiveness by comparing the proposed approach to the existing methods. Finally, this paper is concluded in Section 6.

B I I O B I O O O O O B I O B I I O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Learning video preferences from video content Viewers of video now have more choices than ever. As the number of choices increases, the task of searching through these choices to locate video of interest is becoming more difficult. Current methods for learning a viewer's preferences in order to automate the search process rely either on video having content descriptions or on having been rated by other viewers identified as being similar. However, much video exists that does not meet these requirements. To address this need, we use hidden Markov models to learn the preferences of a viewer by combining visual features and closed captions. Results are provided from some initial experiments using this approach. People today have access to more video than at any time in history. Sources of video include television broadcasts, movie theaters, movie rentals, video databases, and the Internet. While many video choices come from the entertainment domain, other types of video are becoming more common, such as educational lectures at universities and conferences [34] .. As the number of video choices increases, the task of searching for video of interest is becoming more difficult. One approach that viewers take is to search for video within specific genre. In the case of entertainment video, the genre of the video is provided when the video is released. However, there is much video that is unclassified. This has led to research in automatically classifying video by genre. While Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.. MDM/KDD'07, August 12, 2007 , San Jose, California, USA. knowing the genre of video is helpful, the large amounts of video choices within many genre still make finding video of interest a time-consuming process. In addition, this problem is even greater for people who enjoy video from a variety of genre, which seems likely for most people. For these reasons, systems have been developed that can learn a particular person's preferences and make recommendations given these preferences.. There have traditionally been two approaches to identifying video of interest to a viewer. The first is the case-based approach, which utilizes descriptions of the video content. In the case of entertainment video, the description might include the genre of the video, director, actors, and a brief summary of the video. The second is collaborative filtering, which attempts to identify viewers that are considered similar by some measure. Recommendations for the current viewer will be drawn from the positively rated video of these similar viewers.. The major strength of the case-based approach is that it relies strictly on the viewer's profile. Once a viewer's preferences are known, it is a simple task to match these up with video content descriptions. There are, however, several weaknesses to the case-based approach. One is that it takes some effort to produce content descriptions. While this is typically not a problem when dealing with entertainment video such as television or movies, there is much video in video databases and on the Internet for which there are no content descriptions. Another weakness is that the viewer must initially seed the system with some preference information. A viewer may not wish to devote the time and effort to provide enough preference details for the system to perform well. The third weakness is that recommendations will be very similar to previously rated video.. Collaborative filtering does not require the content descriptions used by the case-based approach. Also, unlike the case-based approach, video recommendations are not restricted to video similar to that previously rated by the user if the group the viewer is assigned to has a greater variety of interests. However, it does take some effort to gather enough information about other viewers in order to determine who is similar to the current viewer. A second weakness of collaborative filtering is the latency of a new video spreading. A video can't be recommended if no one has seen and rated it yet.. There are many videos that lack the content descriptions required by the case-based approach and do not have the ratings of other viewers required by collaborative filtering. The approach we have chosen is to extract visual features and closed captions from video in order to learn a viewer's preferences. The visual features and closed captions are combined to produce observation symbols for training hidden Markov models (HMM). A video is a collection of features in which the order that the features appear is important, which suggests that an HMM might be appropriate for classification. We believe that visual features and closed captions are complementary. Visual features represent what is being seen, but miss much of the social interaction. Video dialogue typically doesn't describe what is being seen, but represents the social interaction.. The rest of the paper is organized as follows. Our approach is to learn video preferences using methods more commonly associated with classification of video by genre, so in Section 2 we discuss related work from the video classification field as well as other approaches to video recommendation. Section 3 provides background on the features, clustering, and classification methods necessary to understand our approach. In Section 4 we explain our overall methodology. Section 5 provides details of our initial experiments. Conclusions and suggestions for future work are provided in Section 6. Traditional approaches to video recommendation have been shown to have relatively good performance. However, for reasons described previously, these approaches are not always applicable. To address this need, we have explored the use of visual features and closed captions extracted from video for learning a viewer's preferences. Overall, however, our results were not good enough to clearly show our approach to be a viable alternative to traditional approaches.. While our results were not very encouraging, we still believe that it is possible to learn preferences from video features and that our work can be extended.. We only applied our method to minutes 5-10 of each movie. Other time periods as well as longer or multiple time periods should be investigated.. It can be applied to the task of classifying video by genre. While there has already been much research in this area, there is still room for improvement. It could also be applied at the shot or scene level. Applications include content filtering, such as identifying violent scenes in movies, or the identification of scenes important to the user. Video summarization can also be performed by finding scenes important to many users. Of the research that has been performed in automatically classifying video by genre, very little has attempted to subdivide genre, such as finding action movies that include car chases or separating romantic comedies from dark comedies.. Much of the research in learning video preferences and classifying video by genre has focused primarily on the entertainment video domain. Other domains, such as education, should be explored more to determine how well our approach would apply to them.. Another area where our work could be applied is video learning. As more and more educational video becomes available, students will have a variety of video choices for learning a particular topic. If the student's performance on a test covering a specific topic is tracked, which should be possible with online courses, then video can be recommended that is similar to those that resulted in the best performance by the student. Research related to this work falls into two categories. The first is the previously mentioned video recommendation systems. The second is automatic classification of video by genre. Our proposed methodology begins by extracting the closed captions sets from the training videos that the viewer has rated with the intent of using the times that the closed captions sets are displayed as the mechanism for segmenting the video. This allows us to avoid the error-prone task of automatically detecting shot boundaries.. For each closed captions set, we extract the first video frame to represent the entire time span that the closed captions set is displayed. Visual features are extracted from this video frame.. Some methods for representing text or images suffer from a lack of context. The bag-of-words model, which is a common method for representing documents, does not maintain word order and as a result two documents with essentially the same words but different word order can have different meanings but appear similar when comparing their termfeature representations. Likewise, two different images may appear similar when represented as color histograms. By combining text and visual features, we believe that these limitations can be lessened.. The process for combining the visual features and closed captions begins by clustering the visual features and closed captions separately. The cluster assignment of a closed captions set and the cluster assignment of it corresponding video frame are combined in the form (closed captions set cluster number, video frame cluster number), which becomes an observation symbol for training the HMM An example is shown in Figure 3 . In this example, the hierarchy produced from the closed captions sets has been pruned at a level that The video frame hierarchy has been pruned at a level that produces three clusters, numbered from left to right as 1, 2, and 3. Closed captions set #1 (the first set chronologically) is in cluster 1 while its corresponding frame is in cluster 2, so the observation symbol will be (1,2). Closed captions set #2 (the second set chronologically) is in cluster 1 while its corresponding frame is cluster 1, so it is represented by the observation symbol (1, 1) . This is repeated for all of the closed captions sets and frames extracted from a video clip to generate a sequence of observation symbols that represent a video. The sequence of symbols for each video rated as 'liked' by the viewer are used to train an HMM. This entire process is repeated for those movies rated by the viewer as 'disliked'. Test video sequences are classified according to the HMM that has the highest probability of generating the sequence. In order to validate our approach, we chose to obtain realworld data. For this purpose, we used the MovieLens collaborative filtering data set as a starting point [16] . This data set was produced by 6,040 viewers who had rated movies from a set of 3,883 possible movies for a total of more than 1 million ratings. The demographic information provided of the users is gender, age (grouped into 7 age ranges), occupation (consisting of 21 choices), and zip code. The movie data includes the title and one or more genre. We chose to use video from the entertainment domain due to the fact that it has the closed captions required by our approach and the availability of ratings. We acquired the DVD version of 90 of the movies represented in the MovieLens data set. These movies were from a variety of entertainment genre (e.g., scifi, drama, and so forth) with many classified in multiple genre.. Our data set consisted of 357 viewers who had rated at least 20 of these movies on a 1-5 scale, for a total of 9,708 ratings. The number of movies rated by each viewer ranged from 20 to 69 with a mean of 27. For each viewer we split the ratings into two groups: movies with ratings of 4 or 5 were considered 'liked' while the remainder were considered 'disliked'. For the entire data set, there were 4,771 (49%) disliked movies and 4,937 (51%) liked movies although this is not guaranteed for any particular viewer. Two-thirds of the liked and disliked sets were used for training.. It was not computationally feasible for us to extract and work with features from the full length of each movie, therefore we chose to extract features from only a five minute portion of each movie. In particular, we extracted features from minutes 5 to 10 of each movie. The reason for using this time period as opposed to the first five minutes of each movie is that the very beginning of a movie is often used for displaying credits and therefore may not be representative of the movie as a whole. The visual features might differ as well as there are fewer closed captions. Limiting our method to just a five minute period does have the potential drawback that this time period may not capture what is important to a user. For example, a viewer may prefer movies in which story and character development is drawn out over a long period. Another viewer may enjoy action scenes, which typically don't occur at the very beginning of movies.. The closed captions sets for this time period were extracted and represented using the bag-of-words model. The number of closed captions sets for this five minute period ranged from 32-162, with a mean value of 86. The termfeature vectors representing the closed captions had 4,003 terms. We found that clustering the vectors representing the closed captions was too time-intensive due to the high number of dimensions. To alleviate this problem, we used random projection to reduce the dimensions of the vectors from 4,003 terms to 400 terms.. The idea of random projection is to project a set of points in a high-dimensional space to a randomly selected lowerdimensional subspace [7] . The application of random projection is simple: Given an input matrix X with dimensions N × d where N is the number of samples and d is the dimensionality of each sample, we can transform this matrix to a new matrix X ′ with dimensions N × k by multiplying X by a random matrix R with dimensions d × k such that X ′ = XR. Papadimitriou et al. [26] show that there is a high probability that pairwise Euclidean distances are kept in the projected subspace.. Several ways of generating the transformation matrix R have been proposed [5] . We chose to generate a matrix in which each element is drawn from a standard normal distribution, N (0, 1). Then each column of this matrix is normalized to one [11] .. An advantage of random projection over principal component analysis (PCA), another dimensionality reduction method, is that PCA is very computationally expensive while generating and applying random projections is not. Also, because the application of random projections consists of matrix multiplication, the input matrix X can be partitioned and the matrix R applied to the individual partitions with the results combined if the original matrix X is too large to work with in memory.. To produce the visual features, the first frame from each of the time periods that the closed captions sets were displayed was extracted. Representing each frame by concatenating the RGB values of the pixels would have produced vectors with 253,440 terms. Instead, five levels of a 2D Daubechies 4 wavelet were applied separately to the R, G, and B components, with the results concatenated to form vectors of 363 terms. In addition to reducing the dimensionality, applications of wavelets to images have been shown to improve matching in image retrieval [18] .. The visual features and closed captions were clustered separately using agglomerative hierarchical clustering. We performed exploratory data analysis on a subset of our training data to determine which linkage method and distance measure produced the most balanced hierarchies. We found that in general complete linkage with the Euclidean distance produced balanced hierarchies for the wavelet-transformed pixel values. For the closed captions transformed by random projections, none of the combinations of linkage methods and distance measures produced well-balanced hierarchies which suggests that hierarchical clustering may not be the most appropriate form of clustering for closed captions. For both the visual features and closed captions we performed clustering using complete linkage with the Euclidean distance.. When using hierarchical clustering, it is necessary to prune the hierarchy in order to determine the clusters. Many methods have been proposed for determining the true number of clusters in a data set [25] . We chose to partition the hierarchy into clusters using the method proposed by Krzanowski and Lai [19] :. where g is the number of groups, p is the number of dimensions, and Wg is the within-group-sum-of-squares covariance matrix for group g. The number of groups is the g that maximizes KL(g) =˛D IFF(g) DIFF(g + 1)Ǫ ne disadvantage of this method is that it is unable to determine if the data only represents a single cluster [33] . Calculating the within-group-sum-of-squares is very computationally intensive and therefore we limited our search for the correct number of clusters to cluster sizes of 2-10. Once the clustering was complete, the cluster numbers for the closed captions sets and the corresponding visual features were combined to form the observation symbols for training the HMMs.. The cluster assignments for test samples were determined by finding the training cluster that the test sample would have been assigned to by the complete linkage method using the Euclidean distance as the distance measure.. The 'liked' and 'disliked' HMMs each had two states with equal probability of starting in that state. The initial elements of the transition matrix were all set to have equal likelihood as were the elements of the observation matrix. In constructing the 'liked' and 'disliked' HMMs, we investigated models with 2-10 states with the same number of states in each model. We found that the accuracy, precision, and recall were essentially the same regardless of the number of states. The test samples produced observation symbols that were not present in the training samples, which made it impossible to calculate the log-likelihood of the test sequences. To overcome this, the emission probabilities with values of zero were changed to 10 −6 . Our results from combining closed captions and visual features are shown in Table 1 . We also generated observation symbols from each type of feature alone in order to determine if the combination of features was an improvement. Our combination approach had an average classification accuracy over the 357 viewers of 54.6%, which is only slightly better than what would be expected if the movies were picked at random. The average classification accuracy when using closed captions or visual features alone was 51.4% and 52.7%, respectively. While the mean value of our combination approach is larger than the mean values of using either type of feature separately, the confidence intervals overlap and we therefore can't state that the results are significantly We believe there are several possible reasons for the poor performance of our approach. The first is that out of the 357 users for which we had preference information, 253 of them had rated less than thirty movies. In fact, forty-eight had only rated twenty movies. This is unlikely to be a sufficient amount of data for our approach to effectively learn preferences. When we look at the average results for the viewers who had rated forty or more movies, the mean classification accuracy improves to 61.5%. See Table 2 for the results by number of movies rated.. Another possible problem is that when generating the test observation symbols by combining the cluster numbers for the visual features and closed captions, it's possible to generate observation symbols that never occurred in the training data. Many test sequences contained symbols that never occurred in the training, so even though we gave these symbols an emission probability of 10 −6 to make it possible to calculate the log-likelihood for the sequence, each of these symbols essentially contributed nothing to that calculation. The remaining symbols may not have been enough to effectively learn preferences. A possible solution to this that we can investigate in a future work is to assign observation symbols to test samples by finding the nearest training combination of closed caption and visual features. This will avoid generating observation symbols that never occurred in the training data. It is not possible to generate unseen observation symbols for the test samples when using only a single type of feature, so this can't account for the poor performance of using either type of feature alone.. In an earlier work [6] , we investigated the use of closed captions and DCT coefficients separately. We felt that this work suffered from two problems. First, it did not attempt to combine the text and visual features with the resultant gain in performance that one would expect from such a combination. Second, no consideration was given to the order in which features appear. However, this earlier work does help us to establish a baseline for comparison with the current method in order to determine whether the use of HMMs has improved performance.. The use of closed captions alone in the earlier work had a classification accuracy of 64.04% with a 95% confidence interval of (63.02, 65.05). This exceeds the classification accuracy of 51.4% that we achieved when using closed captions alone in our current work. In our earlier work, all of the closed captions for an entire movie were represented in a single feature vector. In the current work, prior to dimensionality reduction each closed captions set is represented by a feature vector with 4,003 terms for the 4,003 unique words present in the entire data set. However, the maximum number of words that any closed captions set had was eleven which means that more than 99% of the terms were zero. The unlikely overlap of many of the feature vectors makes learning difficult. Using closed captions sets as the segmentation mechanism may not be appropriate since it A better approach may be to segment by combining several closed captions sets, such as considering every ten sets of closed captions a segment. The visual features in the previous work were the DC terms of the discrete cosine transform coefficients and the classification accuracy using these features alone was 59.23% with a 95% confidence interval of (58. 28, 60.19) . The visual features and and methodology were different in the previous work, so it is difficult to make a direct comparison of the effectiveness of different types of visual features.. The results of much of the other work in video recommendation is reported in terms of precision and recall. The precision and recall for our approach that combined closed captions and visual features was 57% and 51%, respectively. Ardissono et al. [1] achieved a precision of 80% and a mean absolute error rate of 30% in their case-based approach to recommendation. The precision of this approach is significantly better than what our approach achieved. Basu et al. [3] achieved precision and recall values of 83% and 34%, respectively. Our approach had worse precision but better recall than this approach.

O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O 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O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Non-isothermal, non-Newtonian Hele-Shaw flows within Cattaneo's heat flux law In this paper, we consider a non-isothermal, non-Newtonian injection process. This leads to the study of a novel elliptic-hyperbolic system. The hyperbolic nature of the system arises because we replace the infinite speed of propagation from classical, thermal elasticity by a finite propagation velocity. We present a formal derivation of the elliptic-hyperbolic system starting from conservations of mass, momentum, and energy in a three-dimensional domain, where the removal of the infinite propagation speed is achieved using Cattaneo's law for heat conduction. The existence of weak solutions to certain elliptic-hyperbolic problems associated with the resulting equations is proved. Injection molding is a manufacturing process widely used for producing parts using a mold having a cavity in the shape of the part being manufactured. Nearly 20% of goods manufactured nowadays use injection molding due to its versatility and low cost [1] . The analysis of injection molding is complicated because of its non-isothermal and non-Newtonian character. Usually the mold surface is cold and the polymer melt is hot. During the curing process initial stresses may occur in the mold; hence, it is essential that the injection process be well monitored with regard to controlling the pressure and temperature. We provide next a short review of the approach taken by Shi, 1992-1996 , [20, 21] in formulating the injection process (Problem I) for non-isothermal, non-Newtonian fluids and study the existence of its weak solutions. Here p is the pressure of the flow and θ is the temperature. Numerical solutions to this and similar problems appear in the engineering literature [25, 24, 9, 10, 27, 51, 53, 52, 1, 50, 34, 61] . Some other related papers are [56, 19, 16, 15] .. In the present paper we replace the diffusion heat conduction equation used in Problem I with a hyperbolic heat conduction equation. We recall that the classical heat (diffusion) equation. has the well-known fundamental solution. If g is bounded, continuous, with g ≥ 0, positive somewhere, then temperature Θ(x, t) at any later time (no matter how soon) is everywhere positive. Therefore we say the heat equation forces infinite propagation speed of the temperature. From a macroscopic continuum sense, the heat conduction phenomenon is often described by Fourier's law, relating the heat flux to the temperature:. Such an expression suffers from some pathological deficiencies, as has been mentioned on many occasions (Maxwell [39] 1867, Onsager [42, 43] 1931). Firstly, it does not take into account memory effects which are present in some materials. Secondly, it predicts that all thermal disturbances at a given point in the body are felt immediately throughout the whole body [46] .. Cattaneo [8] is credited as the first to eliminate this anomaly by proposing a damped version of Fourier's law by introducing a heat flux relaxation term, namely,. where τ is a relaxation time which represents the time required to establish a steady state of heat conduction in an element suddenly exposed to heat flux. He reasoned that heat flow does not start instantaneously, but grows gradually with a relaxation time τ , after the application of a temperature gradient. Similarly, heat flow does not cease immediately, but dies out gradually, after a temperature gradient is removed. As a consequence, numerous theories and postulates exist in the literature on the existence of a finite speed of heat propagation, termed the hyperbolic heat equation [37, 17, 32, 29, 30, 5, 33, 38, 36, 46, 18, 6, 59, 35] . The engineering literature on "hyperbolic conduction" is collected annually in the "Review of Heat Transfer Literature" in the International Journal of Heat and Mass Transfer. The hyperbolic model of heat conduction is more physically realistic and more general than the parabolic model. For situations involving high heat flux devices such as lasers with short duration or high frequency and high temperature gradients, heat is found to propagate at a finite speed. With more emphasis on precision material processing [31, 41, 2, 26, 45, 4, 54, 23] it is likely that an increase in the application of the hyperbolic proposition will take place in the future. In this paper we use Cattaneo's law for heat conduction to formulate a novel elliptic-hyperbolic system through an asymptotic argument. We also establish the existence of a weak solution for a resulting Newtonian non-isothermal case.. In Section 2 of the paper, we derive the two-dimensional non-isothermal, non-Newtonian systems of the significant terms by use of asymptotic expansions. In particular we take into account Cattaneo's law (1.8) for heat conduction. In Section 3, we prove the existence of weak solutions to a resulting system of equations in the Newtonian case. Although the physical models are two dimensional, we shall carry out our proofs for N dimensions. Subsequent research will be directed to the existence of weak solutions for the non-isothermal, non-Newtonian case and numerical investigation of such systems.. The statements of these problems are given below.. Problem II. Find functions θ and p defined in Ω T such that. (1.13). We assume that Ω is a bounded domain in R n with a C 1 boundary, where n ≥ 2. For a given time interval (0, T ),. We further assume that θ 0 , ϕ, and ψ are given functions, while given functions f and p 0 are independent of time t. We also assume that τ , K , λ, k, ρ and c p are positive constants related to physical quantities (such as relaxation time, thermal conductivity, density of the fluid, specific heat, etc.). In this paper, let H 1,s (Ω ) and H 1,s 0 (Ω ) denote the usual Sobolev space equipped with the standard norm. We assume that the boundary data f , θ 0 , and p 0 for Problem II can be extended to functions defined on Ω such that. where 0 < α ≤ 1. We further assume that

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Spatial sound localization in an augmented reality environment Augmented Reality (AR), the overlay of virtual images onto the real world, is an increasingly popular technique for developing new human-computer interfaces. As human navigation and orientation in different environments depend on both visual and auditory information, sound plays a very important role in AR applications. In this paper we explore users' capability to localize a spatial sound (registered with a virtual object) in an AR environment, under different spatial configurations of the virtual scene. The results not only confirm several previous findings on sound localization, but also point out some important new visual-audio cues which should be taken into consideration for effective localization and orientation in AR environment. Finally, this paper provides tentative guidelines for adding spatial sound to AR environments. Augmented reality (AR) involves the overlay of virtual imagery on the real world. It enhances the user's normal view of the world by adding computer-generated visual and auditory information. AR can be used in various application domains, such as visualization, medicine, engineering and education (Azuma, 1997; Azuma, 2001 ).. Most previous research in AR environments has been concerned with overlaying virtual graphics on the real world. In contrast, we are interested in audio enhancements and how spatial sound can combine with graphics to improve performance in an AR application.. This combining of 3D virtual graphics and spatial sound in AR not only offers a new type of applications but also new possibilities for the audio research community. For example, a user could move a tangible object (e.g. cardboard cube) on a table and hear a 3D sound of a motor engine while seeing a virtual model of a car moving with it. Natural interaction with real objects and the environment, and seamless merging between real and virtual content, introduce new research problems which differ from immersive virtual reality. For sound researchers the possibility to freely register and spatially configure the position of sounds with virtual images has appeal for perceptual studies.. In this paper, we conduct an evaluation for AR visual and sound localization in the context of tabletop situations. This is an area that has not been well studied in the past, and this paper provides guidelines that will be useful for AR interface developers. Spatial sound represents an important cue for navigation in space. This experiment explores the possibility of localization in a tabletop augmented reality environment, based on sound and visual cues. We used five different configurations of 3D models to evaluate the impact of different components of spatial sound on the localization performance.. The results of our experiment confirm that humans localize the azimuth of sound source much better than elevation or distance. Localization performance is especially poor when targeting objects are randomly distributed in space. Our experiment shows that localization can be improved if there is some regularity in the distribution. The improvement of elevation perception can also be made with artificial coding. This proved to be an effective method, but it requires some learning,, and it could also sometimes appear to be unnatural and disturbing. We are planning to perform further research into this problem.. This evaluation shows the results of localization of virtual sounds combined with virtual objects. In the future we plan to compare the importance of contradictory virtual and acoustic cues for navigation, i.e. the virtual images and audio cues which do not correspond to one another. We are going to try to confuse the users performing the localization task by not attaching the sounds to 3D models. We are also interested in further exploring the usage of 3D sound for AR applications and how to use perceptual factors to improve the sound rendering. In our pilot study with two users we observed the time necessary for accomplishing each localization task. There were big differences in localization time between users, between different conditions and also between individual trials in each condition. Because of the randomness of time variations, we decided to exclude the observation of time from the main experiment.. The results of the first condition confirmed that azimuth of arbitrary sound source can be located with high accuracy, although non-individualized HRTF filters are used (Wenzel, 1993 , Sodnik, 2005 .. The number of subjects limited us from performing a deeper quantitative analysis of our experiments. This study should be repeated with more test subjects to confirm our pilot results. However, in this paper we describe the first interpretation of these elements in the following paragraph.. The second condition was the evaluation of depth or distance perception of spatial sound, since all models were located in the horizontal plane. The analysis of the results confirmed that the distance perception of near sources is poor (Zhou, 2004) . When sound sources are in close proximity, elevation can play an important role for better perception. The latter was confirmed especially with the third condition of our experiment, whereby the models were equally distributed in the vertical direction. This condition proved to be the most ideal of all for localization and was ranked as the easiest by the users. When the vertical distribution was random, the localization performance dropped. The users reported this task to be the hardest one. With the last condition we attempted to show that localization of randomly distributed objects can be improved with artificial coding or spectrum manipulation. At this stage, we did not get any significant results to demonstrate the claim. Based on good results of previous studies on artificial coding of elevation in the acoustic image (Susnik, 2005) , we expect that also in AR environment the elevation perception could be improved in this way.. The measurement of distances to the targets enabled the observation of learning effects in two different dimensions. There was a noticeable learning effect within each of the ten trials. Comparing the distances in the first, second and third attempts (figure 7), we can observe the users' technique in localizing individual sources. The user's first attempt was based specifically on sound cues when the user macro-localized the target. The microlocalization (the second and third attempt) was based on visual cues. There was a significant difference in learning effect between conditions.. On the other hand, there was no learning effect while performing individual trials in each condition. The distance to the target on the first attempt was related to the sequence of the trial (figure 7). Sometimes the starting distance in the later trials (7, 8, 9) was much greater than in the first few trials (1, 2, 3). Spatial sound has been proven to play an important role in AR applications. Its use has been explored in very different areas, from pure entertainment (Stampfl, 2003a) to video conferencing and remote collaboration (Billinghurst 2001 , Regenbrecht, 2004 , and also perceptual studies (Bormann, 2005) . In this section we review earlier work in adding spatial sound to AR environments.

B I B O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O


Inter-patient distance metrics using SNOMED CT defining relationships Background. Patient-based similarity metrics are important case-based reasoning tools which may assist with research and patient care applications. Ontology and information content principles may be potentially helpful tools for similarity metric development.Methods. Patient cases from 1989 through 2003 from the Columbia University Medical Center data repository were converted to SNOMED CT concepts. Five metrics were implemented: (1) percent disagreement with data as an unstructured ''bag of findings,'' (2) average links between concepts, (3) links weighted by information content with descendants, (4) links weighted by information content with term prevalence, and (5) path distance using descendants weighted by information content with descendants. Three physicians served as gold standard for 30 cases.Results. Expert inter-rater reliability was 0.91, with rank correlations between 0.61 and 0.81, representing upper-bound performance. Expert performance compared to metrics resulted in correlations of 0.27, 0.29, 0.30, 0.30, and 0.30, respectively. Using SNOMED axis Clinical Findings alone increased correlation to 0.37.Conclusion. Ontology principles and information content provide useful information for similarity metrics but currently fall short of expert performance. Improvements in data interchange standards, information systems, and data entry technologies have produced increased patient data in electronic format for clinical information systems. With more automation and creation of electronic health records, the amount of available coded patient data continues to expand. While most clinical databases are primarily used and designed for direct patient care, other important applications for these databases often lag behind, including clinical research and quality functions. Medical informatics data mining research can potentially help to improve the use of clinical databases for these applications. With respect to data mining of patient data, most reported studies use small, manually edited databases in order to examine focused and specific clinical questions [1] [2] [3] . Many believe, however, that one of the great potentials of health care data mining is the automated utilization of real-time large clinical databases for these applications [4, 5] .. Similarity is a fundamental concept that can help with the task of automated information integration. Measures of similarity aim to assess the degree of closeness between cases of interest and produce medically relevant interpretations of patients so that analogous case(s) can be discovered. Useful metrics aim to give a quantifiable evaluation as to how similar two patients are to one another, based upon the context of the question at hand.. Similarity can also be examined from different perspectives. Depending upon the application, a clinical researcher may be interested in identifying sets of similar patients, such as patients who might qualify for an experimental oncology chemotherapy protocol. Furthermore, in theory, similarity metrics may be able to generate new knowledge about how patients relate to one another. Some of the obvious categories of factors that might be important according to the question being answered include: a patient's disease or condition (diagnoses), patient intervention (procedure), and patient environment and pre-existing state (demographics, address).. In clinical medicine, similarity metrics are typically based upon the case, defined as one or several medical encounters, or the entire patient record. If metrics can approach the behavior of experts, they will likely have an important role in case-based reasoning for research and for real-production systems, including decision-support applications. We were interested in exploring the methodological issues with inter-patient distance metrics by examining case-based similarity from a general clinical perspective and in using ontology principles as a tool to examine previously described distance metrics in medical informatics and to construct additional measures. These measures were then evaluated on patient cases with expert evaluation as our gold standard. Inter-patient similarity is a fundamental area of development in datamining research. Defined relationships of the terminology and principles of information content were able to provide valuable information for distance metrics, and narrowing in on the features used in expert determination of similarity with SNOMED CT axes was helpful. These measures, however, currently fall short of expert performance. Inter-patient similarity metrics can potentially help datamining researchers answer complex clinical questions for large populations. The issues with this task remain challenging. This study represents a formal attempt to address and discuss some of the underlying issues with inter-patient distance using ontology and information content principles as tools. While the addition of ontology principles and information content did result in improved metrics, metric performance is still not as good as experts.. Despite the increase in observed correlation when comparing an unstructured ''bag of findings'' to the other four metrics, there was virtually no difference in the correlations in the four different metrics which used SNOMED CT. This was unexpected, as we anticipated that as algorithms progressed from less to more complex (algorithm 2 up to 5), that metric performance would improve and change as more of the described patient similarity principles were incorporated into the metrics. As such, while all the discussed inter-patient similarity principles appear to be important from an intuitive standpoint, which one(s) will be key for inter-patient similarity in practice has yet to be determined. While using descendants within the metrics would intuitively be influenced by intricacies and variations in SNOMED CT, using descendants versus term frequency did not have a negative effect upon metric performance in our experiment.. It is unclear what relative contribution inaccurate coding of data during conversion to SNOMED CT or the somewhat fuzzy structure of SNOMED CT itself had upon the metrics and our results. There was almost certainly some loss of granularity and accuracy in our results due to issues associated with converting from a source terminology (such as ICD9 codings) to SNOMED CT. Our results could potentially be improved if all data were initially encoded in SNOMED CT without the need to convert data from one source terminology to another. Clearly, the usefulness of ontology principles as tools for a particular purpose depends highly upon the quality and granularity of the terminology in question. As such, we speculate that some of the stakeholders in the development of SNOMED CT (pathology or internal medicine) may have improved the quality of concept and hierarchy development in these areas more than those domains with less traditional involvement with SNOMED CT's development (public health or surgery).. We were able to demonstrate that patient similarity assessment is well correlated among expert physician raters given the task of defining similarity as what made clinical sense to them. Similarity for this set of random patient cases appears to correlate most strongly with concepts within the SNOMED CT axes ''Clinical finding,'' ''Body Structure,'' and ''Procedure,'' which roughly correspond to (1) diseases, signs, and symptoms, (2) organ systems, and (3) procedures, respectively. This is perhaps somewhat intuitive but is an interesting observation to formally identify. An interesting follow-up study could be to formally conduct a cognitive analysis of experts with the task of case-based similarity from several perspectives. In this manner, we may be able to understand the cognitive process used by experts and how this changes according the question or task at hand in order to optimize future computer performance. Furthermore, while ICD9-CM was rejected for several of its limitations from a structural and content coverage perspective, it would be interesting to use ICD9-CM in a follow-up experiment to compare its performance to SNOMED CT, as ICD9-CM's coverage of these concept class axes is good. As a follow-up experiment, all five of these metrics could be applied to data from the discharge summaries alone, which was thought by experts to be the highest yield data source. This could help to test the degree to which incomplete SNOMED coding, or other information associations, contributed to the poorer observed performance of the metrics.. In summary, the authors propose several patient-based distance measures with varying complexity, building upon previously described measures. Our evaluation of these measures reveals that useful information can be obtained from these techniques, but further research will be needed in order to achieve the goal of automated utilization of these measures for practical uses. Future work should aim to understand better these correlations, to leverage this knowledge to create better metrics, and to identify subsets of patient data best correlated with experts. The three physician experts rated 30 cases with an overall inter-rater reliability 0.91. The correlation amongst expert rater scores ranged from 0.61 to 0.81, which represents an upper bound for automated performance. There was no statistical difference in the correlation amongst the experts. While the entire electronic chart was available to the experts, for the task of rating case similarity based upon what made clinical sense, all three experts reported that discharge summaries were predominantly used in their similarity score determinations. The second most common source used by the three experts was reported as ICD9-CM codes by one and operative notes by two of the experts.. The average expert rating for each pairwise comparison of the 30 cases was correlated with the results for each metric, as depicted in Table 2 . The structured algorithms had a slightly greater correlation than when data were viewed as an unstructured ''bag of findings'' (Algorithm 1 (0.27) versus Algorithm 2 (0.29) or versus Algorithms 3, 4, or 5 (0.30)), but the differences were not significant. These correlations represent 30% higher of a likelihood that the metrics would agree than disagree with the experts. Furthermore, as expected, experts were statistically more like to agree with one another than any of the algorithms were likely to agree with the experts (p < 0.0001).. Each term was also categorized into its SNOMED CT axis to correlate the axes to expert scores. The metrics were re-calculated along each of the 18 SNOMED CT axes with the second and fifth algorithm. As depicted in Table 3 , the axes that correlated most strongly with experts were axes ''Clinical Finding,'' ''Body Structure,'' and ''Procedure'' for algorithms 2 and 5, respectively. ''Clinical Finding'' for algorithm 2 was significantly more likely to agree with experts than the basic algorithm 2 (p = 0.0080) or ''Procedure'' for algorithm 2 (p = 0.0015) but not more likely to agree than ''Body Structure'' for algorithm 2 (p = 0.11). Similarly, ''Clinical Finding'' for algorithm 5 was significantly more likely to agree with experts than the basic algorithm 5 (p = 0.0025), ''Procedure'' for algorithm 5 (p = 0.036), and ''Body Structure'' for algorithm 5 (p = 0.035). Table 2 Metric performance correlation with average expert ratings

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