Binary Partitioning Research Articles

USING A NOTION OF ACCEPTABLE IN UNCERTAIN ORDINAL DECISION MAKING

We focus on the problem of constructing decision functions to aid in the valuation of alteratives in uncertain decision making. We discuss different types of scales available for representing the payoffs associated with the alternatives. Here we consider the case in which our basic scale is an ordinal case. Here however we augment this ordinal scale by allowing an additional notion. We indicate one special element on the scale which we call the denoted element. We name such a scale a Denoted Ordinal Scale (DOS). We point out that a DOS allows a binary partitioning of the basic ordinal scale which can be associated with differing semantics and used for various purposes. Here we focus on a binary partitioning and use a semantics which provides a classification of payoffs as to whether they are acceptable or not. This allows us to have information such as A is preferred to B but both are acceptable. We show how a DOS with this semantics can be used to construct sophisticated decision functions.

Validation and results of a questionnaire for functional bowel disease in out-patients

BackgroundThe aim was to evaluate and validate a bowel disease questionnaire in patients attending an out-patient gastroenterology clinic in Greece.MethodsThis was a prospective study. Diagnosis was based on detailed clinical and laboratory evaluation. The questionnaire was tested on a pilot group of patients. Interviewer-administration technique was used. One-hundred-and-forty consecutive patients attending the out-patient clinic for the first time and fifty healthy controls selected randomly participated in the study. Reliability (kappa statistics) and validity of the questionnaire were tested. We used logistic regression models and binary recursive partitioning for assessing distinguishing ability among irritable bowel syndrome (IBS), functional dyspepsia and organic disease patients.ResultsMean time for questionnaire completion was 18 min. In test-retest procedure a good agreement was obtained (kappa statistics 0.82). There were 55 patients diagnosed as having IBS, 18 with functional dyspepsia (Rome I criteria), 38 with organic disease. Location of pain was a significant distinguishing factor, patients with functional dyspepsia having no lower abdominal pain (p < 0.001). Significant factors distinguishing between IBS and functional dyspepsia were relief of pain by either antacids or defecation (19% vs 71% and 66% vs 0% respectively). Awakening from pain at night was also a factor distinguishing between IBS and organic disease groups (26% vs 61%, p < 0.01).ConclusionsThis questionnaire for functional bowel disease is a valid and reliable instrument that can distinguish satisfactorily between organic and functional disease in an out-patient setting.

Identification of children with intra-abdominal injuries after blunt trauma

Study Objective: We sought to determine the utility of laboratory testing after adjusting for physical examination findings in the identification of children with intra-abdominal injuries after blunt trauma. Methods: The study was a prospective observational series of children younger than 16 years old who sustained blunt trauma and were at risk for intra-abdominal injuries during a 2½-year period at an urban Level I trauma center. Patients were examined by faculty emergency physicians and underwent standardized laboratory testing. Clinical and laboratory findings were recorded on a standardized data sheet. Intra-abdominal injury was considered present if an injury was documented to the spleen, liver, pancreas, kidney, adrenal glands, or gastrointestinal tract. We performed multiple logistic regression and binary recursive partitioning analyses to identify which physical examination findings and laboratory variables were independently associated with intra-abdominal injury. Results: Of 1,095 enrolled patients, 107 (10%, 95% confidence interval [CI] 8% to 12%) had intra-abdominal injuries. The mean age was 8.4±4.8 years. From both analyses, we identified 6 findings associated with intra-abdominal injury: low systolic blood pressure (adjusted odds ratio [OR] 4.1; 95% CI 1.1 to 15.2), abdominal tenderness (adjusted OR 5.8; 95% CI 3.2 to 10.4), femur fracture (adjusted OR 1.3; 95% CI 0.5 to 3.7), serum aspartate aminotransferase concentration more than 200 U/L or serum alanine aminotransferase concentration more than 125 U/L (adjusted OR 17.4; 95% CI 9.4 to 32.1), urinalysis with more than 5 RBCs per high-powered field (adjusted OR 4.8; 95% CI 2.7 to 8.4), and an initial hematocrit of less than 30% (adjusted OR 2.6; 95% CI 0.9 to 7.5). Conclusion: After adjusting for physical examination findings, laboratory testing contributes significantly to the identification of children with intra-abdominal injuries after blunt trauma. [Holmes JF, Sokolove PE, Brant WE, Palchak MJ, Vance CW, Owings JT, Kuppermann N. Identification of children with intra-abdominal injuries after blunt trauma. Ann Emerg Med. May 2002;39:500-509.]

Infinite-Dilution Binary Diffusion Coefficient, Partition Ratio, and Partial Molar Volume for Ubiquinone CoQ10 in Supercritical Carbon Dioxide

Infinite-dilution binary diffusion coefficient D12 and partition ratio k for ubiquinone CoQ10 in carbon dioxide were measured by a tracer response technique with a poly(ethylene glycol)-coated capillary column at temperatures from 308.15 to 333.15 K and pressures from 8.5 to 30 MPa. D12 and k values were simultaneously determined from a measured response curve by the curve-fitting method. The fitting error between measured and calculated response curves increased with decreasing pressure, as had been the case in our previous studies on various solutes in supercritical CO2 by the Taylor dispersion method. The D12 values were correlated with temperature and CO2 viscosity and the k values with temperature and CO2 density. Moreover, partial molar volumes of CoQ10 in supercritical CO2 were obtained from the k values.

Binary space partitions for axis-parallel line segments: Size-height tradeoffs

We present worst-case lower bounds on the minimum size of a binary space partition (BSP) tree as a function of its height, for a set S of n axis-parallel line segments in the plane. We assume that the BSP uses only axis-parallel cutting lines. These lower bounds imply that, in the worst case, a BSP tree of height O(log n) must have size Ω(n logn) and a BSP tree of size O( n) must have height Ω(n δ) , where δ is a suitable constant.

Binary Partitions Revisited

The restricted binary partition function bk(n) enumerates the number of ways to represent n as n=2a0+2a1+…+2aj with 0⩽a0⩽a1⩽…⩽aj<k. We study the question of how large a power of 2 divides the difference bk(2r+2n)−bk−2(2rn) for fixed k⩾3, r⩾1, and all n⩾1.

Real-time tracking of complex structures with on-line camera calibration

This paper presents a novel three-dimensional model-based tracking system which has been incorporated into a visual servoing system. The tracking system combines modern graphical rendering technology with constrained active contour tracking techniques to create wire-frame-snakes. It operates in real-time at video frame rate (25 Hz) and is based on an internal CAD model of the object to be tracked. This model is rendered using a binary space partition tree to perform hidden line removal and the visible features are identified on-line at each frame and are tracked in the video feed. The tracking system has been extended to incorporate real-time on-line calibration and tracking of internal camera parameters. Results from on-line calibration and visual servoing experiments are presented.

Scaling behaviour of entropy estimates

Entropy estimation of information sources is highly non trivial for symbol sequences with strong long-range correlations. The rabbit sequence, related to the symbolic dynamics of the nonlinear circle map at the critical point as well as the logistic map at the Feigenbaum point have been argued to exhibit long memory tails. For both dynamical systems the scaling behavior of the block entropy of order n has been shown to increase like as log(n). In contrast to probabilistic concepts, we investigate the scaling behavior of certain non-probabilistic entropy estimation schemes suggested by Lempel and Ziv in the context of algorithmic complexity and data compression. These are applied in a sequential manner with the scaling variable being the length N of the sequence. We determine the scaling law for the Lempel-Ziv entropy estimate applied to the case of the critical circle map and the logistic map at the Feigenbaum point in a binary partition.

Exact Size of Binary Space Partitionings and Improved Rectangle Tiling Algorithms

We prove the following upper and lower bounds on the exact size of binary space partition (BSP) trees for a set of n isothetic rectangles in the plane: An upper bound of 3n-1 in general, and an upper bound of 2n-1 if the rectangles tile the underlying space. This improves the upper bounds of 4n in [V. Hai Nguyen and P. Widmayer, Binary Space Partitions for Sets of Hyperrectangles, Lecture Notes in Comput. Sci. 1023, Springer-Verlag, Berlin, 1995; F. d'Amore and P. G. Franciosa, Inform. Process. Lett., 44 (1992), pp. 255--259]. A BSP satisfying the upper bounds can be constructed in O(n log n) time. A worst-case lower bound of 2n-o(n) in general, and $\frac{3n}{2}-o(n)$ if the rectangles form a tiling. The BSP tree is one of the most popular data structures in computational geometry, and hence even small factor improvements of $\frac{4}{3}$ or 2 on the previously known upper bounds that we show improve the performances of applications relying on the BSP tree. As an illustration, we present improved approximation algorithms for certain dual rectangle tiling problems using our upper bounds on the size of the BSP trees.

Identifying spots in microarray images

Microarray technology has provided a way to quantitate the simultaneous expression of a large number of genes. This approach is dependent on reproducible, accurate identification and quantitation of spot intensities. In this paper, clustering-based image segmentation is described to extract the target intensity of the microarray spots. While the technique is generic, its effectiveness on extracting spot intensities on arrays obtained from a two-color (Cy3/Cy5) experiment is discussed. The approximate boundaries of the spots are determined initially by manual alignment of rectangular grids. The pixel intensities of the image (I) inside a grid, is mapped onto a one-dimensional vector (v). The k-means clustering technique is applied to generate a binary partition of v. The median value of the pixel intensities inside each of the clusters for a given spot determines its foreground and the local background intensity. The difference in the median value of the foreground and the background intensity is the desired target intensity of the spot. The results are compared against those obtained using a region growing approach.

Outcome of Older Patients with Severe Pneumonia Predicted by Recursive Partitioning

OBJECTIVES: To develop a prognostic model to predict outcome of older patients with severe pneumonia requiring mechanical ventilation.DESIGN: A nonconcurrent prospective study.SETTING: A 24‐bed intensive care unit (ICU) within two university‐affiliated tertiary care hospitals.PARTICIPANTS: All patients age 75 and older with severe pneumonia between June 1996 and September 1999 were included. Demographic data including activities of daily living (ADL) index score before admission, and clinical and laboratory data were collected in the first 24 hours of admission to the ICU. One hundred four patients (mean age ± standard deviation (SD) 82.3 ± 5.5 years) met the inclusion criteria.MEASUREMENTS: A classification tree was developed using binary recursive partitioning to predict hospital discharge. The model was compared with a logistic regression model using variables selected by the tree analysis and with the Acute Physiologic and Chronic Health Evaluation (APACHE) II.RESULTS: Outcome predictors for the classification tree were use of vasopressors, presence of multilobar pneumonia on chest radiograph, ratio of blood urea nitrogen to creatinine, Glasgow Coma Scale, urine output, and ADL score before admission. The tree achieved a sensitivity of 83.8% (95% confidence interval (CI) 69.2–92.4) and a specificity of 93.3% (95% CI 83–98.1). The predictive accuracy as assessed by the area under the curve (c‐index ± standard error) was significantly higher with the classification tree (0.932 ± 0.03) than with logistic regression and APACHE II, (0.801 ± 0.028 and 0.711 ± 0.049, respectively (P &lt; .05).CONCLUSIONS: The classification tree model demonstrated a superior predictive accuracy to that of logistic regression and APACHE II. If validated prospectively, the classification tree can be used as a tool to assess the outcome of older patients with severe pneumonia requiring mechanical ventilation on admission to the ICU. In addition, the classification tree can be used to assist healthcare workers in providing a concise summary of local outcome experience and prognostic information to patients and their surrogates.

Face segmentation and tracking based on connected operators and partition projection

A new technique for segmenting and tracking human faces in video sequences is presented. The algorithm relies on the concepts of connected operators and partition projection to tackle the problems of face segmentation and tracking, respectively. It uses a connected operator to extract the connected component that more likely belongs to a face. Such a connected operator is implemented by means of a Binary Partition Tree. A set of connected regions (a node in the tree) is selected maximizing the estimation of the likelihood of being part of a face. This way, a first estimate of the face is obtained. Final face segmentation is carried out by a face extraction step that applies the previous maximization in the partition space. Faces are tracked through the sequence based on the partition projection approach. Partition projection accommodates the partition of the previous image into the information of the current frame. The current image is classified into face, no face and uncertain regions by projecting the previous face partition. Therefore, the projection yields the first estimate of the face. The face core component is grown up to obtain the final face segmentation using the previous face extraction process. The technique has been successfully assessed using several test sequences in raw format (MPEG-4 database) as well as in MPEG-1 format (from the MPEG-7 database).

Visual segment tree creation for MPEG-7 Description Schemes

This paper deals with the creation of visual segment trees involved in MPEG-7 Description Schemes. After a brief overview of MPEG-7 Description Schemes in general and of the Segment Description Scheme in particular, tools allowing the creation of segment trees are discussed. The emphasis of the paper is on the creation of hierarchical relationship among segments. For this purpose, it is proposed to create a Binary Partition Tree in a first step and to restructure the tree in a second step. This approach is both efficient and flexible. Several examples involving spatial and temporal partition trees are presented. The proposed approach is appropriate to create both tables of contents and indexes.

A fast multiresolution feature matching algorithm for exhaustive search in large image databases

Most of the content-based image retrieval systems require a distance computation for each candidate image in the database. As a brute-force approach, the exhaustive search can be employed for this computation. However, this exhaustive search is time-consuming and limits the usefulness of such systems. Thus, there is a growing demand for a fast algorithm which provides the same retrieval results as the exhaustive search. We propose a fast search algorithm based on a multiresolution data structure. The proposed algorithm computes the lower bound of distance at each level and compares it with the latest minimum distance, starting from the low-resolution level. Once it is larger than the latest minimum distance, we can remove the candidates without calculating the full-resolution distance. By doing this, we can dramatically reduce the total computational complexity. It is noticeable that the proposed fast algorithm provides not only the same retrieval results as the exhaustive search, but also a faster searching ability than existing fast algorithms. For additional performance improvement, we can easily combine the proposed algorithm with existing tree-based algorithms. The algorithm can also be used for the fast matching of various features such as luminance histograms, edge histograms, and local binary partition textures.

Iceberg-cube computation with PC clusters

In this paper, we investigate the approach of using low cost PC cluster to parallelize the computation of iceberg-cube queries. We concentrate on techniques directed towards online querying of large, high-dimensional datasets where it is assumed that the total cube has net been precomputed. The algorithmic space we explore considers trade-offs between parallelism, computation and I/0. Our main contribution is the development and a comprehensive evaluation of various novel, parallel algorithms. Specifically: (1) Algorithm RP is a straightforward parallel version of BUC [BR99]; (2) Algorithm BPP attempts to reduce I/0 by outputting results in a more efficient way; (3) Algorithm ASL, which maintains cells in a cuboid in a skiplist, is designed to put the utmost priority on load balancing; and (4) alternatively, Algorithm PT load-balances by using binary partitioning to divide the cube lattice as evenly as possible. We present a thorough performance evaluation on all these algorithms on a variety of parameters, including the dimensionality of the cube, the sparseness of the cube, the selectivity of the constraints, the number of processors, and the size of the dataset. A key finding is that it is not a one-algorithm-fit-all situation. We recommend a “recipe” which uses PT as the default algorithm, but may also deploy ASL under specific circumstances.

Can We Predict Poor Outcome at Presentation in Patients with Lobar Hemorrhage?

Objective: Supratentorial lobar hemorrhage can be devastating. Outcome prediction at presentation is important in triage and management decisions as well as appropriate resource utilization. We performed a decision tree analysis combining clinical and CT scan features to predict poor and hopeless outcome at initial presentation in patients with lobar hemorrhage. Methods: We analyzed 81 patients with spontaneous lobar hemorrhage presenting within 48 hours of initial neurologic symptoms. In the first analysis, poor outcome was defined as Glasgow outcome score (GOS) of 1 (death), 2 (vegetative state) or 3 (dependence) at discharge. A second analysis was based on worst possible outcome (GOS 1–2). Binary recursive partitioning was fitted in a model, and odds ratios with 95% confidence intervals (CI) were calculated. Results: Lobes involved were temporal (36%), parietal (33%), frontal (25%) and occipital (6%). Seventy-three percent of patients presented less than 17 h after initial ictus. The probability of poor outcome was 97% (CI 85–100%) in patients with hemorrhage greater than 40 cm³. In the subset of patients with a volume less than 40 cm³, time interval from ictus to presentation (<17 h) together with a Glasgow coma score (GCS) less than or equal to 13 predicted poor outcome. Eighty-five percent (CI 42–99%) of those presenting early with GCS less than or equal to 13 had a poor outcome. In the second analysis, all patients with GCS less than or equal to 12 and septum pellucidum shift >6 mm had GOS of 1 or 2 (CI 72–100%). Conclusion: Poor outcome in patients with lobar hemorrhage is associated with a hemorrhage size of more than 40 cm³, GCS less than or equal to 13, but also dependent on time interval between ictus and presentation. This is consistent with prior studies demonstrating deterioration from enlargement may occur when patients present early on. Stupor and septum pellucidum shift greater than 6 mm on CT scan at presentation predict a hopeless outcome in conservatively treated patients. Ninety-one percent of patients were treated medically, thus these outcomes are largely a reflection of the natural history of spontaneous lobar hemorrhage. These signs may influence triage and management decisions.

On the suitability of GO/UTD modelling of microwave propagation in indoor environments

AbstractThe main aim of this paper is to show the suitability of the geometrical optics and uniform theory of diffraction (GO/UTD) approach for modelling microwave propagation in indoor environments. Implementation details for an efficient method based on a combination of image theory and the binary space partitioning (BSP) algorithm to perform ray tracing are presented. The efficiency of the method allows a full three‐dimensional implementation of the GO/UTD approach. An extensive measurement champaign has been carried out in order to analyse the degree of accuracy achievable by the method. Some of these comparisons between measured and simulated data are presented, and a quantitative analysis of errors is made. The analysis reveals that the degree of precision in the calculation of the signal levels allows not only the signal mean level but also its statistics to be estimated accurately. The error in the mean level of the signal is less than 2 dB in the majority of cases, a maximum error of 3.6 dB having been obtained. The statistics of the signal fit Rice distributions very closely with different values of the rician parameter K. Finally, a brief study of the influence of the number of ray mechanisms considered (reflected, double reflected, etc.) on the accuracy and calculation times is also presented. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Balanced Aspect Ratio Trees: Combining the Advantages of k-d Trees and Octrees

Given a set S of n points on Rd, we show, for fixed d, how to construct in O(nlogn) time a data structure we call the balanced aspect ratio (BAR) tree. A BAR tree is a binary space partition tree on S that has O(logn) depth in which every region is convex and “fat” (that is, has a bounded aspect ratio). While previous hierarchical data structures such as k-d trees, quadtrees, octrees, fair-split trees, and balanced box decompositions can guarantee some of these properties, we know of no previous data structure that combines all of these properties simultaneously. The BAR tree data structure has numerous applications ranging from geometric searching problems in fixed dimensional space to the visualization of graphs and three-dimensional worlds.

The effects of age of cochlear implantation on speech perception outcomes in prelingually deaf children.

We have made a retrospective analysis on 70 prelingually deaf children (78% congenital; age range 2-15 years) followed for up to 5 years post-implant during which both closed set speech perception tests (TAC, WIPI) and open set tasks (PBK, GASP) were administered. We used a binary partitioning algorithm to optimally divide our dataset on the basis of age at implantation This technique achieves an optimal split when the heterogeneity of the data is most reduced (maximal drop in deviance). For the closed set speech perception tests (TAC and WIPI) partitioning best divided-out data at age 4.4 years. For the open set tests optimal division was at a higher age of implantation (GASP word, 5.6 years; PBK word, 8.4 years). Using these partitioning values, we have found statistically significant differences between rate of improvement of scores in the younger implanted children compared with those implanted later.

Measurements of Binary Diffusion Coefficients and Partition Ratios for Acetone, Phenol, α-Tocopherol, and β-Carotene in Supercritical Carbon Dioxide with a Poly(ethylene glycol)-Coated Capillary Column

Binary diffusion coefficients, D12, and partition ratios, k, for the poly(ethylene glycol) (PEG) layer to supercritical carbon dioxide for acetone and some solid solutes such as phenol, α-tocopherol, and β-carotene were measured with a PEG-coated capillary column by a tracer response technique. The D12 values for acetone with the PEG-coated column were consistent with those measured by the Taylor dispersion method in which an uncoated capillary column was employed. The D12 and k values for all of the solutes decrease simply with increasing pressure, and the D12 values were represented by the Schmidt number correlation.