Class proximity measures--dissimilarity-based classification and display of high-dimensional data.

For two-class problems, we introduce and construct mappings of high-dimensional instances into dissimilarity (distance)-based Class-Proximity Planes. The Class Proximity Projections are extensions of our earlier relative distance plane mapping, and thus provide a more general and unified approach to the simultaneous classification and visualization of many-feature datasets. The mappings display all L-dimensional instances in two-dimensional coordinate systems, whose two axes represent the two distances of the instances to various pre-defined proximity measures of the two classes. The Class Proximity mappings provide a variety of different perspectives of the dataset to be classified and visualized. We report and compare the classification and visualization results obtained with various Class Proximity Projections and their combinations on four datasets from the UCI data base, as well as on a particular high-dimensional biomedical dataset.

Direct classification of high-dimensional data in low-dimensional projected feature spaces--comparison of several classification methodologies.

Previously, we introduced a distance (similarity)-based mapping for the visualization of high-dimensional patterns and their relative relationships. The mapping preserves exactly the original distances from all points to any two reference patterns in a special two-dimensional coordinate system, the relative distance plane (RDP). We extend the RDP mapping's applicability from visualization to classification. Several of the classifiers use the RDP directly. These include the standard linear discriminant analysis (LDA), nearest neighbor classifiers, and a transvariation probabilities-based classification method that is natural in the RDP. Several reference directions can also be combined to create new coordinate systems in which arbitrary classifiers can be developed. We obtain increased confidence in the classification results by cycling through all possible reference pairs and computing a misclassification-based weighted accuracy. The classification results on several high-dimensional biomedical datasets are compared.

The classification of benign and malignant human prostate tissue by multivariate analysis of 1H magnetic resonance spectra.

1H magnetic resonance spectroscopy studies (360 MHz) were performed on specimens of benign (n = 66) and malignant (n = 21) human prostate tissue from 50 patients, and the spectral data were subjected to multivariate analysis, specifically linear-discriminant analysis. On the basis of histopathological assessments, an overall classification accuracy of 96.6% was achieved, with a sensitivity of 100% and a specificity of 95.5% in classifying benign prostatic hyperplasia from prostatic cancer. Resonances due to citrate, glutamate, and taurine were among the six spectral subregions identified by our algorithm as having diagnostic potential. Significantly higher levels of citrate were observed in glandular than in stromal benign prostatic hyperplasia (P < 0.05). This method shows excellent promise for the possibility of in vivo assessment of prostate tissue by magnetic resonance.

Differential geometry of proteins. Helical approximations.

We regard a protein molecule as a geometric object, and in a first approximation represent it as a regular parametrized space curve passing through its alpha-carbon atoms (the backbone). In an earlier paper we argued that the regular patterns of secondary structures of proteins (morphons) correspond to geodesics on minimal surfaces. In this paper we discuss methods of recognizing these morphons on space curves that represent the protein backbone conformation. The mathematical tool we employ is the differential geometry of curves and surfaces. We introduce a natural approximation of backbone space curves in terms of helical approximating elements and present a computer algorithm to implement the approximation. Simple recognition criteria are given for the various morphons of proteins. These are incorporated into our helical approximation algorithm, together with more non-local criteria for the recognition of beta-sheet topologies. The method and the algorithm are illustrated with several examples of representative proteins. Generalizations of the helical approximation method are considered and their possible implications for protein energetics are sketched.

Structural interpretation of low-temperature heme-ligand recombination rates in myoglobin.

The nonexponential recombination of photodissociated heme-CO and heme-O2 in myoglobin, which is geminate at T less than 180 K, is interpreted as being due to a narrow, random distribution of ligand transfer distances in the heme pocket. This permits evaluation of the most probable recombination rate which is shown to be consistent with ligand tunneling.

Magnetic resonance spectroscopy of the malignant prostate gland after radiotherapy: a histopathologic study of diagnostic validity.

PURPOSE: Accurate spatial representation of tumor clearance after conformal radiotherapy is an endpoint of clinical importance. Magnetic resonance spectroscopy (MRS) can diagnose malignancy in the untreated prostate gland through measurements of cellular metabolites. In this study we sought to describe spectral metabolic changes in prostatic tissue after radiotherapy and validate a multivariate analytic strategy (based on MRS) that could identify viable tumor. METHODS AND MATERIALS: Transrectal ultrasound-guided prostate biopsies from 35 patients were obtained 18-36 months after external beam radiotherapy. One hundred sixteen tissue specimens were subjected to 1H MRS, submitted to histopathology, and analyzed for correlation with a multivariate strategy specifically developed for biomedical spectra. RESULTS: The sensitivity and specificity of MRS in identifying a malignant biopsy were 88.9% and 92% respectively, with an overall classification accuracy of 91.4%. The diagnostic spectral regions identified by our algorithm included those due to choline, creatine, glutamine, and lipid. Citrate, an important discriminating resonance in the untreated prostate gland, was invisible in all spectra, regardless of histology. CONCLUSIONS: Although the spectral features of prostate tissue markedly change after radiotherapy, MRS combined with multivariate methods of analysis can accurately identify histologically malignant biopsies. MRS shows promise as a modality that could integrate three-dimensional measures of tumor response.

Retrograde cerebral perfusion provides limited distribution of blood to the brain: a study in pigs.

OBJECTIVE: The objective of this study was to investigate flow distribution during retrograde and antegrade cerebral perfusion with India ink as a marker. METHODS: Ten pigs received cerebral perfusion with a solution containing 50% filtered India ink for 5 minutes either antegradely through both internal carotid arteries at a flow of 180 to 200 ml/min (n = 5) or retrogradely via the superior vena cava at a flow of 300 to 500 ml/min (n = 5). The brains were then fixed for quantitative measurement of the density of ink-filled capillaries (reported as a percentage of the total selected area). The assessment was done with the use of an in-house software program. RESULTS: In the antegrade cerebral perfusion group, the intracranial arterial and venous systems were completely filled with ink. The gray matter was colored uniformly black, and light coloring was observed in the white matter. During retrograde cerebral perfusion, the majority of ink was returned to the inferior vena cava, and only a small amount of ink was found in the innominate artery draining from the brain. Massive ink filling was observed in the sagittal sinus and other venous sinuses in all the pigs. Vessels on the surface of the brain and large vessels in the brain were also well filled with ink. However, only 10% of capillaries were filled with ink during retrograde cerebral perfusion relative to the number observed with antegrade cerebral perfusion. CONCLUSIONS: Retrograde cerebral perfusion supplies a limited amount of blood to brain tissue, which flows mainly through superficial and large deep cerebral vessels.

Spatial and free energy distribution patterns of amino acid residues in water soluble proteins.

We have calculated, for the 20 common amino acid residues: probability density functions that characterize the residues' tendency to occupy different locations in proteins; a propensity scale for the residues to be exposed or buried; mean force potentials that characterize the residues' free energy dependence on their degree of exposure; the average composition of water soluble proteins, and the composition of their core and surface. The nature of differences between different hydrophobicity-related scales is discussed.

Antigen-antibody recognition. Model calculations.

Free energy of antigen-antibody binding has been calculated for HyHEL-5, HyHEL-10, and D1.3 complexes. We also have calculated free energies of binding per residue of L- and H- chains of the antibodies, and those of the antigen (lysozyme). The results of the calculations provide support for the notion that TYR and TRP residues may confer on the CDRs of antibodies an enhanced capacity for binding antigens. It was shown also that the composition of residues that provide major part of the binding free energy differs for antibodies and antigens.

Diagnostic potential for cancer via 1H magnetic resonance spectroscopy of colon tissue.

Specimens of colon tissue were examined by 1H MRS (360 MHz) in order to determine the usefulness of rat colon (n = 44) as a model for human colon (n = 60), particularly for the characterization of preneoplastic lesions. Human tissue was characterized by 1H MRS as a precursor to in vivo studies. For both tissues, resonances from mobile lipids were not characteristic of pure mucosa, but correlated with the presence of submucosa. The mean intensities of the resonances at 3.2 and 3.4 ppm (assigned mainly to choline-containing compounds and taurine, respectively) of rat mucosa compared to those of human mucosa, and of rat tumours compared to human tumours, were not significantly different, while both resonances were significantly more intense in rat tumours compared to rat mucosa. The spectra of premalignant lesions in rat colon have features between those due to tumours and normal tissue. We conclude that rat colon is a useful model for human colon in 1H MR spectroscopic studies. MR spectra from human colon control tissue and tumours were classified with 100% accuracy using multivariate analysis.

The registration of MR images using multiscale robust methods.

Acquisition of MR images involves their registration against some prechosen reference image. Motion artifacts and misregistration can seriously flaw their interpretation and analysis. This article provides a global registration method that is robust in the presence of noise and local distortions between pairs of images. It uses a two-stage approach, comprising an optional Fourier phase-matching method to carry out preregistration, followed by an iterative procedure. The iterative stage uses a prescribed set of registration points, defined on the reference image, at which a robust nonlinear regression is computed from the squared residuals at these points. The method can readily accommodate general linear or even nonlinear, registration transformations on the images. The algorithm was tested by recovering the registration transformation parameters when a 256 x 256 pixel T2*-weighted human brain image was scaled, rotated, and translated by prescribed amounts, and to which different amounts of Gaussian noise had been added. The results show subpixel accuracy of recovery when no noise is present, and graceful degradation of accuracy as noise is added. When 40% noise is added to images undergoing small shifts, the recovery errors are less than 3 pixels. The same tests applied to the Woods algorithm gave slightly inferior accuracy for these images, but failed to converge to the correct parameters in some cases of large-scale-shifted images with 10% added noise.

An improved robust hierarchical registration algorithm.

This note describes an improvement to an accurate, robust, and fast registration algorithm (Alexander, M.E. and Somorjai, R.L., Mag. Reson. Imaging, 14:453-468, 1996). A computationally inexpensive preregistration method is proposed, consisting of simply aligning the image centroids, from which estimates of the translation shifts are derived. The method has low sensitivity to noise, and provides starting values of sufficient accuracy for the iterative registration algorithm to allow accurate registration of images that have significant levels of noise and/or large misalignments. Also, it requires a smaller computational effort than the Fourier Phase Matching (FPM) preregistration method used previously. The FPM method provides accurate preregistration for low-noise images, but fails when significant noise is present. For testing the various methods, a 256 x 256 pixel T2*-weighted image was translated, rotated, and scaled to produce large misalignments and occlusion at the image boundaries. The two situations of no noise being present in the images and in which Gaussian noise is added, were tested. After preregistration, the images were registered by applying one or several passes of the iterative algorithm at different levels of preblurring of the input images. Results of using the old and new preregistration methods, as well as no preregistration, are compared for the final accuracy of recovery of registration parameters. In addition, the performances of three robust estimators: Least Median of Squares, Least Trimmed Squares, and Least Winsorized Mean, are compared with those of the nonrobust Least Squares and Woods' methods, and found to converge to correct solutions in cases where the nonrobust methods do not.

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images.

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR approximately 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak's method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.

Exploring regions of interest with cluster analysis (EROICA) using a spectral peak statistic for selecting and testing the significance of fMRI activation time-series.

Much relevant information about activations and artifacts in a functional magnetic resonance imaging (fMRI) dataset can be obtained from an exploratory cluster analysis. In contrast to testing the significance of the measured experimental effect for a given model, unsupervised pattern recognition techniques, such as fuzzy clustering, often find unexpected behavior in addition to expected activations, allowing the exploitation of this element of surprise. The many artifact clusters often discovered might aid the experimenter in deciding whether the dataset is usable, whether some additional preprocessing step is required, or whether the one used has introduced spurious effects. However, clustering alone does not complete the analysis because the membership values that are generated are not indicative of the level of statistical significance with respect to the cluster activation patterns (centroids). This is of particular importance for fMRI datasets for which most time-series are "noise", with no activation patterns. We propose that an initial partition step should precede the clustering step. Only time-series that meet a certain statistical criterion (using a scaled version of Fisher's g-order statistic) are selected for clustering; this typically represents <5% of the whole brain region. The purpose of clustering is to generate a set of cluster centers that are the possible activation patterns; these are used in forming a linear model of all the time-series. The model parameter is tested for significance in both the time and frequency domains. We present a novel method of conducting these tests, which limits the number of false positives. We call the three-step process of initial partition, clustering and the two-domain significance test as exploring regions of interest with cluster analysis (EROICA).

A novel, direct spatio-temporal approach for analyzing fMRI experiments.

We introduce a novel approach to couple temporal similarity with spatial neighborhood information. This is achieved by concatenating the K nearest, spatially contiguous neighbors of a pixel time-course (TC) of T time-instances. This produces a new TC of (K+1)T time instances. Depending on how "nearest" is defined, we have various options. Strictly spatial nearness means augmenting a given TC by its K nearest neighbors in some canonical spatial order. A more powerful and flexible option is to order the TCs to be concatenated according to their temporal similarity to the central voxel TC. For this study, we have chosen Pearson's cross-correlation coefficient as the measure of similarity. For more than a single neighbor, two concatenation options are possible. The direct ordering option requires that the TCs to be concatenated be spatially contiguous to the central pixel. The more flexible indirect option merely demands that one of a chain of temporally similar TCs be spatially connected to the central pixel. We also apply the temporal similarity criterion to the more conventional spatial (median) filtering, and show that it gives superior result to a strict spatial filtering. The method is tested and verified on a null fMRI dataset onto which we superposed two types of "activations" with known temporal behavior and spatial location. It is also applied to a real dataset containing visual activation. We also propose a strategy, based on the flexibility of the method, to determine a consensus, "core" set of activations.

EvIdent: a functional magnetic resonance image analysis system.

EvIdent (EVent IDENTification) is a user-friendly, algorithm-rich, exploratory data analysis software for quickly detecting, investigating, and visualizing novel events in a set of images as they evolve in time and/or frequency. For instance, in a series of functional magnetic resonance neuroimages, novelty may manifest itself as neural activations in a time course. The core of the system is an enhanced variant of the fuzzy c-means clustering algorithm. Fuzzy clustering obviates the need for models of the underlying requisite biological function, models that are often statistically suspect.

Neural network classification of infrared spectra of control and Alzheimer's diseased tissue.

Artificial neural network classification methods were applied to infrared spectra of histopathologically confirmed Alzheimer's diseased and control brain tissue. Principal component analysis was used as a preprocessing technique for some of these artificial neural networks while others were trained using the original spectra. The leave-one-out method was used for cross-validation and linear discriminant analysis was used as a performance benchmark. In the cases where principal components were used, the artificial neural networks consistently outperformed their linear discriminant counterparts; 100% versus 98% correct classifications, respectively, for the two class problem, and 90% versus 81% for a more complex five class problem. Using the original spectra, only one of the three selected artificial neural network architectures (a variation of the back-propagation algorithm using fuzzy encoding) produced results comparable to the best corresponding principal component cases: 98% and 85% correct classifications for the two and five class problems, respectively.

Carcinogenic implications of the neighborhood coherence principle (NCP).

A new hypothesis on carcinogenesis is set forth on the basis of the neighborhood coherence principle (NCP). NCP constitutes a general rule of pattern formation and maintenance. According to this principle, a system of interacting cells can produce and maintain a spatial organization by virtue of cell-cell communication. This hypothesis suggests that this homeostasis primarily results from a NCP-like process implying cell-cell communication. Each cell is constrained by its neighbors to maintain the mature phenotype despite its inherent individual variability. If the cell-cell mature communication happens to be impaired, tissue homeostasis is disrupted and a proliferative state can be initiated. A further potential effect may result from the establishment of NCP-like communication specific for proliferative cells allied to paracrine and outocrine factors which can lock the cells into the proliferative mode. Most mechanisms implied in this hypothesis have already been investigated. There is a large body of experimental results supporting the role of junctional communication in cooperative metabolism, growth, differentiation and tumour-related events. This new hypothesis provides a framework within which these known facts may be put in a theoretical perspective; it might well constitute the unifying theory--as yet missing--in carcinogenesis.

Fuzzy C-means clustering and principal component analysis of time series from near-infrared imaging of forearm ischemia.

Fuzzy C-means clustering and principal components analysis were used to analyze a temporal series of near-IR images taken of a human forearm during periods of venous outflow restriction and complete forearm ischemia. The principal component eigen-time course analysis provided no useful information and the principal component eigen-image analysis gave results that correlated poorly with anatomical features. The fuzzy C-means clustering analysis, on the other hand, showed distinct regional differences in the hemodynamic response and scattering properties of the tissue, which correlated well with the anatomical features of the forearm.

Feasibility of infrared spectroscopy with pattern recognition techniques to identify a subpopulation of mares at risk of producing foals diagnosed with failure of transfer of passive immunity.

OBJECTIVE: To assess the feasibility of a serum-based test using infrared spectroscopy to identify a subpopulation of mares at risk of producing foals susceptible to failure of passive transfer of immunity (FPT) because of mare-associated factors. MATERIALS AND METHODS: Serum was collected from post-parturient mares (n = 126) and their foals at 24-72 h of age. A radial immunodiffusion IgG test was used to determine each foal's serum IgG concentration. Infrared absorbance spectra of dam sera were collected in the wave number range of 400-4000 cm(-1). Following data preprocessing, pattern recognition techniques were used to identify spectroscopic information capable of distinguishing between mares with FPT foals and those with normal foals. The sensitivity and specificity of infrared spectroscopy to detect risk-positive mares were calculated. RESULTS: Five wave number regions were identified as optimal for distinguishing between the two groups of mares: 740.9-785.2 cm(-1), 796.8-816.0 cm(-1), 970.4-993.5 cm(-1), 1371.6-1406.3 cm(-1) and 1632.0-1659.0 cm(-1). Based upon the infrared spectroscopic information within these discriminatory subregions, the spectra provided the risk status of the mares with a classification success rate of 81.0%. The sensitivity of the classification system was 85.7% and specificity was 80.0%. CONCLUSION: This preliminary study demonstrates that infrared spectra of dam serum have the potential to provide the basis for a new periparturient screening method for a subpopulation of mares at risk of having a foal susceptible to FPT. Further development may provide an economic and rapid technique for the pre-parturient assessment of mares.