A methodology to assess the intrinsic discriminative ability of a distance function and its interplay with clustering algorithms for microarray data analysis

Background: Clustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from statistics to computer science. Following Handl et al., it can be summarized as a three step process: (1) choice of a distance function; (2) choice of a clustering algorithm; (3) choice of a validation method. Although such a purist approach to clustering is hardly seen in many areas of science, genomic data require that level of attention, if inferences made from cluster analysis have to be of some relevance to biomedical research. Results: A procedure is proposed for the assessment of the discriminative ability of a distance function. That is, the evaluation of the ability of a distance function to capture structure in a dataset. It is based on the introduction of a new external validation index, referred to as Balanced Misclassification Index (BMI, for short) and of a nontrivial modification of the well known Receiver Operating Curve (ROC, for short), which we refer to as Corrected ROC (CROC, for short). The main results are: (a) a quantitative and qualitative method to describe the intrinsic separation ability of a distance; (b) a quantitative method to assess the performance of a clustering algorithm in conjunction with the intrinsic separation ability of a distance function. The proposed procedure is more informative than the ones available in the literature due to the adopted tools. Indeed, the first one allows to map distances and clustering solutions as graphical objects on a plane, and gives information about the bias of the clustering algorithm with respect to a distance. The second tool is a new external validity index which shows similar performances with respect to the state of the art, but with more flexibility, allowing for a broader spectrum of applications. In fact, it allows not only to quantify the merit of each clustering solution but also to quantify the agglomerative or divisive errors due to the algorithm. Conclusions: The new methodology has been used to experimentally study three popular distance functions, namely, Euclidean distance d2, Pearson correlation dr and mutual information dMI. Based on the results of the experiments, we have that the Euclidean and Pearson correlation distances have a good intrinsic discrimination ability. Conversely, the mutual information distance does not seem to offer the same flexibility and versatility as the other two distances. Apparently, that is due to well known problems in its estimation. since it requires that a dataset must have a substantial number of features to be reliable. Nevertheless, taking into account such a fact, together with results presented in Priness et al., one receives an indication that dMI may be superior to the other distances considered in this study only in conjunction with clustering algorithms specifically designed for its use. In addition, it results that K-means, Average Link, and Complete link clustering algorithms are in most cases able to improve the discriminative ability of the distances considered in this study with respect to clustering. The methodology has a range of applicability that goes well beyond microarray data since it is independent of the nature of the input data. The only requirement is that the input data must have the same format of a "feature matrix". In particular it can be used to cluster ChIP-seq data

Visualization and Analysis of Transformer Attention

The capability to select the relevant portion of the input is a key feature to limit the sensory input and focus on the most informative collected part. The transformer architecture is among the most performing deep neural network architectures due to the attention mechanism. The attention allows us to spot relevant connections between portions of the images and highlight these connections. Since the model is complex, it is not easy to determine which are these connections and the important areas. We discuss a technique to show these areas and highlight the regions most relevant for label attribution

Fuzzy Clustering of Histopathological Images Using Deep Learning Embeddings

Metric learning is a machine learning approach that aims to learn a new distance metric by increasing (reducing) the similarity of examples belonging to the same (different) classes. The output of these approaches are embeddings, where the input data are mapped to improve a crisp or fuzzy classification process. The deep metric learning approaches regard metric learning, implemented by using deep neural networks. Such models have the advantage to discover very representative nonlinear embeddings. In this work, we propose a triplet network deep metric learning approach, based on ResNet50, to find a representative embedding for the unsupervised fuzzy classification of benign and malignant histopathological images of breast cancer tissues. Experiments computed on the BreakHis benchmark dataset, using Fuzzy C-Means Clustering, show the benefit of using very low dimensional embeddings found by the deep metric learning approach

Metric Learning in Histopathological Image Classification: Opening the Black Box

The application of machine learning techniques to histopathology images enables advances in the field, providing valuable tools that can speed up and facilitate the diagnosis process. The classification of these images is a relevant aid for physicians who have to process a large number of images in long and repetitive tasks. This work proposes the adoption of metric learning that, beyond the task of classifying images, can provide additional information able to support the decision of the classification system. In particular, triplet networks have been employed to create a representation in the embedding space that gathers together images of the same class while tending to separate images with different labels. The obtained representation shows an evident separation of the classes with the possibility of evaluating the similarity and the dissimilarity among input images according to distance criteria. The model has been tested on the BreakHis dataset, a reference and largely used dataset that collects breast cancer images with eight pathology labels and four magnification levels. Our proposed classification model achieves relevant performance on the patient level, with the advantage of providing interpretable information for the obtained results, which represent a specific feature missed by the all the recent methodologies proposed for the same purpose

Inter-method reliability of brainstem volume segmentation algorithms in preschoolers with ASD

Introduction: The brainstem has a potential role in the pathophysiology of Autism Spectrum Disorders (ASD) (Roger, 2013). In particular, alterations in brainstem volume and their relationship with sensory/motor abnormalities have been suggested (Trevarthen & Delafield-Butt, 2013). However, the findings in volume alterations of subjects with ASD with respect to matched controls are controversial both in adults and children cohorts (Hardan, 2001; Piven, 1992; Kleiman, 1992). Moreover, the contribution to variability of brainstem volume measurements performed with different automated methods is still unclear. Methods: T1-weighted MRI brain scans of a cohort of 80 preschoolers (20 male controls, 20 male subjects with ASD, 20 female controls, 20 female subjects with ASD, mean age controls 49 months, std 12 months, mean age ASD 49 months, std 14) were processed with three different automated methods to measure the brainstem volume: Freesurfer 5.3 (Fischl, 2002), FSL-FIRST (Patenaude, 2011) and ANTs (Avants, 2011). Analysis of variance was then carried out taking into account gender and total brain volume in order to investigate potential brainstem volume differences between controls/ASD subjects for each method. A direct comparison of brainstem volume assessments in native space was then performed to assess inter-method reliability (correlation has been calculated by Pearson coefficient) and Dice similarity indexes were calculated to evaluate the segmentation agreement across methods. Results:The brainstem volume measurements are reported in scatter plots in Fig. 1 to show the agreement in terms of volume (in mm3) between different methods. The color represents the Dice similarity index (range 0-1 were 1 means total agreement) of the brainstem segmentations obtained by the methods under investigation. In Fig. 2 four examples of brainstem segmentations with the different methods are shown in sagittal view (brainstem segmentations are reported in red, green, blue for Freesurfer, FSL-FIRST and ANTs respectively). Pearson correlation coefficient between FSL-FIRST and Freesurfer brainstem volume assessments was 0.27 (p-value=0.02). It was 0.51 (p-value0.05).Conclusions:The inter-method reliability of automated algorithms for brainstem volume assessment is limited (the mean Dice similarity index barely reaches 0.8 in just one out of 3 comparisons). Inconsistencies across previous studies on brainstem and more in general the lack of evidence for brain biomarkers in ASD may in part be a result of this poor agreements in the extraction of structural features with different methods. Inter-method brainstem volume differences can be attributed to varying definitions of brainstem structure, the use of different templates (e.g. in our study only ANTs processed the brain scans by using an age-specific brain template) and the varying effects of imaging artifacts and acquisition settings. This study suggests that research on brain structure alterations should cross-validate findings across multiple methods before providing biological interpretations

Effect of turmeric powder (Curcuma longa L.) and ascorbic acid on physical characteristics and oxidative status of fresh and stored rabbit burgers

The objective of this study was to evaluate the effect of Curcuma longa powder and ascorbic acid on some quality traits of rabbit burgers. The burgers (burgers control with no additives; burgerswith 3.5 g of turmeric powder/100 g meat; burgers with 0.1 g of ascorbic acid/100 g meat) were analyzed at Days 0 and 7 for pH, color, drip loss, cooking loss, fatty acid profile, TBARS, antioxidant capacity (ABTS, DPPH and FRAP) and microbial growth. The addition of turmeric powder modified the meat color, produced an antioxidant capacity similar to ascorbic acid and determined a lower cooking loss than other formulations. Turmeric powder might be considered as a useful natural antioxidant, increasing the quality and extending the shelf life of rabbit burgers

An Astigmatic Detection System for Polymeric Cantilever-based Sensors

We demonstrate the use of an astigmatic detection system (ADS) for resonance frequency identification of polymer microcantilever sensors. The ADS technology is based on a DVD optical head combined with an optical microscope (OM). The optical head has a signal bandwidth of 80 MHz, allowing thermal fluctuation measurements on cantilever beams with a subnanometer resolution. Furthermore, an external excitation can intensify the resonance amplitude, enhancing the signal- to-noise ratio. The full width at half maximum (FWHM) of the laser spot is 568 nm, which facilitates read-out on potentially submicrometer-sized cantilevers. The resonant frequency of SU-8 microcantilevers is measured by both thermal fluctuation and excited vibration measurement modes of the ADS