Novel Mathematical Model of Breast Cancer Diagnostics Using an Associative Pattern Classification.

Breast cancer is a disease that has emerged as the second leading cause of cancer deaths in women worldwide. The annual mortality rate is estimated to continue growing. Cancer detection at an early stage could significantly reduce breast cancer death rates long-term. Many investigators have studied different breast diagnostic approaches, such as mammography, magnetic resonance imaging, ultrasound, computerized tomography, positron emission tomography and biopsy. However, these techniques have limitations, such as being expensive, time consuming and not suitable for women of all ages. Proposing techniques that support the effective medical diagnosis of this disease has undoubtedly become a priority for the government, for health institutions and for civil society in general. In this paper, an associative pattern classifier (APC) was used for the diagnosis of breast cancer. The rate of efficiency obtained on the Wisconsin breast cancer database was 97.31%. The APC's performance was compared with the performance of a support vector machine (SVM) model, back-propagation neural networks, C4.5, naive Bayes, k-nearest neighbor (k-NN) and minimum distance classifiers. According to our results, the APC performed best. The algorithm of the APC was written and executed in a JAVA platform, as well as the experimental and comparativeness between algorithms.

On the accuracy and computational cost of spiking neuron implementation.

Since more than a decade ago, three statements about spiking neuron (SN) implementations have been widely accepted: 1) Hodgkin and Huxley (HH) model is computationally prohibitive, 2) Izhikevich (IZH) artificial neuron is as efficient as Leaky Integrate-and-Fire (LIF) model, and 3) IZH model is more efficient than HH model (Izhikevich, 2004). As suggested by Hodgkin and Huxley (1952), their model operates in two modes: by using the α's and ß's rate functions directly (HH model) and by storing them into tables (HHT model) for computational cost reduction. Recently, it has been stated that: 1) HHT model (HH using tables) is not prohibitive, 2) IZH model is not efficient, and 3) both HHT and IZH models are comparable in computational cost (Skocik & Long, 2014). That controversy shows that there is no consensus concerning SN simulation capacities. Hence, in this work, we introduce a refined approach, based on the multiobjective optimization theory, describing the SN simulation capacities and ultimately choosing optimal simulation parameters. We have used normalized metrics to define the capacity levels of accuracy, computational cost, and efficiency. Normalized metrics allowed comparisons between SNs at the same level or scale. We conducted tests for balanced, lower, and upper boundary conditions under a regular spiking mode with constant and random current stimuli. We found optimal simulation parameters leading to a balance between computational cost and accuracy. Importantly, and, in general, we found that 1) HH model (without using tables) is the most accurate, computationally inexpensive, and efficient, 2) IZH model is the most expensive and inefficient, 3) both LIF and HHT models are the most inaccurate, 4) HHT model is more expensive and inaccurate than HH model due to α's and ß's table discretization, and 5) HHT model is not comparable in computational cost to IZH model. These results refute the theory formulated over a decade ago (Izhikevich, 2004) and go more in-depth in the statements formulated by Skocik and Long (2014). Our statements imply that the number of dimensions or FLOPS in the SNs are theoretical but not practical indicators of the true computational cost. The metric we propose for the computational cost is more precise than FLOPS and was found to be invariant to computer architecture. Moreover, we found that the firing frequency used in previous works is a necessary but an insufficient metric to evaluate the simulation accuracy. We also show that our results are consistent with the theory of numerical methods and the theory of SN discontinuity. Discontinuous SNs, such LIF and IZH models, introduce a considerable error every time a spike is generated. In addition, compared to the constant input current, the random input current increases the computational cost and inaccuracy. Besides, we found that the search for optimal simulation parameters is problem-specific. That is important because most of the previous works have intended to find a general and unique optimal simulation. Here, we show that this solution could not exist because it is a multiobjective optimization problem that depends on several factors. This work sets up a renewed thesis concerning the SN simulation that is useful to several related research areas, including the emergent Deep Spiking Neural Networks.

Quantitative evaluation of binary digital region asymmetry with application to skin lesion detection.

BACKGROUND: The performance of Computer Aided Diagnosis Systems for early melanoma detection relies mainly on quantitative evaluation of the geometric features corresponding to skin lesions. In these systems, diagnosis is carried out by analyzing four geometric characteristics: asymmetry (A), border (B), color (C) and dimension (D). The main objective of this study is to establish an algorithm for the measurement of asymmetry in biological entities. METHODS: Binary digital images corresponding to lesions are divided into 8 segments from their centroid. For each segment, the discrete compactness value is calculated using Normalized E-Factor (NEF). The asymmetry value is obtained from the sum of the square difference of each NEF value and corresponding value of its opposite by the vertex. Two public skin cancer databases were used. 1) Lee's database with 40 digital regions evaluated by fourteen dermatologists. 2) The PH2 database which consists of 200 images in an 8-bit RGB format. This database provides a pre-classification of asymmetry carried out by experts, and it also indicates if the lesion is a melanoma. RESULTS: The measure was applied using two skin lesion image databases. 1) In Lee's database, Spearman test provided a value of 0.82 between diagnosis of dermatologists and asymmetry values. For the 12 binary images most likely to be melanoma, the correlation between the measurement and dermatologists was 0.98. 2) In the PH2 database a label is provided for each binary image where the type of asymmetry is indicated. Class 0-1 corresponds to symmetry and one axis of symmetry shapes, the completely asymmetrical were assigned to Class 2, the values of sensitivity and specificity were 59.62 and 85.8% respectively between the asymmetry measured by a group of dermatologists and the proposed algorithm. CONCLUSIONS: Simple image digital features such as compactness can be used to quantify the asymmetry of a skin lesion using its digital binary image representation. This measure is stable taking into account translations, rotations, scale changes and can be applied to non-convex regions, including areas with holes.