Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.

Categorical Missing Data Imputation Using Fuzzy Neural Networks with Numerical and Categorical Inputs

There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson’s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Identification of a biomarker panel for colorectal cancer diagnosis

Background Malignancies arising in the large bowel cause the second largest number of deaths from cancer in the Western World. Despite progresses made during the last decades, colorectal cancer remains one of the most frequent and deadly neoplasias in the western countries. Methods A genomic study of human colorectal cancer has been carried out on a total of 31 tumoral samples, corresponding to different stages of the disease, and 33 non-tumoral samples. The study was carried out by hybridisation of the tumour samples against a reference pool of non-tumoral samples using Agilent Human 1A 60-mer oligo microarrays. The results obtained were validated by qRT-PCR. In the subsequent bioinformatics analysis, gene networks by means of Bayesian classifiers, variable selection and bootstrap resampling were built. The consensus among all the induced models produced a hierarchy of dependences and, thus, of variables. Results After an exhaustive process of pre-processing to ensure data quality--lost values imputation, probes quality, data smoothing and intraclass variability filtering--the final dataset comprised a total of 8, 104 probes. Next, a supervised classification approach and data analysis was carried out to obtain the most relevant genes. Two of them are directly involved in cancer progression and in particular in colorectal cancer. Finally, a supervised classifier was induced to classify new unseen samples. Conclusions We have developed a tentative model for the diagnosis of colorectal cancer based on a biomarker panel. Our results indicate that the gene profile described herein can discriminate between non-cancerous and cancerous samples with 94.45% accuracy using different supervised classifiers (AUC values in the range of 0.997 and 0.955)

Identification of a biomarker panel for colorectal cancer diagnosis

Background:Malignancies arising in the large bowel cause the second largest number of deaths from cancer in the Western World. Despite progresses made during the last decades, colorectal cancer remains one of the most frequent and deadly neoplasias in the western countries. Methods: A genomic study of human colorectal cancer has been carried out on a total of 31 tumoral samples, corresponding to different stages of the disease, and 33 non-tumoral samples. The study was carried out by hybridisation of the tumour samples against a reference pool of non-tumoral samples using Agilent Human 1A 60-mer oligo microarrays. The results obtained were validated by qRT-PCR. In the subsequent bioinformatics analysis, gene networks by means of Bayesian classifiers, variable selection and bootstrap resampling were built. The consensus among all the induced models produced a hierarchy of dependences and, thus, of variables. Results: After an exhaustive process of pre-processing to ensure data quality--lost values imputation, probes quality, data smoothing and intraclass variability filtering--the final dataset comprised a total of 8, 104 probes. Next, a supervised classification approach and data analysis was carried out to obtain the most relevant genes. Two of them are directly involved in cancer progression and in particular in colorectal cancer. Finally, a supervised classifier was induced to classify new unseen samples. Conclusions: We have developed a tentative model for the diagnosis of colorectal cancer based on a biomarker panel. Our results indicate that the gene profile described herein can discriminate between non-cancerous and cancerous samples with 94.45% accuracy using different supervised classifiers (AUC values in the range of 0.997 and 0.955).

Comparison of Airborne Laser Scanning Methods for Estimating Forest Structure Indicators Based on Lorenz Curves

The purpose of this study was to compare a number of state-of-the-art methods in airborne laser scan- ning (ALS) remote sensing with regards to their capacity to describe tree size inequality and other indi- cators related to forest structure. The indicators chosen were based on the analysis of the Lorenz curve: Gini coefficient ( GC ), Lorenz asymmetry ( LA ), the proportions of basal area ( BALM ) and stem density ( NSLM ) stocked above the mean quadratic diameter. Each method belonged to one of these estimation strategies: (A) estimating indicators directly; (B) estimating the whole Lorenz curve; or (C) estimating a complete tree list. Across these strategies, the most popular statistical methods for area-based approach (ABA) were used: regression, random forest (RF), and nearest neighbour imputation. The latter included distance metrics based on either RF (NN–RF) or most similar neighbour (MSN). In the case of tree list esti- mation, methods based on individual tree detection (ITD) and semi-ITD, both combined with MSN impu- tation, were also studied. The most accurate method was direct estimation by best subset regression, which obtained the lowest cross-validated coefficients of variation of their root mean squared error CV(RMSE) for most indicators: GC (16.80%), LA (8.76%), BALM (8.80%) and NSLM (14.60%). Similar figures [CV(RMSE) 16.09%, 10.49%, 10.93% and 14.07%, respectively] were obtained by MSN imputation of tree lists by ABA, a method that also showed a number of additional advantages, such as better distributing the residual variance along the predictive range. In light of our results, ITD approaches may be clearly inferior to ABA with regards to describing the structural properties related to tree size inequality in for- ested areas.