In this study, a hybrid model combining discrete wavelet transforms (WTs) and artificial neural networks (ANNs) is used to estimate the monthly streamflow. The WT-ANN hybrid model was developed using the Daubechies main wavelet to predict the streamflow for three gauging stations on the Çoruh river basin one month in advance, with different combinations of air temperature, precipitation, and streamflow variables, and their wavelet transformations. Four different hybrid WT-ANN models were generated and compared with four different conventional ANN models. The dataset was chronologically divided into training, validation, and testing data. The results indicated that the WT-ANN hybrid models performed better than the traditional ANN models for all three stations. Furthermore, the chronologically divided dataset was used to examine the effects of changes in hydrological data over time on model performance. In conclusion, model performances in the training period deteriorated during the validation and testing periods due to structural changes in the hydrological data.

Feature selection is a critical step in regression problems where a large number of continuous explanatory variables explain the same target through different dependency structures. Classical filters may remain sensitive to a single form of dependence, a single scale, or a specific discretization scheme; generalized entropy measures, on the other hand, typically require the parameters to be fixed at a single point. This study proposes a framework that evaluates the Sharma–Mittal entropy volumetrically across a two-dimensional parameter region rather than for a single parameter pair. For the continuous target and explanatory variables, the marginal, joint, and conditional densities are obtained using a Gaussian kernel density estimation; the conditional entropy and information gain surfaces are integrated across the region Ω = [0.05, 0.95]² in the α-β plane to define three indices: PICSME, which measures the conditional uncertainty volume; PIGSME, which measures the gain volume; and NIGSME, which is the ratio of this gain to the total entropy volume of the target. The method is supported by bandwidth consistency and the renormalization of conditional densities; thus, the issue of negative gain that can occur in the continuous variables is resolved, yielding positive and interpretable scores across all six datasets. It is formally demonstrated that the fact that the three indices produce the same ranking is not an empirical observation but rather the result of a monotonicity relationship valid under a fixed target entropy volume. The method is compared with Pearson and Spearman correlations, the Shannon information gain, mutual information, and random forest variable importance across six regression datasets (Airfoil Self-Noise, AirQualityUCI, BodyFat, Meteorology, Concrete, and WineQualityWhite) that differ in their sample size, dimensions, and application domain. The evaluation is not limited to ranking consistency; the out-of-sample prediction performance is measured using least-squares models on the top-k subsets, with rankings calculated from the training partition. The findings show that NIGSME exhibits a performance comparable to that of built-in filters, outperforms them on the Concrete and Meteorology datasets, and never ranks as the weakest method on any dataset. The results demonstrate that volumetric entropy metrics defined across the entire parameter space provide a feature-ranking tool that is independent of parameter selection for continuous variables.

Tr en This study aims to compare the municipal water distribution performance and classify the municipal water distribution systems in the provinces of Turkey using the Gray Relational Hierarchical clustering method for both 2006 and 2016. A correlation analysis was used to determine the variables affecting the distributed water. The Hierarchical gray clusters and the changes during the decade are presented with spatial distribution maps using statistically significant variables. Consequently, the findings reveal that the municipalities of Istanbul, Izmir, Bursa, Gaziantep, and Kocaeli managed water distribution effectively, whereas the municipalities of Konya, Şanlıurfa, Diyarbakır, Samsun, Trabzon, and Sakarya managed it poorly. This study aims to compare the municipal water distribution performance and classify the municipal water distribution systems in the provinces of Turkey using the Gray Relational Hierarchical clustering method for both 2006 and 2016. A correlation analysis was used to determine the variables affecting the distributed water. The Hierarchical gray clusters and the changes during the decade are presented with spatial distribution maps using statistically significant variables. Consequently, the findings reveal that the municipalities of Istanbul, Izmir, Bursa, Gaziantep, and Kocaeli managed water distribution effectively, whereas the municipalities of Konya, Şanlıurfa, Diyarbakır, Samsun, Trabzon, and Sakarya managed it poorly.

Faktör analizi, belirli bir olguyla ilgili ve birbirleriyle ilişkili çok sayıda değişkenin birbirleriyle olan ilişkisini inceleyerek, değişkenlerin sayısını azaltmak ve ilişkisiz yeni değişkenler yaratmak için kullanılan çok değişkenli istatistiksel bir analizdir. Bu çalışmada farklı bir yaklaşım olarak, faktör çıkarmada birleşik entropiden yararlanılmıştır. Buradan elde edilen “Faktörleşme” ile “Açıklayıcı Faktör Analizi” sonuçları karşılaştırılarak benzerlik ve farklılıkları tartışılmıştır. İstatistik ile entropiyi birleştiren bir model kullanılmıştır. Uygulama kısmında ilk olarak istatistikte yaygın olarak kullanılan faktör analizi sonuçları elde edilmiştir. Ardından, kovaryans matrisi yerine birleşik entropi matrisi kullanılan entropi tabanlı yaklaşımla elde edilen matrisle bir karşılaştırma yapılmıştır. Bu bağlamda birleşik entropi matrisi ile elde ettiğimiz sonuçlar ile faktör analizi ile elde ettiğimiz sonuçlar karşılaştırılmıştır. Son durumda ise birleşik entropi matrisi ile elde edilen sonuçlar gösterilmiştir. Ek olarak, bu çalışma ile entropiye teorik destek ile aslında varyans-kovaryans ölçülerinin kullanım alanlarına uygulanabileceği ve desteklenebileceğini göstermek hedeflenmiş ve çözülmesi gereken bazı sorunlara rağmen, alternatif olarak bilinen yöntemlerin yerine önerilmektedir.