Unsupervised Criterion Research Articles

Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection

In this paper, sine trigonometry operational laws (ST-OLs) have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Then, extending these ST-OLs to complex neutrosophic sets (CNSs) forms the core of this work. Some of the mathematical properties are proved based on ST-OLs. Fundamental operations and the distance measures between complex neutrosophic numbers (CNNs) based on the ST-OLs are discussed with numerical illustrations. Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data. The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs (ST-WAAO-CNN & ST-WGAO-CNN) are proved. A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM (complex neutrosophic decision making) method. A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method. To check the validity of the proposed method, entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted. The proposed approach proves to be salient and effective for decision making with complex information.

Semi-supervised extensions of multi-task tree ensembles

Scale inconsistency is a widely encountered issue in multi-output learning problems. Specifically, target sets with multiple real valued or a mixture of categorical and real valued variables require addressing the scale differences to obtain predictive models with sufficiently good performance. Data transformation techniques are often employed to solve that problem. However, these operations are susceptible to different shortcomings such as changing the statistical properties of the data and increase the computational burden. Scale differences also pose problem in semi-supervised learning (SSL) models as they require processing of unsupervised information where distance measures are commonly employed. Classical distance metrics can be criticized as they lose efficiency when variables exhibit type or scale differences, too. Besides, in higher dimensions distance metrics cause problems due to loss of discriminative power. This paper introduces alternative semi-supervised tree-based strategies that are robust to scale differences both in terms of feature and target variables. We propose use of a scale-invariant proximity measure by means of tree-based ensembles to preserve the original characteristics of the data. We update classical tree derivation procedure to a multi-criteria form to resolve scale inconsistencies. We define proximity based clustering indicators and extend the supervised model with unsupervised criteria. Our experiments show that proposed method significantly outperforms its benchmark learning model that is predictive clustering trees.

Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering.

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.

Robust unsupervised dimensionality reduction based on feature clustering for single-cell imaging data

Biological data, and in particular imaging data, have experienced an exponential growth in terms of volume and complexity in the last few years, raising new challenges in the field of machine learning. Unsupervised problems are of particular relevance, as the generation of labels for the data is often labor-intensive, expensive or simply not possible. However, interpretability of the data and the results is key to extract new valuable knowledge from the large-scale datasets that are studied. This highlights the necessity of adequate unsupervised dimensionality reduction techniques that can lower the computational workload necessary to process the dataset, while at the same time providing information on its structure. This paper describes a framework that brings together previous proposals on unsupervised feature clustering, with the goal of providing a scalable, interpretable and robust dimensionality reduction on single-cell imaging data. The framework integrates several inter-feature dissimilarity measures, clustering algorithms, quality criteria to select the best feature clustering, and dimensionality reduction methods that are built on the clustering. For each of these components, several approaches proposed in previous works have been tested and evaluated on three use cases coming from two different imaging datasets, highlighting the best-performing components. Affinity clustering is applied for feature clustering for the first time. The results were validated using statistical tests, showing that many of the combinations tested lowered the complexity of the datasets while maintaining or improving the accuracy yielded by classifiers applied on them. The analysis highlighted affinity clustering as the best algorithm for feature clustering, with median differences of up to 8.9% and 0.9% in accuracy with respect to FSFS and hierarchical clustering. Representation entropy obtained a median difference of 13.0% and 0.8% with respect to class separability and silhouette index, respectively, as a robust unsupervised criterion to select the cluster set. Dissimilarities based on Pearson’s correlation performed slightly better than the alternatives, with a median improvement of 2.8% with respect to the cosine distance.

View-based weight network for 3D object recognition

Projective methods generally achieve better results in 3D object recognition in recent years. This may be similar to that human visual 3D shapes rely on various 2D observations which are unconscious on retina. Each projection is treated fairly in existing methods. However, we note that different viewpoint images of the same object have different discriminative features, and only some of images are completely significant. We propose a novel View-based Weight Network (VWN) for 3D object recognition where the different view-based weights are assigned to different projections. The trainable view-level weights are incorporated as a pooling layer of the multi-view residual network. The pooling layer contains 7 sub-layers. Meanwhile, we find a simple unsupervised criterion to evaluate the prediction results before they output. To improve the recognition accuracy, a new multi-channel integrated classifier combining Extreme Learning Machine, KNN, SVM and Random Forest is proposed based on the criterion. The multi-channel classifier can make the accuracy of Top1 close to Top2. Experiments on Princeton ModelNet 3D datasets demonstrate our proposed method outperforms the state-of-the-art approaches significantly in recognition accuracy.

Modificações paisagísticas e implicações térmicas no distrito administrativo de Belém, Pará

As modificações paisagísticas no uso e cobertura da terra podem implicar em alterações na dinâmica de ecossistemas e no clima local. Assim, objetivou-se verificar se o padrão de uso e cobertura da terra contribui para a existência e ou aumento de ilhas de calor no distrito de Mosqueiro, Pará. Foram levantados dados qualitativos por meio de entrevistas não formais com moradores para se conhecer as formas de uso e manejo das propriedades. Os dados quantitativos foram obtidos através de imagens temáticas da ilha correspondentes ao período menos chuvoso da região nos anos de 2010, 2013 e 2015. A classificação do uso e cobertura da terra na ilha de Mosqueiro seguiu o critério não supervisionado. Os dados de temperatura de superfície (TS) foram obtidos por meio dos valores de radiância espectral, da banda termal dos satélites Landsat 5 e 8. Para determinação de ilha de calor, considerou-se a resultante da diferença das temperaturas entre a classe de área urbana e a de floresta. No período de 2010 a 2015, constatou-se redução de área em 9,1% de floresta, pelo crescimento da infraestrutura urbana e pelo desmatamento na região, fato corroborado com a percepção dos moradores locais. Essas modificações resultaram em mudanças na TS, com aumento médio de 5.15°C, mesmo que não se tenha constatado a ocorrência de ilha de calor no espaço urbano. Diante do exposto, verificou-se que as variações da TS estão inteiramente relacionadas às mudanças nas classes de uso e cobertura da terra na ilha e que tende a intensificar sem o planejamento ambiental adequado.

A Survey On Unsupervised Evaluation Criteria For Image Clustering Validation

The evaluation of clustering results is the most difficult and frustrating part of cluster analysis. The challenge is to validate the obtained results without any apriori information. Validity indexes are widely used approach for evaluation of clustering results. These approaches can use three criteria: i) external (also called supervised) criteria: this type is based on comparing the obtained results with a previously known result (frequently called ground truth) and compute the similarity, ii) internal criteria (also called unsupervised) criteria: estimate the quality of the result using internal information of the data alone, and iii) relative criteria: thismeans multiple usages of one of the two above types ofdifferent results and see which is better than the other. Therefore we can say: depending on the information available and the problem type, different types of indexes might be used for cluster validation. Sometimes due to the complexity of the datasets, one validity index is not sufficient to evaluate the quality of the obtained results, and then a combination of two or more index should be used. In this paper, a basic general review on evaluation criteria is first given and then the focus is spotted on unsupervised criteria as they are much more useful, thanks to their objective functionality.

A stochastic gravitational approach to feature based color image segmentation

In this paper, a novel image segmentation algorithm based on the theory of gravity is presented, which is called as “stochastic feature based gravitational image segmentation algorithm (SGISA)”. The proposed SGISA uses color, texture, and spatial information to partition the image into homogenous and semi-compact segments. The proposed method benefits from the advantages of both clustering and region growing image segmentation techniques. The SGISA is equipped with a new operator called “escape” that is inspired by the concept of escape velocity in physics. Moreover, motivated by heuristic search algorithms, we incorporate a stochastic characteristic with the SGISA, which gives algorithm the ability to search the image for finding the fittest regions (pixels) that are suitable for merging. Several experiments on various standard images as well as Berkley standard image database are reported. Results are compared with a well-known clustering based segmentation method, C-means, a gravitational based clustering method (SGC), and the well-known mean-shift method. The results are reported using unsupervised criteria and pre-ground-truthed measures. The obtained results confirm the effectiveness of the proposed method in color image segmentation.

Spike Detection and Clustering With Unsupervised Wavelet Optimization in Extracellular Neural Recordings

Automatic and accurate detection of action potentials of unknown waveforms in noisy extracellular neural recordings is an important requirement for developing brain-computer interfaces. This study introduces a new, wavelet-based manifestation variable that combines the wavelet shrinkage denoising with multiscale edge detection for robustly detecting and finding the occurrence time of action potentials in noisy signals. To further improve the detection performance by eliminating the dependence of the method to the choice of the mother wavelet, we propose an unsupervised optimization for best basis selection. Moreover, another unsupervised criterion based on a correlation similarity measure was defined to update the wavelet selection during the clustering to improve the spike sorting performance. The proposed method was compared to several previously proposed methods by using a wide range of realistic simulated data as well as selected experimental recordings of intracortical signals from freely moving rats. The detection performance of the proposed method substantially surpassed previous methods for all signals tested. Moreover, updating the wavelet selection for the clustering task was shown to improve the classification performance with respect to maintaining the same wavelet as for the detection stage.

Hybrid dimensionality reduction method based on support vector machine and independent component analysis.

This paper presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) and data independence (unsupervised criterion). Classification accuracy is used as a metric to evaluate the performance of the method. By minimizing the structural risk, projection originated from the decision boundaries directly improves the classification performance from a supervised perspective. From an unsupervised perspective, projection can also be obtained based on maximum independence among features (or attributes) in data to indirectly achieve better classification accuracy over more intrinsic representation of the data. Orthogonality interrelates the two sets of projections such that minimum redundancy exists between the projections, leading to more effective dimensionality reduction. Experimental results show that the proposed hybrid dimensionality reduction method that satisfies both criteria simultaneously provides higher classification performance, especially for noisy data sets, in relatively lower dimensional space than various existing methods.

Hybrid active learning for reducing the annotation effort of operators in classification systems

Active learning is understood as any form of learning in which the learning algorithm has some control over the input samples due to a specific sample selection process based on which it builds up the model. In this paper, we propose a novel active learning strategy for data-driven classifiers, which is based on unsupervised criterion during off-line training phase, followed by a supervised certainty-based criterion during incremental on-line training. In this sense, we call the new strategy hybrid active learning. Sample selection in the first phase is conducted from scratch (i.e. no initial labels/learners are needed) based on purely unsupervised criteria obtained from clusters: samples lying near cluster centers and near the borders of clusters are expected to represent the most informative ones regarding the distribution characteristics of the classes. In the second phase, the task is to update already trained classifiers during on-line mode with the most important samples in order to dynamically guide the classifier to more predictive power. Both strategies are essential for reducing the annotation and supervision effort of operators in off-line and on-line classification systems, as operators only have to label an exquisite subset of the off-line training data resp. give feedback only on specific occasions during on-line phase. The new active learning strategy is evaluated based on real-world data sets from UCI repository and collected at on-line quality control systems. The results show that an active learning based selection of training samples (1) does not weaken the classification accuracies compared to when using all samples in the training process and (2) can out-perform classifiers which are built on randomly selected data samples.

Novel Unsupervised Feature Filtering of Biological Data

Many methods have been developed for selecting small informative feature subsets in large noisy data. However, unsupervised methods are scarce. Examples are using the variance of data collected for each feature, or the projection of the feature on the first principal component. We propose a novel unsupervised criterion, based on SVD-entropy, selecting a feature according to its contribution to the entropy (CE) calculated on a leave-one-out basis. This can be implemented in four ways: simple ranking according to CE values (SR); forward selection by accumulating features according to which set produces highest entropy (FS1); forward selection by accumulating features through the choice of the best CE out of the remaining ones (FS2); backward elimination (BE) of features with the lowest CE. We apply our methods to different benchmarks. In each case we evaluate the success of clustering the data in the selected feature spaces, by measuring Jaccard scores with respect to known classifications. We demonstrate that feature filtering according to CE outperforms the variance method and gene-shaving. There are cases where the analysis, based on a small set of selected features, outperforms the best score reported when all information was used. Our method calls for an optimal size of the relevant feature set. This turns out to be just a few percents of the number of genes in the two Leukemia datasets that we have analyzed. Moreover, the most favored selected genes turn out to have significant GO enrichment in relevant cellular processes.

Rainfall frequency and seasonality identification through artificial neural networks

The artificial neural network technique is experimented to cope with the study of the sub-annual seasonal non-stationarity of the rainfall process. The homogeneity of the climatic signals inside each of the natural 12 monthly classes is analyzed, adopting a multilayer feed-forward network with error back-propagation. The possibility of identifying ‘monthly based seasons’ from only daily rainfall data is found to be quite limited. The coupling of rainfall and temperature statistics is instead confirmed to be a fundamental climatic indicator. Contrary to what is commonly expected, the season uncertainty appears higher in summer and in winter than in spring or autumn. The hypothesis of defining any monthly based pluviometric regime is however demonstrated to be generally difficult to sustain, revealing the necessity of adopting an unsupervised criterion to identify any seasonal filter of the rainfall process.

Unsupervised learning for Boltzman Machines

An unsupervised learning algorithm for a stochastic recurrent neural network based on the Boltzmann Machine architecture is formulated in this paper. The maximization of the mutual information between the stochastic output neurons and the clamped inputs is used as an unsupervised criterion for training the network. The resulting learning rule contains two terms corresponding to Hebbian and anti-Hebbian learning. It is interesting that these two terms are weighted by the amount of information transmitted in the learning synapse, giving an information-theoretic interpretation of the proportionality constant of Hebb's biological rule. The anti-Hebbian term, which can be interpreted as a forgetting function, supports the optimal coding. In this way, optimal nonlinear and recurrent implementations of data compression of Boolean patterns are obtained. As an example, the encoder problem is simulated and trained in an unsupervised way in a one layer network. Compression of non-uniform distributed binary data is included. Unsupervised classification, even for continuous inputs, is shown for the cases of four overlapping Gaussian spots and for a real-world example of thyroid diagnosis. In comparison with other techniques, the present model requires an exponentially smaller number of weights for the classification problem.

Unsupervised learning for Boltzman Machines

An unsupervised learning algorithm for a stochastic recurrent neural network based on the Boltzmann Machine architecture is formulated in this paper. The maximization of the mutual information between the stochastic output neurons and the clamped inputs is used as an unsupervised criterion for training the network. The resulting learning rule contains two terms corresponding to Hebbian and anti-Hebbian learning. It is interesting that these two terms are weighted by the amount of information transmitted in the learning synapse, giving an information-theoretic interpretation of the proportionality constant of Hebb's biological rule. The anti-Hebbian term, which can be interpreted as a forgetting function, supports the optimal coding. In this way, optimal nonlinear and recurrent implementations of data compression of Boolean patterns are obtained. As an example, the encoder problem is simulated and trained in an unsupervised way in a one layer network. Compression of non-uniform distributed binary data is i...