The most popular technique to train a neural network is backpropagation. Recently, the Forward-Forward technique has also been introduced for certain learning tasks. However, in real life, human learning does not follow any of these techniques exclusively. The way a human learns is basically a combination of forward learning, backward propagation and cooperation. Humans start learning a new concept by themselves and try to refine their understanding hierarchically during which they might come across several doubts. The most common approach to doubt solving is a discussion with peers, which can be called cooperation. Cooperation/discussion/knowledge sharing among peers is one of the most important steps of learning that humans follow. However, there might still be a few doubts even after the discussion. Then the difference between the understanding of the concept and the original literature is identified and minimized over several revisions. Inspired by this, the paper introduces Forward-Cooperation-Backward (FCB) learning in a deep neural network framework mimicking the human nature of learning a new concept. A novel deep neural network architecture, called Multi Encoding Uni Decoding neural network model, has been designed which learns using the notion of FCB. A special lateral synaptic connection has also been introduced to realize cooperation. The models have been justified in terms of their performance in dimension reduction on four popular datasets. The ability to preserve the granular properties of data in low-rank embedding has been tested to justify the quality of dimension reduction. For downstream analyses, classification has also been performed. An experimental study on convergence analysis has been performed to establish the efficacy of the FCB learning strategy.

Dimension reduction is one of the most sought-after methodologies to deal with high-dimensional ever-expanding complex datasets. Non-negative matrix factorization (NMF) is one such technique for dimension reduction. Here, a multiple deconstruction multiple reconstruction deep learning model (DN3MF) for NMF targeted towards low rank approximation, has been developed. Non-negative input data has been processed using hierarchical learning to generate part-based sparse and meaningful representation. The novel design of DN3MF ensures the non-negativity requirement of the model. The use of Xavier initialization technique solves the exploding or vanishing gradient problem. The objective function of the model has been designed employing regularization, ensuring the best possible approximation of the input matrix. A novel adaptive learning mechanism has been developed to accomplish the objective of the model. The superior performance of the proposed model has been established by comparing the results obtained by the model with that of six other well-established dimension reduction algorithms on three well-known datasets in terms of preservation of the local structure of data in low rank embedding, and in the context of downstream analyses using classification and clustering. The statistical significance of the results has also been established. The outcome clearly demonstrates DN3MF’s superiority over compared dimension reduction approaches in terms of both statistical and intrinsic property preservation standards. The comparative analysis of all seven dimensionality reduction algorithms including DN3MF with respect to the computational complexity and a pictorial depiction of the convergence analysis for both stages of DN3MF have also been presented.

Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this paper are inspired by this idea. They aim to deal with high-dimensional data by discovering its low rank approximation by determining a unique pair of factor matrices. The model, named Input Guided Multiple Deconstruction Single Reconstruction neural network for Non-negative Matrix Factorization (IG-MDSR-NMF), ensures the non-negativity constraints of both factors. Whereas Input Guided Multiple Deconstruction Single Reconstruction neural network for Relaxed Non-negative Matrix Factorization (IG-MDSR-RNMF) introduces a novel idea of factorization with only the basis matrix adhering to the non-negativity criteria. This relaxed version helps the model to learn more enriched low dimensional embedding of the original data matrix. The competency of preserving the local structure of data in its low rank embedding produced by both the models has been appropriately verified. The superiority of low dimensional embedding over that of the original data justifying the need for dimension reduction has been established. The primacy of both the models has also been validated by comparing their performances separately with that of nine other established dimension reduction algorithms on five popular datasets. Moreover, computational complexity of the models and convergence analysis have also been presented testifying to the supremacy of the models.

Dimension reduction is one of the most sought-after strategies to cope with high-dimensional ever-expanding datasets. To address this, a novel deep-learning architecture has been designed with multiple deconstruction and single reconstruction layers for non-negative matrix factorization aimed at low-rank approximation. This design ensures that the reconstructed input matrix has a unique pair of factor matrices. The two-stage approach, namely, pretraining and stacking, aids in the robustness of the architecture. The sigmoid function has been adjusted in such a way that fulfils the non-negativity criteria and also helps to alleviate the data-loss problem. Xavier initialization technique aids in the solution of the exploding or vanishing gradient problem. The objective function involves regularizer that ensures the best possible approximation of the input matrix. The superior performance of MDSR-NMF, over six well-known dimension reduction methods, has been demonstrated extensively using five datasets for classification and clustering. Computational complexity and convergence analysis have also been presented to establish the model.

One of the most commonly used approaches for handling complex datasets with high dimensions is dimension-ality reduction. In this scenario, a single deconstruction single reconstruction neural network model for non-negative matrix factorization technique under neural network framework has been developed aiming towards low rank approximation. With the help of hierarchical learning, the pervasiveness of the non-negative input data has been processed to produce a part-based, sparse, and meaningful representation. A modification of the He initialization technique to initialize weights maintaining the non-negativity criteria of the model, has also been proposed. Necessary modification of the ReLU activation function has been made for inhibiting a layer's entire population of neurons from simultaneously adjusting their weights. Regularization has been used in the design of the model's objective function to minimize the risk of overfitting. To prove the competency of the proposed model, the results have been analyzed and compared with that of six other leading dimension reduction techniques on three popular datasets for classification. The analysis of the same has justified the effectiveness and superiority of the model over some others. Additionally the computational complexity of the model has been discussed.

One of the most commonly used approaches to deal with complex high-dimensional datasets is dimensionality reduction. In this scenario, a shallow neural network model for non-negative matrix factorization has been developed for low rank approximation. We have used hierarchical learning to ma-nipulate the ubiquity of nonnegative input data to generate part-based, sparse, and meaningful representations. A modification of the He initialization technique has been proposed to initialize the weights while maintaining the non-negative criterion of the model. A necessary modification of the ReLU activation function has been made to suppress all neurons in a layer from adjusting their weights simultaneously. Regularization has been used in the model's objective function to reduce the risk of overfitting. To demonstrate the efficacy of the proposed model, we have analyzed and compared the results with six well known dimensionality reduction methods on five popular datasets for clustering. We have also discussed the computational complexity of the model.

Deduplication is mainly used to solve the problem of space and is known as a space-efficient technique. A two step algorithm called ‘brushing’ has been proposed in this paper to solve individual file deduplication. The main aim of the algorithm is to overcome the space related problem, at the same time the algorithm also takes care of time complexity problem. The proposed algorithm has extremely low RAM overhead. The first phase of the algorithm checks the similar entities and removes them thus grouping only unique entities and in the second phase while the unique file is hashed, the unique entities are represented as index values thereby reducing the size of the file to a great extent. Test results shows that if a file contains 40–50 % duplicate data, then this technique reduces the size up to 2/3 of the file. This algorithm has a high deduplication throughput on the file system.

The world today is facing the problem of ever-increasing level of pollution of water bodies. The seriousness of this problem calls for specialized attention to predict future trend. Data mining is the most popular technique for handling huge amount of geo-spatial data. The variety and size of information to be processed for proper trend analysis towards water quality management makes the use of data mining concepts all the more relevant. This paper summarizes the on-going researches involving data mining applications in this area. The applications have been observed to use the techniques of ANN, Fuzzy, or GIS modeling for feature-wise classification of water pollutants. The parameters need to be clustered depending upon their area of application. The respective advantages of each model in classifying the parameters have been identified. The authors have arrived at a set of parameters best suited for analyzing the effect of pollutants on the river Churni, an effluent of the river Bhagirathi.