Rajat K. De

Chayan Maitra, Dibyendu B. Seal, Rajat K. De

The task of dimensionality reduction and visualization of high-dimensional datasets remains a challenging problem since long. Modern high-throughput technologies produce newer high-dimensional datasets having multiple views with relatively new data types. Visualization of these datasets require proper methodology that can uncover hidden patterns in the data without affecting the local and global structures within the data. To this end, however, very few such methodology exist, which can realise this task. In this work, we have introduced a novel unsupervised deep neural network model, called NeuroDAVIS, for data visualization. NeuroDAVIS is capable of extracting important features from the data, without assuming any data distribution, and visualize effectively in lower dimension. It has been shown theoritically that neighbourhood relationship of the data in high dimension remains preserved in lower dimension. The performance of NeuroDAVIS has been evaluated on a wide variety of synthetic and real high-dimensional datasets including numeric, textual, image and biological data. NeuroDAVIS has been highly competitive against both t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) with respect to visualization quality, and preservation of data size, shape, and both local and global structure. It has outperformed Fast interpolation-based t-SNE (Fit-SNE), a variant of t-SNE, for most of the high-dimensional datasets as well. For the biological datasets, besides t-SNE, UMAP and Fit-SNE, NeuroDAVIS has also performed well compared to other state-of-the-art algorithms, like Potential of Heat-diffusion for Affinity-based Trajectory Embedding (PHATE) and the siamese neural network-based method, called IVIS. Downstream classification and clustering analyses have also revealed favourable results for NeuroDAVIS-generated embeddings.

Sourav Ghosh, Chayan Maitra, Rajat K. De

Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based on requirement. Projecting the data in a higher-dimensional space helps in unfolding intricate patterns, enhancing the performance of the underlying models. On the other hand, dimensionality reduction is helpful in denoising data while capturing maximal information, as well as reducing execution time and memory.In this context, it is not always statistically evident whether the transformed embedding retains the local and global structure of the original data. Most of the existing metrics that are used for comparing the local and global shape of the embedding against the original one are highly expensive in terms of time and space complexity. In order to address this issue, the objective of this study is to formulate a novel metric, called Clustering guided METric (CMET), for quantifying embedding quality. It is effective to serve the purpose of quantitative comparison between an embedding and the original data. CMET consists of two scores, viz., CMET_L and CMET_G, that measure the degree of local and global shape preservation capability, respectively. The efficacy of CMET has been demonstrated on a wide variety of datasets, including four synthetic, two biological, and two image datasets. Results reflect the favorable performance of CMET against the state-of-the-art methods. Capability to handle both small and large data, low algorithmic complexity, better and stable performance across all kinds of data, and different choices of hyper-parameters feature CMET as a reliable metric.

Prasun Dutta, Koustab Ghosh, Rajat K. De

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.

Chayan Maitra, Rajat K. De

Visualizing high-dimensional datasets through a generalized embedding has been a challenge for a long time. Several methods have shown up for the same, but still, they have not been able to generate a generalized embedding, which not only can reveal the hidden patterns present in the data but also generate realistic high-dimensional samples from it. Motivated by this aspect, in this study, a novel generative model, called G-NeuroDAVIS, has been developed, which is capable of visualizing high-dimensional data through a generalized embedding, and thereby generating new samples. The model leverages advanced generative techniques to produce high-quality embedding that captures the underlying structure of the data more effectively than existing methods. G-NeuroDAVIS can be trained in both supervised and unsupervised settings. We rigorously evaluated our model through a series of experiments, demonstrating superior performance in classification tasks, which highlights the robustness of the learned representations. Furthermore, the conditional sample generation capability of the model has been described through qualitative assessments, revealing a marked improvement in generating realistic and diverse samples. G-NeuroDAVIS has outperformed the Variational Autoencoder (VAE) significantly in multiple key aspects, including embedding quality, classification performance, and sample generation capability. These results underscore the potential of our generative model to serve as a powerful tool in various applications requiring high-quality data generation and representation learning.

Prasun Dutta, Rajat K. De

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.