Abstract--Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor perf or-mance of the traditional iterative gradient-based learnin g algorithms. Although the famous extreme learning machine (ELM) has successfully addressed the problems of slow convergenc e, it still has computational robustness problems brought by inp ut weights and biases randomly assigned. Thus, in order to over - come the aforementioned problems, in this paper, a novel typ e neural network based on Gegenbauer orthogonal polynomials, termed as GNN, is constructed and investigated. This model c ould overcome the computational robustness problems of ELM, whi le still has comparable structural simplicity and approximat ion capability. Based on this, we propose a regularized weights direct determination (R-WDD) based on equality-constrain ed optimization to determine the optimal output weights. The R - WDD tends to minimize the empirical risks and structural ris ks of the network, thus to lower the risk of over fitting and impro ve the generalization ability. This leads us to a the final GNN wi th R-WDD, which is a unified learning mechanism for binary and multi-class classification problems. Finally, as is verifie d in the various comparison experiments, GNN with R-WDD tends to have comparable (or even better) generalization performan ces, computational scalability and efficiency, and classificati on robustness, compared to least square support vector machine ( LS-SVM), ELM with Gaussian kernel. ESEARCHES on artificial feed-forward neural networks (FNNs) have become increasingly active and popular, for it is one of the most powerful tools in artificial intelligenc e field.

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic topology used to extract topological information from data - in unsupervised learning is an uncommon and a novel approach. A notable aspect of this methodology consists in analyzing data at multiple resolutions which allows to distinguish true features from noise based on the extent of their persistence. We evaluate the performance of our algorithm on synthetic data and compare it to other well-known clustering algorithms such as K-means, hierarchical clustering and DBSCAN. We illustrate its application in the context of a case study of water quality in the Chesapeake Bay.

Predicting the relationship between a molecule's structure and its odor remains a difficult, decades-old task. This problem, termed quantitative structure-odor relationship (QSOR) modeling, is an important challenge in chemistry, impacting human nutrition, manufacture of synthetic fragrance, the environment, and sensory neuroscience. We propose the use of graph neural networks for QSOR, and show they significantly out-perform prior methods on a novel data set labeled by olfactory experts. Additional analysis shows that the learned embeddings from graph neural networks capture a meaningful odor space representation of the underlying relationship between structure and odor, as demonstrated by strong performance on two challenging transfer learning tasks. Machine learning has already had a large impact on the senses of sight and sound. Based on these early results with graph neural networks for molecular properties, we hope machine learning can eventually do for olfaction what it has already done for vision and hearing.

What enables Stochastic Gradient Descent (SGD) to achieve better generalization than Gradient Descent (GD) in Neural Network training? This question has attracted much attention. In this paper, we study the distribution of the Stochastic Gradient Noise (SGN) vectors during the training. We observe that for batch sizes 256 and above, the distribution is best described as Gaussian at-least in the early phases of training. This holds across data-sets, architectures, and other choices.

If there is one application of Machine Learning that is known to be particularly useful and often successful, that is classification. Classification is the task of assigning a given entry to a single class (e.g. Usually, each entry to be processed is represented numerically as a vector of numbers, which can encode high-level features (e.g. the length of the tail, the presence of stripes or spots, etc.) or low-level ones (e.g. the value of each pixel in an image). Over the years, a lot of different classifiers have been explored by the community, the most popular ones being artificial neural networks, decision trees, support -vector machines, or other algorithms such as k-means clustering. In this article I will focus on neural networks, but the argument can be adapted to other types of classifiers.

Let's starts with the WHY we need to perform Dimensionality Reduction before analyzing data and coming down to some inferences, it is often necessary to visualize the data set, in order to get an idea of it. But, nowadays data sets contain a lot of random variables (also called features) due to which it becomes difficult in visualizing the data set. Sometimes it is even impossible to visualize such high dimensional data as we humans fall astray after we reach a dimension higher than 3. Here is where we come across dimensionality reduction. The process of reducing the number of random variables of the data set under consideration, via obtaining a set of principal variables.

This article provides insight on the mindset, approach, and tools to consider when solving a real-world ML problem. It covers questions to consider as well as collecting, prepping and plotting data. A complementary Domino project is available. Collecting and prepping data are core research tasks. While the most ideal situation is to start a project with clean well-labeled data, the reality is that data scientists spend countless hours on obtaining and prepping data. As Domino is committed to supporting data scientists and accelerating research, we reached out to Addison-Wesley Professional (AWP) Pearson for the appropriate permissions to excerpt "Predicting Social-Media Influence in the NBA" from the book, Pragmatic AI: An Introduction to Cloud-Based Machine Learning by Noah Gift. The excerpt dives into techniques for collecting, prepping, and plotting data. Many thanks to AWP Pearson for providing the permissions to excerpt the work as well as providing the data and code for us to include in a complementary Domino project. Sports is a fascinating topic for data scientists because there is always a story behind every number. Just because an NBA player scores more points than another player, it doesn't necessarily mean [they] add more value to the team. As a result, there has been a recent explosion in individual statistics that try to measure a player's impact.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts.

Humans learn from past experiences, computers learn from previous data.

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one in the subspace spanned by the inducing basis and the other in the orthogonal complement to this subspace. We show that this formulation recovers existing approximations and at the same time allows to obtain tighter lower bounds on the marginal likelihood and new stochastic variational inference algorithms. We demonstrate the efficiency of these algorithms in several Gaussian process models ranging from standard regression to multi-class classification using (deep) convo-lutional Gaussian processes and report state-of-the-art results on CIF AR-10 with purely GPbased models.