Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data such as images. Learning a lower-dimensional embedding that can better reflect the geometry of the dataset is therefore instrumental for performance. We propose a new approach for this task where the embedding is performed by a differentiable model such as a deep neural network. By rewriting the $k$-means clustering algorithm as an optimal transport task, and adding an entropic regularization, we derive a fully differentiable loss function that can be minimized with respect to both the embedding parameters and the cluster parameters via stochastic gradient descent. We show that this new formulation generalizes a recently proposed state-of-the-art method based on soft-$k$-means by adding constraints on the cluster sizes. Empirical evaluations on image classification benchmarks suggest that compared to state-of-the-art methods, our optimal transport-based approach provide better unsupervised accuracy and does not require a pre-training phase.

Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity matrix is generated from data. In the second one, spectral clustering is applied on the affinity matrix. However, the affinity matrix produced by two-stage methods cannot fully reveal the similarity between data points from the same subspace (intra-subspace similarity), resulting in inaccurate clustering. Besides, most approaches fail to solve large-scale clustering problems due to poor efficiency. In this paper, we first propose a new scalable sparse method called Iterative Maximum Correlation (IMC) to learn the affinity matrix from data. Then we develop Piecewise Correlation Estimation (PCE) to densify the intra-subspace similarity produced by IMC. Finally we extend our work into a Sparse-Dense Subspace Clustering (SDSC) framework with a dense stage to optimize the affinity matrix for two-stage methods. We show that IMC is efficient when clustering large-scale data, and PCE ensures better performance for IMC. We show the universality of our SDSC framework as well. Experiments on several data sets demonstrate the effectiveness of our approaches. Moreover, we are the first one to apply densification on affinity matrix before spectral clustering, and SDSC constitutes the first attempt to build a universal three-stage subspace clustering framework.

Public transport is one of the major forms of transportation in the world. This makes it vital to ensure that public transport is efficient. This research presents a novel real-time GPS bus transit data for over 500 routes of buses operating in New Delhi. The data can be used for modeling various timetable optimization tasks as well as in other domains such as traffic management, travel time estimation, etc. The paper also presents an approach to reduce the waiting time of Delhi buses by analyzing the traffic behavior and proposing a timetable. This algorithm serves as a benchmark for the dataset. The algorithm uses a constrained clustering algorithm for classification of trips. It further analyses the data statistically to provide a timetable which is efficient in learning the inter- and intra-month variations.

The task of Visual Commonsense Reasoning is extremely challenging in the sense that the model has to not only be able to answer a question given an image, but also be able to learn to reason. The baselines introduced in this task are quite limiting because two networks are trained for predicting answers and rationales separately. Question and image is used as input to train answer prediction network while question, image and correct answer are used as input in the rationale prediction network. As rationale is conditioned on the correct answer, it is based on the assumption that we can solve Visual Question Answering task without any error - which is over ambitious. Moreover, such an approach makes both answer and rationale prediction two completely independent VQA tasks rendering cognition task meaningless. In this paper, we seek to address these issues by proposing an end-to-end trainable model which considers both answers and their reasons jointly. Specifically, we first predict the answer for the question and then use the chosen answer to predict the rationale. However, a trivial design of such a model becomes non-differentiable which makes it difficult to train. We solve this issue by proposing four approaches - softmax, gumbel-softmax, reinforcement learning based sampling and direct cross entropy against all pairs of answers and rationales. We demonstrate through experiments that our model performs competitively against current state-of-the-art. We conclude with an analysis of presented approaches and discuss avenues for further work.

In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could not be obtained from any of the constituent learning algorithms alone. The idea of combining multiple algorithms was first developed by computer scientist and Professor Michael Kerns, who was wondering whether "weakly learnability is equivalent to strong learnability ". The goal was turning a weak algorithm, barely better than random guessing, into a strong learning algorithm. It turned out that, if we ask the weak algorithm to create a whole bunch of classifiers (all weak for definition), and then combine them all, what may figure out is a stronger classifier. AdaBoost, which stays for'Adaptive Boosting', is a machine learning meta-algorithm which can be used in conjunction with many other types of learning algorithms to improve performance. In this article, I'm going to provide an idea of the maths behind Adaboost, plus I'll provide an implementation in Python.

To kick off this series, will start with something simple yet foundational: linear regression via ordinary least squares. While not exciting, linear regression finds widespread use both as a standalone learning algorithm and as a building block in more advanced learning algorithms. The output layer of a deep neural network trained for regression with MSE loss, simple AR time series models, and the "local regression" part of LOWESS smoothing are all examples of linear regression being used as an ingredient in a more sophisticated model. Linear regression is also the "simple harmonic oscillator" of machine learning; that is to say, a pedagogical example that allows us to present deep theoretical ideas about machine learning in a context that is not too mathematically taxing. There is also the small matter of it being the most widely used supervised learning algorithm in the world; although how much weight that carries I suppose depends on where you are on the "applied" to "theoretical" spectrum. However, since I can already feel your eyes glazing over from such an introductory topic, we can spice things up a little bit by doing something which isn't often done in introductory machine learning - we can present the algorithm that [your favorite statistical software here] actually uses to fit linear regression models: QR decomposition. It seems this is commonly glossed over because it involves more linear algebra than can be generally assumed, or perhaps because the exact solution we will derive doesn't generalize well to other machine learning algorithms, not even closely related variants such as regularized regression or robust regression.

Let's play around with datasets to visualize how the decision boundary changes as'k' changes. Let's have a quick review… K Nearest Neighbor(KNN) algorithm is a very simple, easy to understand, versatile and one of the topmost machine learning algorithms. In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbours, with the object being assigned to the class most common among its k nearest neighbours (k is a positive integer, typically small). If k 1, then the object is simply assigned to the class of that single nearest neighbour.

Understand the fundamental assumptions of time series data and how to take advantage of them. Transforming a data set into a time-series. Start coding in Python and learn how to use it for statistical analysis. Carry out time-series analysis in Python and interpreting the results, based on the data in question. Examine the crucial differences between related series like prices and returns.

This machine learning for beginners tutorial course covers what is machine learning, machine learning algorithms like linear regression, binary classification, decision tree, random forest and unsupervised algorithm like k means clustering in detail with complete hands on demo. There is machine learning complete project and machine learning interview questions as well in this machine learning full course video to prepare you for the job interview. It is a 32 hrs instructor led machine learning training provided by Intellipaat which is completely aligned with industry standards and certification bodies. If you've enjoyed this machine learning training, Like us and Subscribe to our channel for more similar machine learning videos and free tutorials. Ask us in the comment section below.

Transferring knowledge across many streaming processes remains an uncharted territory in the existing literature and features unique characteristics: no labelled instance of the target domain, covariate shift of source and target domain, different period of drifts in the source and target domains. Autonomous transfer learning (ATL) is proposed in this paper as a flexible deep learning approach for the online unsupervised transfer learning problem across many streaming processes. ATL offers an online domain adaptation strategy via the generative and discriminative phases coupled with the KL divergence based optimization strategy to produce a domain invariant network while putting forward an elastic network structure. It automatically evolves its network structure from scratch with/without the presence of ground truth to overcome independent concept drifts in the source and target domain. The rigorous numerical evaluation has been conducted along with a comparison against recently published works. ATL demonstrates improved performance while showing significantly faster training speed than its counterparts.