Cross-Domain Recommendation (CDR) and Cross-System Recommendation (CSR) have been proposed to improve the recommendation accuracy in a target dataset (domain/system) with the help of a source one with relatively richer information. However, most existing CDR and CSR approaches are single-target, namely, there is a single target dataset, which can only help the target dataset and thus cannot benefit the source dataset. In this paper, we focus on three new scenarios, i.e., Dual-Target CDR (DTCDR), Multi-Target CDR (MTCDR), and CDR+CSR, and aim to improve the recommendation accuracy in all datasets simultaneously for all scenarios. To do this, we propose a unified framework, called GA (based on Graph embedding and Attention techniques), for all three scenarios. In GA, we first construct separate heterogeneous graphs to generate more representative user and item embeddings. Then, we propose an element-wise attention mechanism to effectively combine the embeddings of common entities (users/items) learned from different datasets. Moreover, to avoid negative transfer, we further propose a Personalized training strategy to minimize the embedding difference of common entities between a richer dataset and a sparser dataset, deriving three new models, i.e., GA-DTCDR-P, GA-MTCDR-P, and GA-CDR+CSR-P, for the three scenarios respectively. Extensive experiments conducted on four real-world datasets demonstrate that our proposed GA models significantly outperform the state-of-the-art approaches.

Regression is a method to predict the target variable y which possesses the best linear relationship between the given independent and dependent values. The major goal of regression is to inspect the relationship between the input feature x with that of the target value y and then outputs a continuous-valued output for the unknown value given as the input. Simple Linear regression uses a single independent variable to predict a dependent variable by fitting the best linear relationship. Here'y' is the dependent variable. The term'bo' is the constant.

Linear Discriminant Analysis is one of the commonly used supervised technique for dimensionality reduction. It is also used in classification problems and for data visualizations. Dimensionality Reduction is the transformation or projection of data from higher-dimensional space to lower-dimensional space. How is LDA different from PCA? The major distinction between LDA and PCA is that, LDA focuses on finding the axes that maximize the separation between multiple classes.

Generally, clustering is grouping multi-dimensional datasets into closely related groups. Classical representatives of clustering algorithms are K-means Clustering and Self-Organizing Map (SOM). You can easily find numerous resources for those algorithm explanations. This time, let me introduce to all of you another efficient clustering algorithm but seemingly no many researchers pay attention: Centroid Neural Network for Unsupervised Competitive Learning. Please click here to have a closer looking at the original paper.

As we know that Clustering is a powerful unsupervised knowledge discovery tool used nowadays to segment our data points into groups of similar features types. However, each algorithm of clustering works according to the parameters. Similarity-based techniques (K-means clustering algorithm working is based on similarity of the data points and is tasked with designating how many clusters are available, while hierarchical clustering algorithms decide when to assign finished clusters manually. Generally used density-based clustering technique is DBSCAN which requires two parameters about how it defines its Core Points, but finding the parameters is an extremely difficult task. DBSCAN's relatively algorithm is called OPTICS (Ordering Points to Identify Cluster Structure).

The flexibility of decision boundaries in neural networks that are unguided by training data is a well-known problem typically resolved with generalization methods. A surprising result from recent knowledge distillation (KD) literature is that random, untrained, and equally structured teacher networks can also vastly improve generalization performance. It raises the possibility of existence of undiscovered assumptions useful for generalization on an uncertain region. In this paper, we shed light on the assumptions by analyzing decision boundaries and confidence distributions of both simple and KD-based generalization methods. Assuming that a decision boundary exists to represent the most general tendency of distinction on an input sample space (i.e., the simplest hypothesis), we show the various limitations of methods when using the hypothesis. To resolve these limitations, we propose matured dumb teacher based KD, conservatively transferring the hypothesis for generalization of the student without massive destruction of trained information. In practical experiments on feed-forward and convolution neural networks for image classification tasks on MNIST, CIFAR-10, and CIFAR-100 datasets, the proposed method shows stable improvement to the best test performance in the grid search of hyperparameters. The analysis and results imply that the proposed method can provide finer generalization than existing methods.

Generalised Linear Models (GLMs McCullagh & Nelder 1989; Nelder & Wedderburn 1972) are frequently used in different applications to predict a univariate response due to the ease of interpretation of the parameter estimates as well as the large availability of software that facilitates simple analyses. A common assumption in GLMs is that the covariates specified (including potential interaction terms) have a linear relationship with the mean of the response after transformation through the link function. Extensions such as Generalised Additive Models (GAMs T. J. Hastie & Tibshirani 1990; Wood 2017) require the specification of the main and interaction effects via a sum of (potentially non-linear) predictors. In GAMs, the non-linear relationship is usually captured via basis expansions of the covariates and constrained by a smoothing parameter. However, in problems where the numbers of covariates and/or observations are large, the linearity assumption may not be verified and, more importantly, it may not be simple to specify the covariates and their interactions that impact most on the response.

Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1000\times$ on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance.

In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum levels. We seek this connection through the introduction of Fokker-Planck equations on data graphs. Besides introducing new forms of mean shift algorithms on graphs, we provide new theoretical insights on the behavior of the family of diffusion maps in the large sample limit as well as provide new connections between diffusion maps and mean shift dynamics on a fixed graph. Several numerical examples illustrate our theoretical findings and highlight the benefits of interpolating density-driven and geometry-based clustering algorithms.

Manifold-valued functional data analysis (FDA) recently becomes an active area of research motivated by the raising availability of trajectories or longitudinal data observed on non-linear manifolds. The challenges of analyzing such data come from many aspects, including infinite dimensionality and nonlinearity, as well as time-domain or phase variability. In this paper, we study the amplitude part of manifold-valued functions on $\mathbb{S}^2$, which is invariant to random time warping or re-parameterization. Utilizing the nice geometry of $\mathbb{S}^2$, we develop a set of efficient and accurate tools for temporal alignment of functions, geodesic computing, and sample mean calculation. At the heart of these tools, they rely on gradient descent algorithms with carefully derived gradients. We show the advantages of these newly developed tools over its competitors with extensive simulations and real data and demonstrate the importance of considering the amplitude part of functions instead of mixing it with phase variability in manifold-valued FDA.