Across fields such as machine learning, social science, geography, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1 constraints. Although these models are to a large extend similar or even equivalent, they are presented under different names, and their similarity is not well known. This paper highlights similarities among five popular models, latent budget analysis (LBA), latent class analysis (LCA), end-member analysis (EMA), probabilistic latent semantic analysis (PLSA), and nonnegative matrix factorization (NMF). We focus on an essential issue-identifiability-of these models and prove that the solution of LBA, EMA, LCA, PLSA is unique if and only if the solution of NMF is unique. We also provide a brief review for algorithms of these models. We illustrate the models with a time budget dataset from social science, and end the paper with a discussion of closely related models such as archetypal analysis.

We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that block majorization minimization can be reformulated as a block mirror descent method, with the Bregman divergence adaptively updated at each iteration, we establish subsequential convergence for BMMe. We use this method to design efficient algorithms to tackle nonnegative matrix factorization problems with the $\beta$-divergences ($\beta$-NMF) for $\beta\in [1,2]$. These algorithms, which are multiplicative updates with extrapolation, benefit from our novel results that offer convergence guarantees. We also empirically illustrate the significant acceleration of BMMe for $\beta$-NMF through extensive experiments.

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and unmixing of hyperspectral images. In such applications, the robustness of the algorithm to noise is the key to the success. Hottopixx has been shown to be robust to noise, and its robustness can be further enhanced through postprocessing. However, there is a drawback. Hottopixx and its postprocessing require us to estimate the noise level involved in the matrix we want to factorize before running, since they use it as part of the input data. The noise-level estimation is not an easy task. In this paper, we overcome this drawback. We present a refinement of Hottopixx and its postprocessing that runs without prior knowledge of the noise level. We show that the refinement has almost the same robustness to noise as the original algorithm.

We consider nonnegative time series forecasting framework. Based on recent advances in Nonnegative Matrix Factorization (NMF) and Archetypal Analysis, we introduce two procedures referred to as Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF). SMM is a simple and powerful method based on time window prediction using Completion of Nonnegative Matrices. This new procedure combines low nonnegative rank decomposition and matrix completion where the hidden values are to be forecasted. LCF is two stage: it leverages archetypal analysis for dimension reduction and clustering of time series, then it uses any black-box supervised forecast solver on the clustered latent representation. Theoretical guarantees on uniqueness and robustness of the solution of NMF Completion-type problems are also provided for the first time. Finally, numerical experiments on real-world and synthetic data-set confirms forecasting accuracy for both the methodologies.

In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for linear BSS, and is referred to as SNPALQ. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.

Clean.io, a startup that helps digital publishers protect themselves from malicious ads, recently announced that it has raised $5 million in Series A funding. The Baltimore-based company isn't the only organization promising to fight malvertising (such as ads that force visitors to redirect to another website). But as co-founder wrote Seth Demsey told me last year, Clean.io CEO Matt Gillis told me via email this week that the challenge will "always" be evolving." "Just like an antivirus company needs to constantly be updating their definitions and improving their protections, we always need to be alert to the fact that bad actors will constantly try to evade detection and get over and around the walls that you put in front of them," Gillis wrote. The company says its technology is now used on more than 7 million websites for customers including WarnerMedia's Xandr (formerly AppNexus), The Boston Globe and Imgur. Clean.io has now raised a total of $7.5 million. The Series A was led by Tribeca Venture Partners, with participation from Real Ventures, Inner Loop Capital, and Grit Capital Partners. Gillis said he'd initially planned to fundraise at the end of February, but he had to put those plans on hold due to COVID-19. He ended up doing all his pitching via Zoom ("I saw more than my fair share of small NY apartments") and he praised Tribeca's Chip Meakem (who previous investments include AppNexus) as "a world class partner." Of course, the pandemic's impact on digital advertising goes far beyond pausing Gillis' fundraising process. And when it comes to malicious ads, he said that with the cost of digital advertising declining precipitously in late March, "bad actors capitalized on this opportunity." "We saw a pretty constant surge in threat levels from mid-March until early May," Gillis continued. "Demand for our solutions have remained strong due to the increased level of attacks brought on by the pandemic.

A well-crafted data strategy is key to enhancing patient experience and controlling healthcare industry costs, according to Bill Gillis, CIO at Beth Israel Deaconess Care Organization. In an interview at the recent CDM Media CIO Boston Summit, Gillis discussed how data can be used to revolutionize the healthcare industry. In this video, he talks about the benefits of big data for the healthcare industry and highlights how AI and machine learning investments streamline manual processes and improve interoperability. Editor's note: The following transcript has been edited for clarity and length. Do organizations need a chief data officer?

Columnist Ed Baig reviews Pixel, which features the high-IQ Google Assistant and a competitive, high-end smartphone camera. Guests inspect the new Pixel phone by Google after it was introduced at a Google product event in San Francisco, Calif., Oct 4, 2016. SAN FRANCISCO -- When Google's new smartphone goes on sale this week, no one is expecting an iPhone-like hit -- at least not right away. Despite a splashy launch and a "Made by Google" marketing campaign, not to mention some positive reviews, the Pixel is still taking on the likes of the wildly popular iPhone. Samsung's recent spate of troubles may boost Pixel sales with defecting Note and Galaxy owners, but not enough to make a serious dent in the high-end smartphone market, analysts say.

Business is booming at Google's parent company, Alphabet, even as it loses billions of dollars on kooky-sounding projects that may never produce any revenue. Most of the losses are concentrated in Alphabet's'X'' lab, a wellspring of far-out ideas that has become known as a'moonshot factory' since Google co-founder Sergey Brin launched it about six years ago. The lab is responsible for some once-zany projects, such as Google's self-driving cars, that matured into potentially revolutionary technology. FILE - In this Monday, Feb. 1, 2016, file photo, electronic screens post prices of Alphabet stock at the Nasdaq MarketSite in New York. Business is booming at Google¿s parent company, Alphabet Inc., even as it loses billions of dollars on risky projects that may never produce any revenue.

SAN FRANCISCO -- Google parent Alphabet reported first-quarter earnings that fell short of analyst expectations as growing losses from the tech giant's investments in speculative businesses, from self-driving cars to speedy Internet access, overshadowed Google's booming advertising business. Class A shares of Alphabet (GOOGL) fell 6% after hours to 732. They've rallied 44% in the past 12 months. "Alphabet has made it pretty clear they weren't going to stop their investments in other areas, and they spent a little bit more than some people may have liked," said BGC Financial analyst Colin Gillis. "You don't necessarily like to see costs and losses growing faster than revenue, but that's where Alphabet's future is going to be." Chief Financial Officer Ruth Porat, who joined the company last May in a hire investors hoped would curb spending, assured investors that Alphabet is "thoughtfully pursuing big bets."