Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes. We present a large-scale GPU study of seven algorithm families (over 30 configurations) on absolute Pearson correlation and tail pairwise dependence matrices from Extreme Value Theory, two proxies for empirical risk-factor estimation on large portfolios. A trace-identity reformulation eliminates all $n \times n$ intermediates, so a single GPU reaches $n \approx 10^5$ and multi-node distribution scales to $n = 10^6$ and beyond. Under a two-phase protocol, eleven methods converge at moderate scale; six remain efficient enough at $n = 10^5$ (five AdaGrad-family plus ADMM), and five AdaGrad-family methods still converge at $n = 10^6$: AdaGrad, RMSprop, and three we introduce (Piecewise AdaGrad, Row-Stochastic SVRG, Block-SVRG AdaptGrow). At $n = 10^6$ the fastest solver tracks the matrix spectrum: Block-SVRG AdaptGrow wins on the flat, ill-conditioned tail-dependence spectrum, where its lower per-iteration cost decides a long factorization, and full-batch AdaGrad wins on the dominant-low-rank correlation spectrum, where the run is short. We also benchmark spherical K-means as a hard-label baseline: cheaper when angular cluster structure is present, yet provably degenerate once the matrix collapses toward a single common factor, where the soft factorization remains necessary.
Financial sentiment extraction has largely relied on news text and supervised extraction against return labels alone, leaving 10-K filings -- and volatility, the target risk disclosure is arguably best suited to informing -- comparatively unexplored. We extend a supervised lexicon-learning approach to 10-K filings and their Item 1A risk-factor sections, training sentiment scores against both return and volatility labels at three levels of aggregation: sector, portfolio, and individual firm. Across 1,383 filings from 94 Nasdaq-100 technology constituents (2006--2023), we evaluate the resulting twelve sentiment metrics on classification accuracy, correlation with realised market outcomes, and qualitative lexical content. Full-filing text produces more accurate sentiment at the sector and portfolio level for both targets, but this reverses at the individual-firm level, where the narrower Item 1A section performs better -- an effect we attribute to the interaction between document volume and the amount of independent training signal available at each level of aggregation. A Loughran-McDonald dictionary baseline is consistently, strongly negatively correlated with price at every level tested, underscoring the value of a supervised approach for regulatory disclosure text. These findings, and the design choices they motivate, establish the sentiment-generation methodology underlying a subsequent, larger-scale, multi-source system.