Linear dimensionality reduction: Survey, insights, and generalizations

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.JPC and ZG received funding from the UK Engineering and Physical Sciences Research Council (EPSRC EP/H019472/1). JPC received funding from a Sloan Research Fellowship, the Simons Foundation (SCGB#325171 and SCGB#325233), the Grossman Center at Columbia University, and the Gatsby Charitable Trust.This is the author accepted manuscript. The final version is available from MIT Press via http://jmlr.org/papers/v16/cunningham15a.htm

Excitatory and Inhibitory Subnetworks Are Equally Selective during Decision-Making and Emerge Simultaneously during Learning

Inhibitory neurons, which play a critical role in decision-making models, are often simplified as a single pool of non-selective neurons lacking connection specificity. This assumption is supported by observations in the primary visual cortex: inhibitory neurons are broadly tuned in vivo and show non-specific connectivity in slice. The selectivity of excitatory and inhibitory neurons within decision circuits and, hence, the validity of decision-making models are unknown. We simultaneously measured excitatory and inhibitory neurons in the posterior parietal cortex of mice judging multisensory stimuli. Surprisingly, excitatory and inhibitory neurons were equally selective for the animal’s choice, both at the single-cell and population level. Further, both cell types exhibited similar changes in selectivity and temporal dynamics during learning, paralleling behavioral improvements. These observations, combined with modeling, argue against circuit architectures assuming non-selective inhibitory neurons. Instead, they argue for selective subnetworks of inhibitory and excitatory neurons that are shaped by experience to support expert decision-making

Induction, Philosophical Conceptions of

How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as Lorenzo Valla and Rudolph Agricola, Paduan Aristotelians such as Agostino Nifo, Jacopo Zabarella, and members of the medical faculty, writers on philosophy of mind such as the Englishman John Case, writers of reasoning handbooks, and Francis Bacon

The Value of Success: Acquiring Gains, Avoiding Losses, and Simply Being Successful

A large network of spatially contiguous, yet anatomically distinct regions in medial frontal cortex is involved in reward processing. Although it is clear these regions play a role in critical aspects of reward-related learning and decision-making, the individual contributions of each component remains unclear. We explored dissociations in reward processing throughout several key regions in the reward system and aimed to clarify the nature of previously observed outcome-related activity in a portion of anterior medial orbitofrontal cortex (mOFC). Specifically, we tested whether activity in anterior mOFC was related to processing successful actions, such that this region would respond similarly to rewards with and without tangible benefits, or whether this region instead encoded only quantifiable outcome values (e.g., money). Participants performed a task where they encountered monetary gains and losses (and non-gains and non-losses) during fMRI scanning. Critically, in addition to the outcomes with monetary consequences, the task included trials that provided outcomes without tangible benefits (participants were simply told that they were correct or incorrect). We found that anterior mOFC responded to all successful outcomes regardless of whether they carried tangible benefits (monetary gains and non-losses) or not (controls). These results support the hypothesis that anterior mOFC processes rewards in terms of a common currency and is capable of providing reward-based signals for everything we value, whether it be primary or secondary rewards or simply a successful experience without objectively quantifiable benefits

An extracellular steric seeding mechanism for Eph-ephrin signaling platform assembly

Erythropoetin-producing hepatoma (Eph) receptors are cell-surface protein tyrosine kinases mediating cell-cell communication. Upon activation, they form signaling clusters. We report crystal structures of the full ectodomain of human EphA2 (eEphA2) both alone and in complex with the receptor-binding domain of the ligand ephrinA5 (ephrinA5 RBD). Unliganded eEphA2 forms linear arrays of staggered parallel receptors involving two patches of residues conserved across A-class Ephs. eEphA2-ephrinA5 RBD forms a more elaborate assembly, whose interfaces include the same conserved regions on eEphA2, but rearranged to accommodate ephrinA5 RBD. Cell-surface expression of mutant EphA2s showed that these interfaces are critical for localization at cell-cell contacts and activation-dependent degradation. Our results suggest a 'nucleation' mechanism whereby a limited number of ligand-receptor interactions 'seed' an arrangement of receptors which can propagate into extended signaling arrays

The Cancer Hub Approach for Upper Gastrointestinal Surgery During COVID-19 Pandemic: Outcomes from a UK Cancer Centre.

BACKGROUND: The coronavirus disease 2019 (COVID-19) pandemic caused unprecedented disruption to global healthcare delivery. In England, the majority of elective surgery was postponed or cancelled to increase intensive care capacity. Our unit instituted the 'RM Partners Cancer Hub' at the Royal Marsden Hospital in London, to deliver ongoing cancer surgery in a 'COVID-lite' setting. This article describes the operational set-up and outcomes for upper gastrointestinal (UGI) cancer resections performed during this period. METHODS: From April 2020 to April 2021, the Royal Marsden Hospital formed the RM Partners Cancer Hub. This approach was designed to coordinate resources and provide as much oncological treatment as feasible for patients across the RM Partners West London Cancer Alliance. A UGI surgical case prioritisation strategy, along with strict infection control pathways and pre-operative screening protocols, was adopted. RESULTS: A total of 231 patients underwent surgery for confirmed or suspected UGI cancer during the RM Partners Cancer Hub, with 213 completed resections and combined 90-day mortality rate of 3.5%. Good short-term survival outcomes were demonstrated with 2-year disease free survival (DFS) and overall survival (OS) for oesophageal (70.8% and 72.9%), gastric (66.7% and 83.3%) and pancreatic cancer resections (68.0% and 88.0%). One patient who developed perioperative COVID-19 during the RM Partners Cancer Hub operation made a full recovery with no lasting clinical sequelae. CONCLUSION: Our experience demonstrates that the RM Partners Cancer Hub approach is a safe strategy for continuing upper gastrointestinal (GI) resectional surgery during future periods of healthcare service disruption

Melaena with Peutz-Jeghers syndrome: a case report

Introduction: Peutz-Jeghers syndrome (PJS) is a rare familial disorder characterised by mucocutaneous pigmentation, gastrointestinal and extragastrointestinal hamartomatous polyps and an increased risk of malignancy. Peutz-Jeghers polyps in the bowel may result in intussusception. This complication usually manifests with abdominal pain and signs of intestinal obstruction. Case Presentation: We report the case of a 24-year-old Caucasian male who presented with melaena. Pigmentation of the buccal mucosa was noted but he was pain-free and examination of the abdomen was unremarkable. Upper gastrointestinal endoscopy revealed multiple polyps. An urgent abdominal computed tomography (CT) scan revealed multiple small bowel intussusceptions. Laparotomy was undertaken on our patient, reducing the intussusceptions and removing the polyps by enterotomies. Bowel resection was not needed. Conclusion: Melaena in PJS needs to be urgently investigated through a CT scan even in the absence of abdominal pain and when clinical examination of the abdomen shows normal findings. Although rare, the underlying cause could be intussusception, which if missed could result in grave consequences

Colorectal cancer linkage on chromosomes 4q21, 8q13, 12q24, and 15q22

A substantial proportion of familial colorectal cancer (CRC) is not a consequence of known susceptibility loci, such as mismatch repair (MMR) genes, supporting the existence of additional loci. To identify novel CRC loci, we conducted a genome-wide linkage scan in 356 white families with no evidence of defective MMR (i.e., no loss of tumor expression of MMR proteins, no microsatellite instability (MSI)-high tumors, or no evidence of linkage to MMR genes). Families were ascertained via the Colon Cancer Family Registry multi-site NCI-supported consortium (Colon CFR), the City of Hope Comprehensive Cancer Center, and Memorial University of Newfoundland. A total of 1,612 individuals (average 5.0 per family including 2.2 affected) were genotyped using genome-wide single nucleotide polymorphism linkage arrays; parametric and non-parametric linkage analysis used MERLIN in a priori-defined family groups. Five lod scores greater than 3.0 were observed assuming heterogeneity. The greatest were among families with mean age of diagnosis less than 50 years at 4q21.1 (dominant HLOD = 4.51, α = 0.84, 145.40 cM, rs10518142) and among all families at 12q24.32 (dominant HLOD = 3.60, α = 0.48, 285.15 cM, rs952093). Among families with four or more affected individuals and among clinic-based families, a common peak was observed at 15q22.31 (101.40 cM, rs1477798; dominant HLOD = 3.07, α = 0.29; dominant HLOD = 3.03, α = 0.32, respectively). Analysis of families with only two affected individuals yielded a peak at 8q13.2 (recessive HLOD = 3.02, α = 0.51, 132.52 cM, rs1319036). These previously unreported linkage peaks demonstrate the continued utility of family-based data in complex traits and suggest that new CRC risk alleles remain to be elucidated. © 2012 Cicek et al