Matrix Coherence and the Nystrom Method

The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this assumption to the concept of matrix coherence and connect matrix coherence to the performance of the Nystrom method. Making use of related work in the compressed sensing and the matrix completion literature, we derive novel coherence-based bounds for the Nystrom method in the low-rank setting. We then present empirical results that corroborate these theoretical bounds. Finally, we present more general empirical results for the full-rank setting that convincingly demonstrate the ability of matrix coherence to measure the degree to which information can be extracted from a subset of columns

Introversion, Play, and Childhood: The Ideas Behind the Remnants

Closed and confined spaces provide my introverted personality a place to examine, explore, and unwind. Being an introvert has inspired this senior thesis exhibition, exploring the relationship between interior and exterior spaces and child-like play. Growing up I didn’t crave a social life outside of my nuclear family and home. I spent a majority of my time inside my bedroom, but curious about the lively atmosphere outside of my bedroom. The act of play with my siblings would break down my introverted tendencies and present me with new objects, toys, and materials to explore. Now, my dorm room has become my refuge, similar to my childhood bedroom, and play has been found when I experiment and make work in the art studios. Inspired by my childhood toys, the books, boxes, and objects I make are derived from my introverted childhood. I use repetition within the candy wrapper folios of the books to give visual impact and mimic the multiples of the boxes themselves, as well as many of my childhood toys. Some boxes have been made to custom fit the item inside creating contrast between a nondescript exterior and a bright and colorful interior. Other boxes hold remnants of items from a celebration I would discover once the party was over when I felt comfortable emerging from my room. The text and imagery on the inside of the box lids, as well as using primary colors inside with a cream exterior provide context to the interior and exterior conversation. The archival boxes are in contradiction to the non-archival objects inside. This pairing comments on the relationship of precious versus non-precious and the celebration of commonplace items, like candy wrappers which are normally discarded. I am interested in the relationship between the viewer, the object, and the space in between, while simultaneously inviting the viewer to interact with the work. The combination of the formal qualities, the desired tactility, and the small scale of the pieces produces a coherent senior thesis exhibition that is interactive, targets a wide audience, and is adaptable to any available space. As a printmaker who is drawn to bookbinding, Barbara Barnes Allen and Subodh Gupta are two artists who influence my work. I have taken inspiration from Allen’s use of everyday items and Gupta’s use of sculpture and repetition. Taking inspiration from these artists and life experiences, I have used bookbinding and box construction in this senior thesis exhibition to portray fragments of the introversion from my childhood

Professional Practices: Cumulation of Work

I juxtapose sharp and organic shapes, which are inspired by ideas of plants, landscape and architectural design because of the clean lines and minimalistic forms. Line quality is used to show space, and enhance a minimalistic aesthetic, while the use of line and value in architectural drawings changes perspective and manipulates the viewer’s eye. As well as plants, landscape, architectural design, my work is about containers, containing space, and the manipulation of a man-made space. The geometric motif running through the body of work is primarily boxes and can be seen as a reduced form mimicking shapes one interacts with on a day-to-day basis. I am interested in the relationship between the viewer, the form, and the space in between them. The combination of these formal qualities determine the composition of the work and whether or not it is set in an atmosphere. Loneliness, space, and minimalism inform my work. As a printmaker who works in etching primarily, I am influenced by Ann Kavanagh and her use of line and composition in her photo-etchings, photographs, and Japanese woodcuts. Loneliness is the lack of something, and I use minimalism to show that through sharp, uncluttered lines, rich values, and unconventional spacing of the plates. By composing the space of the page with line and value, loneliness is depicted through an altered perspective, whether that be from the outside looking in or a dramatically skewed angle. I am interested in the evolution of a space within the confinement of a man-made space, mostly the size of the plate or page