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以LDA主題模型與負二項迴歸分析線上商品評論及其有用性

為了解決Data singular or plu的問題，作者陳映霖 這樣論述：

隨著線上購物的發展，線上評論已然成為消費者在進行購買決策時，不可或缺的指標。而為了幫助消費者篩選線上評論，線上評論除原先包含評論者身分、評級、文字評論、圖片、評論時間的組成外，一些電商平台發展出評論有用性等投票機制。本研究透過隱含狄利克雷分布(Latent Dirichlet allocation，LDA)，分析辛辛納提大學的卡爾·H·林德納商學院的平板電腦數據集樣本，分析線上評論及其有用性，以為業者在有幫助的消費者評論中，尋找出影響購買決策的關鍵主題及辭彙，使其持續精進自身商品，以貼近消費者需求，提升使用滿意度。研究結果顯示在不同主題分類下的有用評論，能夠找出消費者更在乎的關鍵詞，並使用負

二項分配觀察評論有用性與各主題之間的關係，發現描述作業系統與硬體設備相關的主題顯著影響評論有用性。

數學形態學導出多參數持續同調之層狀結構

為了解決Data singular or plu的問題，作者胡全燊 這樣論述：

Topological Data Analysis (TDA), a fast-growing research topic in applied topology, uses techniques in algebraic topology to capture features from data. Its importance has been discovered in many areas, such as medical image processing, molecular biology, machine learning, and pattern recognition.

Persistent homology (PH) is vital in topological data analysis that detects local changes in filtered topological spaces. It measures the robustness and significance of homological objects in spaces' deformation, such as connected components, loops, or higher dimensional voids. In Morse theory, filt

ered spaces for persistent homology usually rely on a single parameter, such as the sublevel set filtration of height functions. Recently, as a generalization of persistent homology, computational topologists began to be interested in multi-parameter persistent homology. Multi-parameter persistent h

omology (or multi-parameter persistence) is an algebraic structure established on a multi-parametrized network of topological spaces and has more fruitful geometric information than persistent homology. So far, finding methods to extract features in multi-parameter persistence is still an open and

concentrating topic in TDA. Also, examples of multi-parameter filtration are still rare and limited. The three principal contributions of this dissertation are as follows. First, we combined persistent homology features (persistence statistics and persistence curves) and machine learning models for

analyzing medical images. We found that adding topological information into machine learning models can improve recognition accuracy and stability. Second, unlike traditional construction for multi-parameter filtrations in Euclidean spaces, we propose a framework for constructing multi-parameter fi

ltrations from digital images through mathematical morphology and discrete geometry. Multi-parameter persistence derived from mathematical morphology is more efficient for computing and contains intuitive geometric attributes of objects, such as the sizes or robustness of local objects in digital im

ages. We involve these features to remove the salt and pepper noise in digital images as an application. Compared with current denoise algorithms, the proposed approach has a more stable accuracy and keeps the topological structures of original data. The third part of this dissertation focuses on us

ing sheaf theory to analyze the lifespans of objects in multi-parameter persistence. The multi-parameter persistence has a natural sheaf structure by equipping the Alexandrov topology on the based partially ordered set. This sheaf structure uncovers the gluing properties of local image regions in th

e multi-parameter filtration. We referred to these properties as a fingerprint of the filtration and applied them for the character recognition task. Finally, we propose using sheaf operators to define ultrametric norms on local spaces in multi-parameter persistence. Like persistence barcodes, this

metric provides finer geometric and topological quantities.