Learn to Make a Machine Learn Presentation by Dr. Angana Chakraborty
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This document discusses machine learning techniques for information retrieval and nearest neighbor searches, specifically locality sensitive hashing (LSH). It introduces context based LSH (conLSH), which incorporates contextual information to improve nearest neighbor searches for ordered data like biological sequences. Finally, it outlines some real-life applications of LSH techniques like custom recommendations, biological sequence analysis, and action recognition in videos.
![LOCALITY SENSITIVE HASHING
APPROXIMATE NEAREST NEIGHBOUR SEARCH
Locality Sensitive Hashing:[1]
A family of hash functions is called
-sensitive if
if then
if then , Where,
.
ℋ : ℝd
→ U (R, cR, P1, P2)
∀p, q ∈ ℝd
∥ p − q ∥≤ R Prℋ[h(p) = h(q)] ≥ P1
∥ p − q ∥≥ cR Prℋ[h(p) = h(q)] ≤ P2
P1 > P2
[1]Andoni, A. and Indyk, P. (2008). Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In
Communications of the ACM - 50th anniversary issue, pages 117{122}. ACM.
LSH
LSH Table
0 1 2 3 4 5 6 7 8 9
0123
hLSH(2)=hLSH(5)=hLSH(8)=3](https://image.slidesharecdn.com/presentationbyanganachakraborty-201215170229/85/Learn-to-Make-a-Machine-Learn-Presentation-by-Dr-Angana-Chakraborty-4-320.jpg)
![CONTEXT BASED LOCALITY SENSITIVE HASHING (conLSH)
Context:[2]
be a sequence of length .
A context at position of , for , is a subsequence of length
is the context factor.
x : (x1x2…xn) n
ith
x i ∈ {λ + 1,…, n − λ} (xi−λ, …, xi, …, xi+λ) 2λ + 1
λ
[2]Angana Chakraborty, Sanghamitra Bandyopadhyay, “conLSH: Context based Locality Sensitive Hashing for Mapping of noisy SMRT
Reads”, Computational Biology and Chemistry, Elsevier, 107206 (2020), doi:10.1016/j.compbiolchem.2020.107206.
conLSH:[2]
: set of all length- words over and be the set of all length- words over , for .
A -sensitive LSH family of functions mapping from to is called
-sensitive, if for each , there are positions and with such that for all
one has whenever holds.
X d Σ U 2λ + 1 Σ 2λ + 1 < d
(R, cR, P1, P2) ℋ X U (R, cR, λ, P1, P2)
h ∈ ℋ ih jh λ + 1 ≤ ih, jh ≤ d − λ
p, q ∈ X h(p) = h(q) p[ih − λ…ih…ih + λ] = q[jh − λ…jh…jh + λ]](https://image.slidesharecdn.com/presentationbyanganachakraborty-201215170229/85/Learn-to-Make-a-Machine-Learn-Presentation-by-Dr-Angana-Chakraborty-6-320.jpg)
Learn to Make a Machine Learn Presentation by Dr. Angana Chakraborty
- 1. LEARN TO MAKE A MACHINE LEARN Dr. Angana Chakraborty Assistant Professor, W.B.E.S. Sister Nibedita Govt. Gen. Degree College for Girls Kolkata, West Bengal Faculty Induction Program-02 Guru Jambheswar University of Science & Technology, Hisar
- 2. MACHINE LEARNING IN E-COMMERCE
- 3. INFORMATION RETRIEVAL !Input: A collection of points and a Query in !Processing: Build the data structure and search points nearest to the Query . !Return: The closest data point(s). Some distance metric is used to measure the similarity between the data objects. n ℝd
- 4. LOCALITY SENSITIVE HASHING APPROXIMATE NEAREST NEIGHBOUR SEARCH Locality Sensitive Hashing:[1] A family of hash functions is called -sensitive if if then if then , Where, . ℋ : ℝd → U (R, cR, P1, P2) ∀p, q ∈ ℝd ∥ p − q ∥≤ R Prℋ[h(p) = h(q)] ≥ P1 ∥ p − q ∥≥ cR Prℋ[h(p) = h(q)] ≤ P2 P1 > P2 [1]Andoni, A. and Indyk, P. (2008). Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In Communications of the ACM - 50th anniversary issue, pages 117{122}. ACM. LSH LSH Table 0 1 2 3 4 5 6 7 8 9 0123 hLSH(2)=hLSH(5)=hLSH(8)=3
- 5. CONTEXT BASED LOCALITY SENSITIVE HASHING (conLSH) LSH conLSH LSH Table (a) 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0123 012345 hLSH(2)=hLSH(5)=hLSH(8)=3 conLSH Table (b) hconLSH(1)=hconLSH(7)=0 hconLSH(2)=hconLSH(8)=1 Suitable for ordered data
- 6. CONTEXT BASED LOCALITY SENSITIVE HASHING (conLSH) Context:[2] be a sequence of length . A context at position of , for , is a subsequence of length is the context factor. x : (x1x2…xn) n ith x i ∈ {λ + 1,…, n − λ} (xi−λ, …, xi, …, xi+λ) 2λ + 1 λ [2]Angana Chakraborty, Sanghamitra Bandyopadhyay, “conLSH: Context based Locality Sensitive Hashing for Mapping of noisy SMRT Reads”, Computational Biology and Chemistry, Elsevier, 107206 (2020), doi:10.1016/j.compbiolchem.2020.107206. conLSH:[2] : set of all length- words over and be the set of all length- words over , for . A -sensitive LSH family of functions mapping from to is called -sensitive, if for each , there are positions and with such that for all one has whenever holds. X d Σ U 2λ + 1 Σ 2λ + 1 < d (R, cR, P1, P2) ℋ X U (R, cR, λ, P1, P2) h ∈ ℋ ih jh λ + 1 ≤ ih, jh ≤ d − λ p, q ∈ X h(p) = h(q) p[ih − λ…ih…ih + λ] = q[jh − λ…jh…jh + λ]
- 7. REAL LIFE APPLICATIONS !Customised suggestion in e-commerce platform !Faster algorithms for real-time results. !Training based on demographical, age-based preferences !Biological Sequence similarity search !Mutation and SNP detection !Phylogenetic tree reconstruction !Action recognition in video sequences
- 8. BIBLIOGRAPHY ➤ Andoni, A. and Indyk, P. (2008). Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In Communications of the ACM - 50th anniversary issue, pages 117{122}. ACM. ➤ Chakraborty, A. and Bandyopadhyay, S. (2020), “conLSH: Context based Locality Sensitive Hashing for Mapping of noisy SMRT Reads”, Computational Biology and Chemistry, Elsevier, 107206 (2020), doi:10.1016/ j.compbiolchem.2020.107206. ➤ Chakraborty, A. and Morgenstern, B. and Bandyopadhyay, S. (2019), S-conLSH: Alignment-free gapped mapping of noisy long reads", bioRxiv 801118, 2019. ➤ Chakraborty, A. and Bandyopadhyay, S. (2014). A Layered Locality Sensitive Hashing based Sequence Similarity Search Algorithm for Web Sessions. 2nd ASE International Conference on Big Data Science and Computing, Stanford University, CA, USA. ➤ Zielezinski, A., Girgis, H. Z., Bernard, G., Leimeister, C.-A., Tang, K., Dencker, T., Lau, A. K., Rohling, S., Choi, J., Waterman, M. S., Comin, M., Kim, S.-H., Vinga, S., Almeida, J. S., Chan, C. X., James, B., Sun, F., Morgenstern, B., and Karlowski, W. M. (2019). Benchmarking of alignment-free sequence comparison methods. Genome Biology, accepted for publication.
- 9. END