INFO 4300 / CS4300 Information Retrieval. slides adapted from Hinrich Schütze s, linked from

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1 INFO 4300 / CS4300 Information Retrieval slides adapted from Hinrich Schütze s, linked from IR 12: Latent Semantic Indexing and Relevance Feedback Paul Ginsparg Cornell University, Ithaca, NY 6 Oct / 39

2 Overview 1 Recap 2 Motivation for query expansion 3 Relevance feedback: Basics 4 Relevance feedback: Details 2/ 39

3 Outline 1 Recap 2 Motivation for query expansion 3 Relevance feedback: Basics 4 Relevance feedback: Details 3/ 39

4 Term term Comparison To compare two terms, take the dot product between two rows of C, which measures the extent to which they have similar pattern of occurrence across the full set of documents. The i,j entry of CC T is equal to the dot product between i,j rows of C Since CC T = UΣV T V ΣU T = UΣ 2 U T = (UΣ)(UΣ) T, the i, j entry is the dot product between the i, j rows of UΣ. Hence the rows of UΣ can be considered as coordinates for terms, whose dot products give comparisons between terms. (Σ just rescales the coordinates) 4/ 39

5 Document document Comparison To compare two documents, take the dot product between two columns of C, which measures the extent to which two documents have a similar profile of terms. The i,j entry of C T C is equal to the dot product between the i,j columns of C Since C T C = V ΣU T UΣV T = V Σ 2 V T = (V Σ)(V Σ) T, the i,j entry is the dot product between the i,j rows of V Σ Hence the rows of V Σ can be considered as coordinates for documents, whose dot products give comparisons between documents. (Σ again just rescales coordinates) 5/ 39

6 Term document Comparison To compare a term and a document Use directly the value of i,j entry of C = UΣV T This is the dot product between i th row of UΣ 1/2 and j th row of V Σ 1/2 So use UΣ 1/2 and V Σ 1/2 as coordinates Recall UΣ for term term, and V Σ for document document comparisons can t use a single set of coordinates to make both between document and term and within term or document comparisons, but difference is only Σ 1/2 stretch. 6/ 39

7 Pseudo-document document Comparison How to represent pseudo-documents, and how to compute comparisons? e.g., given a novel query, find its location in concept space, and find its cosine w.r.t existing documents, or other documents not in original analysis (SVD). A query q is a vector of terms, like the columns of C, hence considered a pseudo-document Derive representation for any term vector q to be used in document comparison formulas. (like a row of V as earlier) Constraint: for a real document q = d (j) (= j th column C ij ), and before truncation (i.e., for C k = C), should give row of V Use q (s) = quσ 1 for comparing pseudodocs to docs 7/ 39

8 Pseudo-document document Comparison: q (s) = quσ 1 Consider the j, i component of C T UΣ 1 = (V ΣU T )UΣ 1 = V By inspection, the j th row of l.h.s. corresponds to the case q = d (j) : ( C T UΣ 1) ji = ( d(j) UΣ 1) i and the r.h.s. V ji is the j th row of V, as desired for comparing docs. So use q (s) = quσ 1, which sums corresponding rows of UΣ, hence corresponds to placing pseudo-document at centroid of corresponding term points (up to rescaling of rows by Σ). (Just as row of V scaled by Σ 1/2 or Σ can be used in semantic space for making term doc or doc doc comparisons.) Note: all of above after any preprocessing used to construct C 8/ 39

9 Selection of singular values t d t m m m m d Σ k V T k C k U k t d t k k k k d m is the original rank of C. k is the number of singular values chosen to represent the concepts in the set of documents. Usually, k m. Σ 1 k defined only on k-dimensional subspace. 9/ 39

10 More on query document comparison query = vector q in term space components q i = 1 if term i is in the query, and otherwise 0 any query terms not in the original term vector space ignored In VSM, similarity between query q and j th document d (j) given by the cosine measure : q d (j) q d (j) Using term document matrix C ij, this dot product given by the j th component of q C: d (j) = C e (j) ( e (j) = j th basis vector, single 1 in j th position, 0 elsewhere). Hence Similarity( q, d (j) ) = cos(θ) = q d (j) q d (j) = q C e (j) q C e (j). (1) 10/ 39

11 Now approximate C C k In the LSI approximation, use C k (the rank k approximation to C), so similarity measure between query and document becomes q d (j) q d (j) = q C e (j) q C e (j) = q C k e (j) q C k e (j) = q d (j) q d (j), (2) where d (j) = C k e (j) = U k Σ k V T e (j) is the LSI representation of the j th document vector in the original term document space. Finding the closest documents to a query in the LSI approximation thus amounts to computing (2) for each of the j = 1,...,N documents, and returning the best matches. 11/ 39

12 Pseudo-document To see that this agrees with the prescription given in the course text (and the original LSI article), recall: j th column of V T k represents document j in concept space : ˆd(j) = V T k e (j) query q is considered a pseudo-document in this space. LSI document vector in term space given above as d (j) = C k e (j) = U k Σ k V T k e (j) = U k Σ k ˆd(j), so follows that ˆd(j) = Σ 1 k UT k d (j) The pseudo-document query vector q is translated into the concept space using the same transformation: ˆq = Σ 1 k UT k q. 12/ 39

13 Compare documents in concept space Recall the i,j entry of C T C is dot product between i,j columns of C (term vectors for documents i and j). In the truncated space, C T k C k = (U k Σ k V T k )T (U k Σ k V T k ) = V kσ k U T k U kσ k V T k = (V kσ k )(V k Σ k ) T Thus i,j entry the dot product between the i, j columns of (V k Σ k ) T = Σ k V T k. In concept space, comparison between pseudo-document ˆq and document ˆd (j) thus given by the cosine between Σ k ˆq and Σk ˆd (j) : (Σ k ˆq) Σk ˆd(j) Σ k ˆq Σk ˆd(j) = ( qt U k Σ 1 k Σ k)(σ k Σ 1 k UT k d (j) ) U T k q UT k d (j) = q d (j) U T k q d (j), (3) in agreement with (2), up to an overall q-dependent normalization which doesn t affect similarity rankings. 13/ 39

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15 Outline 1 Recap 2 Motivation for query expansion 3 Relevance feedback: Basics 4 Relevance feedback: Details 15/ 39

16 How can we improve recall in search? Main topic today: two ways of improving recall: relevance feedback and query expansion Example Query q: [aircraft] Document d contains plane, but doesn t contain aircraft. A simple IR system will not return d for q. Even if d is the most relevant document for q! Options for improving recall Local: Do a local, on-demand analysis for a user query Main local method: relevance feedback Global: Do a global analysis once (e.g., of collection) to produce thesaurus Use thesaurus for query expansion 16/ 39

17 Outline 1 Recap 2 Motivation for query expansion 3 Relevance feedback: Basics 4 Relevance feedback: Details 17/ 39

18 Relevance feedback: Basic idea The user issues a (short, simple) query. The search engine returns a set of documents. User marks some docs as relevant, some as nonrelevant. Search engine computes a new representation of the information need should be better than the initial query. Search engine runs new query and returns new results. New results have (hopefully) better recall. 18/ 39

19 Relevance feedback We can iterate this: several rounds of relevance feedback. We will use the term ad hoc retrieval to refer to regular retrieval without relevance feedback. We will now look at three different examples of relevance feedback that highlight different aspects of the process. 19/ 39

20 Relevance Feedback: Example 1 20/ 39

21 Results for initial query 21/ 39

22 User feedback: Select what is relevant 22/ 39

23 Results after relevance feedback 23/ 39

24 Vector space example: query canine (1) source: Fernando Díaz 24/ 39

25 Similarity of docs to query canine source: Fernando Díaz 25/ 39

26 User feedback: Select relevant documents source: Fernando Díaz 26/ 39

27 Results after relevance feedback source: Fernando Díaz 27/ 39

28 Example 3: A real (non-image) example Initial query: New space satellite applications Results for initial query: (r = rank) r NASA Hasn t Scrapped Imaging Spectrometer NASA Scratches Environment Gear From Satellite Plan Science Panel Backs NASA Satellite Plan, But Urges Launches of Smaller Probes A NASA Satellite Project Accomplishes Incredible Feat: Staying Within Budget Scientist Who Exposed Global Warming Proposes Satellites for Climate Research Report Provides Support for the Critics Of Using Big Satellites to Study Climate Arianespace Receives Satellite Launch Pact From Telesat Canada Telecommunications Tale of Two Companies User then marks relevant documents with +. 28/ 39

29 Expanded query after relevance feedback new space satellite application nasa eos launch aster instrument arianespace bundespost ss rocket scientist broadcast earth oil measure 29/ 39

30 Results for expanded query r * NASA Scratches Environment Gear From Satellite Plan * NASA Hasn t Scrapped Imaging Spectrometer When the Pentagon Launches a Secret Satellite, Space Sleuths Do Some Spy Work of Their Own NASA Uses Warm Superconductors For Fast Circuit * Telecommunications Tale of Two Companies Soviets May Adapt Parts of SS-20 Missile For Commercial Use Gaping Gap: Pentagon Lags in Race To Match the Soviets In Rocket Launchers Rescue of Satellite By Space Agency To Cost $90 Million 30/ 39

31 Outline 1 Recap 2 Motivation for query expansion 3 Relevance feedback: Basics 4 Relevance feedback: Details 31/ 39

32 Key concept for relevance feedback: Centroid The centroid is the center of mass of a set of points. Recall that we represent documents as points in a high-dimensional space. Thus: we can compute centroids of documents. Definition: µ(d) = 1 D v(d) d D where D is a set of documents and v(d) = d is the vector we use to represent document d. 32/ 39

33 Centroid: Examples x x x x 33/ 39

34 Rocchio algorithm The Rocchio algorithm implements relevance feedback in the vector space model. Rocchio chooses the query q opt that maximizes q opt = arg max[sim( q,µ(d r )) sim( q,µ(d nr ))] q Closely related to maximum separation between relevant and nonrelevant docs Making some additional assumptions, we can rewrite q opt as: q opt = µ(d r ) + [µ(d r ) µ(d nr )] D r : set of relevant docs; D nr : set of nonrelevant docs 34/ 39

35 Rocchio algorithm The optimal query vector is: q opt = µ(d r ) + [µ(d r ) µ(d nr )] 1 = 1 dj + [ dj 1 dj ] D r D r D nr dj D r dj D r dj D nr We move the centroid of the relevant documents by the difference between the two centroids. 35/ 39

36 Exercise: Compute Rocchio vector x x x x x x circles: relevant documents, X s: nonrelevant documents 36/ 39

37 Rocchio illustrated qopt µ R µnr µ R µ NR x x x x x x µ R : centroid of relevant documents µ NR : centroid of nonrelevant documents µ R µ NR : difference vector Add difference vector to µ R to get q opt q opt separates relevant/nonrelevant perfectly. 37/ 39

38 Rocchio 1971 algorithm (SMART) Used in practice: q m = α q 0 + βµ(d r ) γµ(d nr ) = α q 0 + β 1 dj γ 1 D r D nr dj D r dj D nr dj q m : modified query vector; q 0 : original query vector; D r and D nr : sets of known relevant and nonrelevant documents respectively; α, β, and γ: weights attached to each term New query moves towards relevant documents and away from nonrelevant documents. Tradeoff α vs. β/γ: If we have a lot of judged documents, we want a higher β/γ. Set negative term weights to 0. Negative weight for a term doesn t make sense in the vector space model. 38/ 39

39 Positive vs. negative relevance feedback Positive feedback is more valuable than negative feedback. For example, set β = 0.75, γ = 0.25 to give higher weight to positive feedback. Many systems only allow positive feedback. 39/ 39